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Digitized  by  the  Internet  Archive 

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http://www.archive.org/details/economictheoryofOOwell 


THE 


Economic  Theory 


Location  of  Railways. 


IN    PREPARATION 

By  the  Same  Author 

In  one  thin  volume  of  ordinary  pocket-book  form  and  size 

THE 

FIELD  WORK 

OF 

RAILWAY     LOCATION 

AND 

Laying  Out  of  Works 

ACCORDING  TO  THE 

MOST  RECENT  AND  APPROVED  PRACTICE 
ON  AMERICAN   RAILWAYS. 


In  this  volume  will  be  included  various  formulae  and  methods 
never  heretofore  published  for  the  expeditious  and  correct  con- 
duct of  the  mechanical  work  of  location.  It  is  hoped  to  give 
everything  which  is  essential  and  nothing  which  is  unessential 
to  a  thorough  understanding  of  the  principles  and  methods  ol 
instrumental  field-work,  when  conducted  to  insure  final  excel- 
lence in  the  simplest  way  and  with  due  subordination  to  eco- 
nomic considerations.  The  tables,  while  strictly  limited  to  the 
requirements  of  good  practice,  will  be  an  especial  teature, 
modelled  typographically  on  the  best  German  models. 


a  Fernstrom,  Civi  Engm 

THE 

ECONOMIC    THEORY 


Location  of  Railways 


AN  ANALYSIS  OF  THE  CONDITIONS  CONTROLLING  THE 
LAYING     OUT     OF     RAILWAYS     TO     EFFECT 
THE  MOST  JUDICIOUS  EXPENDI- 
TURE   OF    CAPITAL 


BY 

ARTHUR   MELLEN   WELLINGTON 

M.  Am.  Soc.  C.E. 

lATE     PRINCIPAL    ASSISTANT    ENGINEER    FOR    LOCATION    AND    SURVEYS    MEXICAN    NATIONAL    RAIL- 
WAY,    ASSISTANT     GENEKAL     MANAGER     IN    CHARGE    OF    LOCATION     MEXICAN   CEN- 
TRAL   RAILWAY    AND    CHIEF    ENGINEER    OF    THE   AMERICAN    LINE 
FROM     VERA     CRUZ     TO     THE     CITY    OF     MEXICO 


"  For  it  is  clear  that  in  whatever  it  is  our  duty  to  act,  those  matters  also  it  is  our  duty  to  study." 

— Dr.  Thomas  Arnold 

REVISED  AND  ENLARGED  EDIXftrafCrn.. 

NEW  YORK 


John  Wiley  &  Sons 

15  AsTOR  Place 


Engineering  News 
Tribune  Building 


London  :  E.  &  F.  N.  Spon 
1887 


Copyright, 

t887, 

Bv  A.  M.  WELLINGTON. 


1«457B 


Dbummokd  &  Nhxj, 

Electrotypers, 

New  York. 


TO  THE 

GREAT  MEN  OF 
A  FORMER  GENERATION, 
WHO  ORIGINATED  THE  AMERICAN 
RAILWAY   SYSTEM,  THIS  ATTEMPT  TO  IM- 
PROVE   UPON    THEIR    PRACTICE    IS    ADMIRINGLY 
INSCRIBED,    IN    TOKEN    OF    RESPECT 
FOR    THEIR    FAR-SIGHTED 
SAGACITY  AND  STILL 
UNEQUALLED 
SKILL. 


ig;  Fernstrfeia,  -.^  h  '^"S'i- 


PREFACE. 


Only  in  a  very  figurative  sense  can  this  book  be  said  to  be  a  "  revised 
edition"  of  the  little  volume  under  the  same  title  which  the  writer  pub- 
lished ten  years  ago.  The  substance  of  the  old  book  remains  unchanged, 
so  far  as  it  went,  but  every  page  and  sentence  has  been  rewritten,  except 
the  dedication.  The  most  important  change  in  the  nature  of  an  addition 
is  the  much  greater  attention  given  to  traffic  and  revenue  questions, 
which  are  particularly  likely  to  be  underrated  or  forgotten.  The  mechan- 
ics of  curve  resistance  have  been  discussed,  it  is  hoped,  more  adequately 
than  heretofore,  and  on  a  more  solid  basis  of  experimental  fact,  with  some 
important  practical  questions  which  depend  thereon.  The  theory  of  the 
effect  of  variations  in  velocity  on  the  motion  of  trains  is  an  entirely  new 
addition,  supplying  one  of  the  most  important  omissions  of  the  former 
edition  and  of  other  engineering  text-books.  The  theory  of  various  de- 
tails of  the  locomotive,  which  did  not  seem  to  have  been  elsewhere  ade- 
quately discussed  for  the  purposes  of  this  volume,  has  been  given,  it  is 
hoped,  more  fully  and  correctly  than  heretofore.  Parts  IV.  and  V.  are 
entirely  new. 

On  the  other  hand,  the  new  edition  has  been  abbreviated  by  omitting 
the  discussions,  some  thirty  in  all,  where  reasons  why  the  writer  felt  com- 
pelled to  differ  from  some  previously  published  conclusions  or  estimates 
were  given  in  detail.  This  seemed  necessary  ten  years  ago,  but  at 
present  it  appeared  as  if  the  space  might  be  better  used. 

The  number  of  engravings  has  been  increased  from  half  a  dozen  to 
313,  the  number  of  pages  from  216  to  950,  and  the  number  of  tables  from 
44  to  204.  All  of  the  tables,  with  a  few  exceptions  noted  in  connection 
with  each,  are  original  computations  of  the  writer  or  compilations  from 
original  sources  of  information.  As  practically  all  the  work  of  prepar- 
ing them,  and  of  rewriting  the  text,  has  been  done  outside  of  those  hours 
which  are  ordinarily  and  more  rationally  regarded  as  working  hours,  a 
long  delay  in  republication  has  been  unavoidable  ;  but  if  there  be  truth 


VI 11  PREFACE. 


enough  in  the  old  antithesis  of  "easy  writing"  and  "curst  hard  reading" 
to  hold  good  when  twisted  WTong  end  to,  there  should  be  some  com- 
pensation in  store  for  any  reader  who  may  have  chanced  to  be  annoyed 
by  the  delay. 

In  order  to  adapt  the  volume  to  the  more  convenient  use  of  all  classes 
of  readers,  three  sizes  of  type  have  been  used  : 

Long  Primer  type  is  used  for  those  parts  of  the  volume 
which  were  deemed  most  likely  to  be  such  as  every  interested 
reader  would  wish  to  read,  including  those  who  desire  only  to 
ascertain  the  more  important  conclusions,  free  from  technicali- 
ties. 

Bourgeois  type  is  used  for  discussions  which  relate  more  to  the  details 
of  the  subject  than  to  principles,  and  hence  may  be  passed  over  by  those 
who  are  not  engineers,  or  who  are  ready  to  take  the  reasons  for  what  is 
printed  in  larger  t5^pe  for  granted.  Nevertheless,  much  of  the  matter 
which  is  printed  in  this  smaller  type,  as  for  instance  the  long  chapter  on 
the  locomotive  engine  and  the  whole  of  Part  V.,  is  among  the  most  im- 
portant in  the  book  for  the  professional  engineer. 

Breviep.  type  is  used  for  minor  notes  and  comments  which  it  seemed  essen- 
tial or  desirable  to  give,  as  of  much  possible  importance  to  those  wishing  to  look 
into  the  subject,  or  some  particular  branch  thereof,  with  still  greater  care,  but 
which  might  otherwise  be  passed  over. 

The  mathematical  form  of  discussion  has  been  intentionally  avoided, 
first,  because  the  book  has  been  written  for  practical  men  as  well  as  for 
students,  and  mathematical  methods  are  apt  to  repel  them  ;  and  secondly, 
and  chiefly,  because  mathematical  methods  of  solution  are  not  only  inex- 
pedient, but  positively  dangerous  for  the  class  of  problems  considered. 
When  the  difficulty  of  a  problem  lies  only  in  finding  out  what  follows  from 
certain  fixed  premises,  mathematical  methods  furnish  invaluable  wings 
for  flying  over  intermediate. obstructions  ;  but  whenever  the  chief  diffi- 
culty of  a  problem  lies  in  the  multiplicity  and  dubiousness  of  the  prem- 
ises themselves,  and  in  reconciling  them  with  each  other,  there  is 
no  safe  course  but  to  remain  continuously  on  the  solid  ground  of  con- 
crete fact.  The  invidious  but  simple  fact  of  proving  this  by  instances 
the  writer  will  not  attempt. 

To  fully  set  forth  in  any  one  volume  these  premises  for  the  correct 
laying  out  of  railways,  which  include  almost  everything  connected  with 
their  construction,  operation,  and  finances,  and  vary  in  each  case,  would 


PREFA  CE.  ix 


t)e  impossible.  The  purpose  in  view  has  been  merely  to  give  between 
the  covers  of  one  book  whatever  was  necessary  for  some  approach  to  a 
correct  solution  of  every  probable  problem,  which  could  not  be  found 
in  other  publications.  This  necessarily  led  to  a  large  book,  since  this 
work  still  remains  the  only  one  on  its  subject  in  the  language.  Sev- 
eral of  a  somewhat  similar  nature  have  appeared  in  French  and  German 
since  the  first  edition  of  this  work  was  published,  but  from  difference  of 
operating  conditions,  and  their  profuse  use  of  mathematics,  the  resem- 
blance is  not  close. 

The  word  "ton"  in  this  volume  means  2000  lbs.,  unless  otherwise  ex- 
plicitly stated. 

The  term  "  velocity-head "  has  been  borrowed  from  hydraulics  to 
designate  a  somewhat  different  thing,  which  heretofore  has  had  no  name 
at  all.  The  "velocity- head  "  of  hydraulics  and  of  this  volume  are  closely 
related  but  not  identical,  and  should  not  be  confused. 

Grades  have  been  designated  for  the  most  part  by  their  rate  per  cent 
and  not  by  their  rate  per  mile,  in  accordance  wdth  an  increasing  custom 
which  may  well  become  universal,  as  the  more  rational.  The  approxi- 
mate rate  per  mile  is  given  at  once  by  multiplying  the  per  cent  by  50 
(52.8). 

Owing  to  the  great  number  of  tables,  and  the  probability  that  others 
might  be  added  in  future  editions,  it  was  impossible  to  even  attempt  to 
refer  in  the  text  to  all  those  which  contained  a  given  class  of  information. 
To  insure  doing  this  reference  must  be  had  to  the  Index,  which  it  has 
been  endeavored  to  make  very  complete. 

Most  of  the  computations  of  percentages,  costs  per  mile,  and  the  like, 
in  this  volume,  were  made  with  a  slide-rule — an  instrument  too  little 
known  and  used  by  engineers.  Hence  many  errors  of  i  or  2  in  the 
third  digit,  or  of  one  or  two  tenths  of  one  per  cent,  probably  exist,  but, 
it  is  hoped,  few  of  a  more  serious  nature.  The  admirable  computing 
instrument  of  Mr.  Edwin  Thatcher,  which  would  have  insured  greater 
accuracy  with  but  little  more  trouble,  was  secured  by  the  writer  too  late 
to  be  of  much  service. 

The  author  will  be  at  all  times  pleased  to  receive  corrections  of  typo- 
graphical or  other  errors,  or  supposed  errors,  extensions  of  any  of  the 
tables,  or  other  similar  matter. 

A.  M.  W. 

Tribune  Building,  New  York,  May,  1887. 


V 


Ei  Fernstrciij,    /:  i,  ^ngtn. 


PREFACE  TO  THE   FIRST   EDITION. 


The  investigation  of  which  this  volume  is  the  fruit  had  its  origin  in 
the  preparation  of  a  few  notes  for  an  anticipated  location,  and  has  since 
gradually  expanded  into  a  single  magazine  article,  a  short  series  of 
papers,  and  at  last  into  a  volume.  Even  the  latter  has  been  expanded 
far  beyond  the  writer's  original  intention  by  the  close  and,  it  is  to  be 
feared,  tedious  attention  to  detail  which  he  found  continually  more 
needful ;  and  it  is  kept  within  its  present  dimensions  only  by  excluding 
considerable  matter  and  superficially  considering  or  neglecting  altogether 
a  number  of  subjects  which  the  writer  deems  of  real  importance  for  the 
correct  conduct  of  location.  In  the  improbable  event  that  the  sale  of 
this  volume  should  justify  a  thorough  revision  at  some  future  day,  he 
hopes  to  produce  one  more  in  keeping  with  the  professional  interest  and 
importance  of  the  subject,  by  rectifying  the  faults  of  omission  and  com- 
mission which  he  clearly  perceives. 

The  writer  does  not  intend  to  imply,  however,  that  he  has  fallen  into 
unacknowledged  errors  of  fact  or  theory.  All  known  errors  have  been 
frankly  corrected  as  soon  as  discovered.  For  such  others  as  may  prob- 
ably exist  the  writer  can  only  hope  that  they  will  be  regarded  with 
that  leniency  which  an  exploration  of  a  neglected  field  of  labor  may 
fairly  ask.  For  such  the  present  volume  is,  with  all  its  imperfections. 
A  recognition  of  the  value  of  previous  discussions  of  the  same  subjects 
would  be  a  more  welcome  duty;  but  the  writer  deems  it  but  simple 
justice  to  himself  and  his  readers  to  declare  frankly  that,  so  far  as  his 
knowledge  extends  and  he  is  competent  to  judge,  all  of  the  few  existing 
discussions  of  the  various  leading  topics  of  this  volume  are  so  superficial 
or  so  imperfect  in  method  as  to  have  little  or  no  value  as  a  guide  for 
location.  Some  of  them  express  correct  views,  and  some  of  them  will 
sometimes  give  correct  results ;  but  none  of  them  are  trustworthy,  and 
several  of  those  which  are  given  under  distinguished  names  are  incredi- 
bly defective.     The  various  problems  of  location,  in  fact,  have  been  dis- 


XU  PREFACE    TO    THE  FIRST  EDITION. 

cussed  or  neglected  by  technical  writers  with  an  airy  lightness  which 
would  convince  an  unskilful  reader  that  they  were  either  too  simple,  or 
too  unimportant,  or  too  well  understood,  for  any  careful  analysis.  And 
yet  there  is  no  field  of  professional  labor  in  which  a  limited  amount  of 
modest  incompetency,  at  Si 5°  per  month,  can  set  so  many  picks  and 
shovels  and  locomotives  at  work  to  no  purpose  whatever. 

As  a  natural  consequence  of  this  general  negligence,  all  our  railways 
are  uneconomically  located,  most  of  them  in  respect  to  their  general 
route  and  system  of  gradients,  and  all  of  them  in  respect  to  the  minor 
details  of  alignment,  and  in  many  cases  these  errors  are  shockingly 
evident.  ...  In  the  care  taken  in  this  respect  we  are  not  advancing 
beyond,  but  rather  falling  below,  the  standard  set  up  forty  years  ago, 
when  the  art  of  designing  railways  started  out  in  this  country  with  such 
brilliant  promise.  The  works  of  Latrobe  and  Jervis  and  Thomson  and 
Whistler  show  a  truly  remarkable  ability,  considering  their  early  day, 
and  bear  the  clearest  marks  of  original  and  self-reliant  thought :  but  the 
great  men  of  that  earlier  day  have  no  successors ;  for  we  have  done 
nothing  but  copy  them  ill  ever  since,  and  a  copyist  is  not  a  successor. 
We  copy  their  errors,  but  we  do  not  copy  that  admirable  habit  of  per- 
sonal investigation  and  far-sighted  intellectual  courage  which  created 
precedents,  and  has  made  the  work  of  their  hands — in  despite  of  many 
faults — the  high-water  mark  of  American  locating  skill. 


CONTENTS. 


PAGE: 

Introduction, i 


PART  I. 

ECONOMIC   PREMISES, 

CHAP. 

I.  The  Inception  of  Railway  Projects  and  Conditions 

GOVERNING   IT, I3. 

II.  The  Modern  Railway  Corporation,     .......    28. 

III.  The  Nature  and   Causes   connected   with   Location 

WHICH   MODIFY    THE  VOLUME   OF   RAILWAY   REVENUE,      .      48- 

IV.  The  Probable  Volume  of  Traffic  and  Law  of  Growth 

THEREIN, 75 

V.  Operating  Expenses, io6= 

[Maintenance  of  Way,  118;  Fuel,  132;  Repairs  of  Engines, 
139;  Repairs  of  Cars,  160;  Train- wages,  etc.,  168;  Summary, 
18a] 

PART  II. 

THE  MINOR  DETAILS  OF  ALIGNMENT 

VI.  The  Nature  and  Relative  Importance  of  the  Minor 

Details  of  Alignment, .185. 

VII.  Distance, 195. 

[Effect  on  Operating  Expenses,  198;  Effect  on  Receipts,  211; 
Law  as  to  Connections,  219;  Moral  Effect  of  Short  Line,  239.] 

VJII.  Curvature, 242; 

[Danger  of  Accident,  245;  Statistics  of  Curvature,  259;  Diffi- 
culty in  Making  Time,  268;  Effect  on  Smooth  Riding  of  Cars,  275; 


y 


XIV  CONTENTS. 

CHAP.  p^GE 

Moral  Effect  to  deter  Travel,  276;  Effect  to  obstruct  the  use 
of  Heavy  Engines,  278;  Mechanics  of  Curve  Resistance,  2S1 ; 
Rail-sections,  307;  Effect  on  Operating  Expenses,  313;  Long 
Tangents,  324.] 

IX.  Rise  and  Fall, 327 

[Classes  of,  330;  Laws  of  Accelerated  and  Retarded  Motion, 
331;  Virtual  Profiles,  346;  Safe  Lin:iits  of  Undulations  of  Grades, 
356;  Limits  of  Classes,  366;  Effect  on  Operating  Expenses,  375; 
Estimating  Amount  of,  384;  Vertical  Curves,  3S5.] 

PART  III. 

LIMITING   GRADIENTS  AND    CURVATURE. 

X.  The  Relative  Importance  of  Gradients, 395 

XL  The  Locomotive  Engine, 399 

[Tables    of  Standard  Dimensions,  407;    Running-Gear,  421; 
Tractive  Power,  434;  The  Locomotive  Boiler,  449;  The  Cylin- 
•      der  Power,  457;  Theoretical  Gain  by  Expansion,  467;    Causes 
of  Loss  of  Efficiency,  470. J 
XII.  Rolling-Stock, 485 

XIII.  Train  Resistance, 492 

[Freight-Train  Resistance,  496;  Starting  Resistances,  511; 
Effect  of  Size  of  Wheel  and  Axle,  513;  Velocity  Resistances, 
517;  Train-Resistance  Table,  524;   Engine  Friction,  530.] 

XIV.  The  Effect  of  Grades  on  Train-Load, 536 

[Table  of  Capacity  of  all  Engines  on  all  Grades,  544;  Percent- 
age of  Change  in  Net  Load  from  a  Change  in  any  Grade,  554  ] 
XV.  The  Effect  of  Train-Load  on  Operating  Expenses,  560 
[Cost  of  Increasing  Weight  of  Engines,  560;  Cost  of  Increas- 
ing Number  of  Engines,  568;  Proportion  of  Traffic  affected  by 
Rate  of  Ruling  Grade,  576;  Effect  of  a  Difference  in  Ruling 
Grade,  on  the  Cost  of  Distance,  Curvature,  and  Rise  and  Fall, 
5S1.]  . 

XVI.  Assistant  Engines, 585 

[Power  of  Assistant  Engines,  591;  Duty  of  Assistant  Engines, 
598;  Cost  of  Assistant  Engines,  601;    Comparison  of  Pusher 
Grades  with  Uniform  Gradients,  604.] 
XVII.  The  Balance  of  Grades  for  Unequal  Traffic,     .    .  608 
XVI'II.  Limiting  Curvature  and  Compensation  therefor,    .  620 


CONTENTS.  XV 


CHAP.  PAGE 

XIX.  The  Limit  of  Maximum  Curvature, 635 

[The  Inherent  Costliness  of  Sharp  Curvature,  638;  The 
Limiting  Effect  of  Curvature,  645.] 

XX.  The  Choice   of   Gradients,  and    Devices   for  Re- 
ducing Them, 659 

[How  to  Project  Low  Grades,  660;  How  to  Project  Pusher 
Grades; — Easy  Gradients,  666;  Heavy  Gradients,  669;  Expe- 
dients for  reducing  the  Rate  and  Cost  of  High  Grades,  675; 
Great  Inclines  of  the  World,  699.] 

PART   IV. 

LARGER  ECONOMIC  PROBLEMS. 

XXI.  Trunk  Lines  and  Branch  Lines, 707 

[Law  of  Geometric  Increment  of  TraflBc.  70S;  Trunk  Lines, 
Non-Competitive,  71S;  Competitive  Trunk  Lines,  723; 
Branch  Lines,  731.] 

XXII.  Light  Rails  and  Light  Railways, 737 

[Rails,  737;  Expedient  Economies,  748;  Rails  and  Track 
Labor,  758.] 

XXIII.  The  Economy  of  Construction,   ........  762 

[Least  harmful  Economies,  764;  Most  harmful  Economies, 
768;  Cross-ties,  775;  Storms  and  Structures,  781.] 

XXIV.  The  Improvement  of  Old  Lines, 785 

[Usual  Defects,  787;  Constructing  Virtual  Profile,  798; 
Remedying  Defects,  799.] 

XXV.  Grade  Crossings  and  Interlocking, 809 

XXVI.  Terminals, 818 

PART  V. 

THE  CONDUCT  OF  LOCATION. 

XXVII.  The  Art  of  Reconnaissance, 831 

XXVIII.  Ocular  Illusions, 843 

XXIX.  When  to  make  Surveys, 856 

XXX.  The  Field-work  of  Surveys, Z60 

XXXI.  Topography:  its  Uses  and  Abuse, 874 

XXXII.  Mapping  and  Projecting  Location, Z%6' 

XXXIII.  The  Estimation  of  Quantities, 895 


XVI  CONTENTS. 


APPENDICES. 

CHAP.  PAGB 

A.  Experiments  on  the  Resistances  of  Rolling-Stock,    .    .  909 

B.  Experiments  with  New  Apparatus  on  Journal  Friction 

AT  Low  Velocities, 913 

C.  The   American   Line  from   Vera  Cruz  to   the  City  of 

Mexico  via  Jalapa,  with  Notes  on  the  Best  Methods 
of  surmounting  High  Elevations  by  Rail, 92$ 

[The  usual  List  of  Tables  is  omitted,  as  too  voluminous.  The 
tables  and  engravings  are  separately  indexed  at  the  back  of  the 
book.] 


INDEX 


TO   THE   MORE   IMPORTANT 

JiULES,    TABLES,  FORMULA,    AND    FINAL    CONCLUSIONS, 

WHICH    MAY    BE    NEEDED 

FOR   IMMEDIATE   APPLICATION. 


"  It  may  be  remarked  that  it  was  no  part  of  the  purpose  of  this  volume  to 
furnish  a  collection  of  mere  rules,  professing  to  require  only  an  ability  to 
read  for  their  successful  application.  Rules  can  seldom  be  safely  applied 
without  a  clear  understanding  of  the  principles  on  which  they  rest." 

—J.  B.  Henck,  Preface  to  "  Field-Book." 


\^T/iis  index  has  purposely  been  tnade  and  kept  as  brie f  as  possible.  It  HAS  NC 
-CROSS-REFERENCES  NOR  DOUBLE  REFERENCES.  For  anything  not  found,  see  Gen- 
eral Ifzdex,  where  the  subjoined  references  are  repeated,  and  for  the  most  part  in 

•SMALL   CAPITALS.] 


Assistant  Engines- 

PAGE 

Advantages               .                ,                 .                .                0                .                 ,           - 

.        589 

Balance  of  grades  for       ...... 

593 

Cost  of  service       ....... 

602 

vs.  Uniform  grades           ...... 

604 

Projecting              ....... 

666 

Branch  Lines- 

Rules  for  laying  out          ...... 

733-6 

Cable  Railways                       ...... 

686 

Choice  between  close  lines             .            .            . 

5S3 

Construction- 

Order  of  expedient  economies      .             . 

764 

Worst  errors  in      .             .             .             .             .             .            .             . 

768 

Curvature- 

Compensation  for              ....... 

632 

XVIU 


INDEX   TO   CONCLUSIONS 


Curvature- 
Effect  on  accidents 

"        expenses 

"        use  of  heavy  engines 

"        making  time 

"        smooth  riding  of  cars 
Maximum  limit  of 
Moral  effect  of 

Curve  Resistance- 
Conclusions  as  to  .  , 

Dead  Weight- 
Passenger,  why  tends  to  increase 

Distance- 
Effect  on  competitive  receipts 

'*        non-competitive  receipts 
"        expenses 
Increasing,  to  secure  more  traffic 
Law  as  to  connections      . 
Moral  effect  of  short  line 
Freight-Train  Speed  . 

Grade-Crossings— 

And  interlocking  . 

Grades- 
Balance  of,  for  unequal  traffic,  table 
Effect  on  passenger  traffic 

"        train-load,  law  as  to 
General  law  for  choosing 
How  to  reduce  in  easy  country 
Pusher  grades,  pros  and  cons  for 
Relative  importance  of  gradients,  example 
Train-load  on  all  grades,  table 
Trains  affected  by  grades 
Value  of  reducing  grades 

Growth  of  Traffic- 
Geometric  law  as  to 
Proper  allowance  for 

Inclined  Planes 

Light  Railways- 
Proper  direction  for  economy 

Location— 

A  priori  basis  for 
General  law  for  good 


PAGE 

.  258 

.  321 

.  281 

.  274 

.  275 

.  653 

.  277 

.  304 

.  567 

.  22S 

234-6 

.  209 

.  238 

•  219 
.  240 

.  371 

.  811 

.  185 

.  580 
554-6 

.  660 

.  665 

•  669 
.  396 
.  546 
.  576 
.  572 

.  715 
80-86 

.  686 

,  761 

,  18 

.  660 


FOR  IMMEDIATE  APPLICATION. 


XIX 


Locomotives- 
Adhesive  traction  limits  . 
Dimensions,  etc.  . 
Train-load  on  all  grades  . 

Long  Tangents- 
Value  of    .  . 

Mapping  Surveys 

Minor  Details— (Distance,  Curvature,  and  Rise  and 
Comparative  importance 

Narrow  Gauge 

Old  Lines- 
Best  manner  of  improving 
Usual  defects  to  be  corrected 

Operating  Expenses- 
Percentages  .  . 

Rails- 
Proper  form  of     .  . 
"      weight  of  , 

Reconnaissance- 
Choice  of  lines  to  survey 
Fundamental  rule  for 

Revenue— 

Per  head  of  population     , 

Rise  and  Fall- 
Effect  on  operating  expenses 
Estimating  amount  of 
Limits  of  classes  . 
Safe  limits  for 

Sags- 

In  grade-lines,  to  what  extent  admissible 

Superelevation- 
Proper  rule  for     . 

Surveys- 
Choice  of  lines  to  run       .  .  . 

Switchbacks— 

For  thin  traffic  and  great  inclines 

Tarmini— 

Location  of  ...  . 

Topography— 

(Physical  geography),  Harmonizing  line  with 
(Mapping),  Its  uses  and  abuse     . 

Towns- 
Loss  from  not  going  to    . 


Fall.) 


PAGE 

•     437 
407-10 

.     544 
.     324 


.  186 

.  751 

.  80S 

.  788 

.  17^ 

.  30S 
747,  761 

.  857 

.  835 

.  104- 

.  38r 

.  384 

.  374 
363-8 

.  368 

.  301 

.  860 

.  950 

.  67 

.  655 

.  880 

.  63-4 


XX 


INDEX   TO   CONCLUSIONS, 


Traffic- 
How  to  estimate  the  probable  volume  of 

Train-mile— 

Cost  by  items        .  .        -  -, 

Train  Resistance- 
Freight,  amount    .        •    . 
Passenger,  amount 

Trunk  Lines- 
Competitive,  conditions  of  success 
Non-competitive,  rule  for  laying  out 

Valley  Lines— 

And  inundations  . 

Merits  of,  for  railway  lines 

Valleys- 
Descending  into    . 

Vertical  Curves- 
Laying  out  .  •  . 
Length  of  . 

Virtual  Profile- 
Nature  and  use  of  .  • 


PAGE 

86,  95-102 

.  179 

.  502 
.  518 

.  731 
.  720 

.  783 
.  850 

.  682 

.  387 
.  365 

346,  351,  354 


THE  ECONOMIC  THEORY  OF  THE 
LOCATION  OF  RAILWAYS. 


INTRODUCTION. 

As  the  correct  solution  of  any  problem  depends  primarily  on 
a  true  understanding  of  what  the  problem  really  is,  and  wherein 
lies  its  difficulty,  we  may  profitably  pause  upon  the  threshold  of 
our  subject  to  consider  first,  in  a  more  general  way,  its  real 
nature  ;  the  causes  which  impede  sound  practice  ;  the  condi- 
tions on  which  success  or  failure  depends  ;  the  directions  in 
which  error  is  most  to  be  feared.  Thus  we  shall  more  fully  at- 
tain that  great  prerequisite  for  success  in  any  work — a  clear 
mental  perspective,  saving  us  from  confusing  the  obvious  with 
the  important,  and  the  obscure  and  remote  with  the  unim- 
portant. 


It  would  be  well  if  engineering  were  less  generally  thought 
of,  and  even  defined,  as  the  art  of  constructing.  In  a  certain  im- 
portant sense  it  is  rather  the  art  of  not  constructing  ;  or,  to  de- 
fine it  rudely  but  not  inaptly,  it  is  the  art  of  doing  that  well 
with  one  dollar,  which  any  bungler  can  do  with  two  after  a 
fashion. 

There  are,  indeed,  certain  great  triumphs  of  engineering 
genius — the  locomotive,  the  truss  bridge,  the  steel  rail — which  so 
rude  a  definition  does  not  cover,  for  the  bungler  cannot  attempt 
them  at  all  ;  but  such  are  rather  invention  than  engineering 
proper.  There  is  also  in  some  branches  of  engineering,  as  in 
I 


IN  TROD  UCTION. 


bridge-building,  a  certain  other  side  to  it,  not  covered  by  such  a 
definition,  which  consists  in  doing  that  safely,  at  some  cost  or 
other,  which  the  bungler  is  likely  to  try  to  do  and  fail.  He 
therefore,  in  such  branches,  who  is  simply  able  to  design  a  struc- 
ture which  will  not  fall  down,  may  doubtless  in  some  measure 
be  called  an  engineer,  although  certainly  not  one  of  a  very  high 
type. 

But  to  such  engineering  as  is  needed  for  laying  out  railways, 
at  least,  the  definition  given  is  literally  applicable,  for  the  eco- 
nomic problem  is  all  there  is  to  it.  The  ill-designed  bridge  breaks 
down  ;  the  ill-designed  dam  gives  way  ;  the  ill-designed  boiler 
explodes  ;  the  badly  built  tunnel  caves  in,  and  the  bungler's 
bungling  is  betrayed.  But  a  little  practice  and  a  little  study  of 
field  geometry  will  enable  an}?-  one  of  ordinar)?-  intelligence, 
without  any  engineering  knowledge  whatever  in  the  larger 
sense,  to  lay  out  a  railway  from  almost  anywhere  to  anywhere, 
which  will  carry  the  locomotive  with  perfect  safety,  and  perhaps 
show  no  obtrusive  defects  under  what  is  too  often  the  only  test — 
inspection  after  construction  from  the  rear  end  of  a  palace-car. 
Thus,  for  such  work,  the  healthful  checks  which  reveal  the 
bungler's  errors  to  the  world  and  to  himself  do  not  exist.  Na- 
ture, unhappily,  has  provided  no  way  for  the  locomotive — like 
Mr.  Jingle's  intelligent  pointer — to  refuse  to  pass  over  an  ill- 
designed  railway  as  it  refuses  to  pass  over  an  ill-designed  bridge. 

Therefore,  since  there  is  no  natural  line  between  safety  and 
danger  to  mark  even  so  rude  a  distinction  as  that  between  the 
utterly  bad  and  the  barely  tolerable,  in  the  kind  of  engineering 
work  we  are  to  study,  one  may  fairly  say  that  the  locating  en- 
gineer has  but  the  one  end  before  him  to  justify  his  existence  as 
such — to  get  the  most  value  for  a  dollar  which  nature  permits  ; 
and  but  one  failure  to  fear — that  he  will  not  do  so.  Except  as 
his  work  necessarily  involves  the  preliminary  design  of  construc- 
tive details,  he  has  no  lives  to  save  or  imperil ;  and  the  young  en- 
gineer cannot  too  early  nor  too  forcibly  have  it  impressed  upon 
his  mind  that  it  takes  no  skill  worth  speaking  of  to  do  such  work 
after  a  fashion,  unless  in  the  comparatively  few  localities  (rare  in- 


IN  TROD  UCTION. 


deed  in  the  United  States)  where  to  get  a  reasonable  line  of  any- 
kind  is  something  of  a  feat.  His  true  function  and  excuse  for 
being  as  an  engineer,  as  distinguished  from  a  skilled  workman, 
begins  and  ends  in  comprehending  and  striking  a  just  balance 
between  topographical  possibilities,  first  cost,  and  future  reve- 
nue and  operating  expenses. 

While  this,  in  a  certain  sense,  is  peculiar  to  the  branch  of  en- 
gineering we  are  to  study,  yet  a  curiously  close  analogy  may  be 
drawn,  tending  to  show  that  it  is  as  essentially  true  of  all  other 
branches  of  engineering  as  of  this.  For  example,  it  is  beyond 
doubt  that  the  true  reason  for  the  striking  progress  in  bridge- 
building  in  recent  years  has  been,  not  that  men  have  been  driven 
into  excellence  by  "  the  responsibility  of  human  life"  resting  on 
them  ; — for,  after  the  types  have  once  been  invented,  a  relatively 
low  order  of  engineering  skill  suffices  to  reduce  that  risk  alone 
to  a  minimum.  But  the  impelling  force  has  been  the  keen  com- 
petitive struggle  to  bring  the  first  cost  of  every  bridge  as  low  as 
possible,  and  yet  do  nothing  which  shall  injure  its  permanent 
efficiency  and  compel  it  to  be  speedily  rebuilt  ;  nothing,  in  other 
words,  which  shall  increase  the  future  "  maintenance  and  oper- 
ating expenses."  But  whereas  the  "  operating  expenses"  of  bad 
bridge-engineering  come  in  a  series  of  startling  catastrophes 
which  shock  the  community  and  dismay  the  moneyed  interests 
concerned,  causing  good  work  to  be  appreciated  and  insisted  on, 
and  scaring  off  the  amateurs  and  'prentice  hands  from  "  med- 
dling and  muddling,"  after  the  manner  of  their  kind,  the  operat- 
ing expenses  from  bad  railway  location  come  by  a  gentle  but 
unceasing  ooze  from  every  pore  which  attracts  no  attention, 
albeit  resulting  in  a  loss  vastly  larger  than  any  possible  loss 
from  bad  construction  ;  for  it  requires  some  training  and  experi- 
ence even  to  appreciate  the  loss  as  existing,  and  still  more  of 
both  to  appreciate  it  as  remediable.  In  fact  no  one  can  do  so, 
except  in  the  most  general  way,  without  special  investigation  of 
each  special  case.  Errors  which,  even  if  committed,  are  not 
likely  to  be  discovered,  are  rarely  much  feared,  and  at  last  the 
consciousness  that  there  is  ddneer  of  error  becomes  dulled. 


4 


IN  TROD  UCTION. 


In  these  facts  we  have  plain  reasons  why  average  practice  in 
laying  out  railways  should  inevitably  tend,  as  it  does  tend,  to  be 
and  remain  of  a  low  grade.  It  is  not  difficult,  in  fact,  to  see 
reasons  why  it  can  never  well  be  otherwise,  except  in  degree, 
unless  the  progress  of  science  should  wholly  change  the  nature 
of  the  work  ;  and  a  correct  appreciation  of  how  great  is  this 
danger,  and  why  it  exists,  will  greatly  help  to  save  the  student 
from  it. 

The  permanent  difficulty  lies  in  this  :  High  efficiency  in  any 
art  or  calling  in  which  many  minds  of  no  phenomenal  gifts  are 
engaged  requires  that  every  man's  work  should  be  readily  com- 
parable either  with  a  certain  uniform  standard  or  with  the  work 
of  his  fellows.  In  constructive  engineering  this  is  possible. 
Broadly  speaking,  a  hundred-foot  bridge  is  a  hundred-foot 
bridge,  the  world  over.  It  has  everywhere  to  fulfil  but  two 
primary  conditions  :  It  must  carry  a  certain  nearly  uniform  load 
per  foot,  and  it  must  not  fall  down.  The  same  is  in  substance 
true  of  every  form  of  constructive  engineering.  Every  man's 
practice  therein,  therefore,  is  comparable,  and  is  compared,  with 
the  highest  level  of  practice,  the  world  over.  Those  most  highly 
skilled  are  discovered  and  recognized.  The  moderately  skilled 
perceive  and  correct  their  deficiencies.  The  hopelessly  unskilled 
retire  to  other  pursuits. 

In  laying  out  railway  lines,  and  less  strikingly  in  some  other 
analogous  kinds  of  engineering  work,  this  is  forever  impossible. 
We  cannot  reduce  the  laws  of  topography,  nor  even  of  finance,  to 
equations  and  formulae.  Every  line  is  a  problem  by  itself,  with 
its  own  peculiar  physical  and  commercial  conditions,  so  that  the 
engineer  is  deprived  of  the  aid  to  be  had  by  comparing  with, 
and  copying  the  details  of,  the  practice  of  others.  Under  these 
circumstances,  the  difference  of  conditions  will  be  apt  to  be  hon- 
estly accepted  by  the  reader  who  may  have  sinned  against  good 
practice,  and  by  all  others  concerned,  as  the  reasons  why  an- 
other line,  one  hundred  or  one  thousand  miles  off,  should  have 
cost  so  much  less  and  yet  be  so  much  better  worth  owning  than 
his  own.     He  who  has   done  well,  therefore,  is  cut  off  from  any 


INTRODUCTION.  5 


absolute  knowledge  and  general  recognition  of  that  fact,  and 
the  guilty  reader,  who  has  done  ill,  is  cut  off  from  the  still 
greater  gain  which  w^ould  come  to  him  from  a  revelation  of 
where  and  wherein  he  has  done  ill.  In  most  such  cases  each 
will  have  in  some  detail  shown  better  judgment  than  the  other  ; 
but  from  the  lack  of  unquestionable  evidence  of  this,  each  is 
denied  the  instruction  which  he  might  otherwise  receive  from 
that  fact,  and  so  is  in  great  danger  if  falling  into  th^  most  natu- 
ral and  most  human  error,  believing  that  all  that  he  has  done 
is  good,  which  has  not  been  proven  to  be  bad,  and  so  ceasing  to 
make  effort  to  improve  upon  what  is  good  enough  to  pass,  and 
merely  multiplying  errors  with  advancing  experience,  without 
really  advancing  in  knowledge. 

For  these  reasons  the  student  should  begin  with  the  conscious- 
ness that  the  level  of  average  practice  in  railway  location,  his 
own  included,  is  by  its  nature  restricted,  not  to  the  sum  of  the 
united  abilities  of  all  those  who  are  or  have  been  engaged  in  it, 
as  in  constructive  engineering,  but  to  the  average  individual  level 
of  capacity  and  knowledge.  No  more  is  needed  than  this  un- 
doubted fact  to  prove  to  demonstration  that  average  practice  is 
and  must  be,  both  comparatively  and  absolutely,  of  a  pretty  low 
grade  ;  and  hence  it  becomes  every  one  who  may  be  entrusted 
with  such  work  to  have  constantly  before  him  the  fact  that  he 
stands  thus  alone,  and  to  scrutinize  with  the  sternest  skepti- 
cism, the  conclusions  which  he  may  reach,  remembering  that  his 
danger  of  grave  errors  of  judgment  is  thereby  multiplied  many- 
fold.  As  he  measures  only  by  his  own  knowledge,  all  the  work 
he  does  will  naturally  seem  good  even  if  really  bad. 

To  the  preceding,  which  may  be  called  the  subjective  ob- 
stacles to  good  practice,  must  be  added  another  and  perhaps  a 
greater  one.  Inasmuch  as  no  one  can  even  know  for  himself 
the  absolute  quality  of  his  own  skill  in  this  particular  branch  of 
engineering,  it  is  almost  a  natural  corollary  that  corporations 
should  very  uniformly  decline  to  take  it  for  granted,  by  assum- 
ing that  there  are  any  measurable  differences  in  qualifications  for 
such  work  among  those  who  have  proved  their   competency  in 


IN  TROD  UCTIOIV. 


Other  branches  of  engineering.  Hence  it  happens  that  railway- 
location  tends  more  and  more  to  be  entrusted  to  those  to  whom 
it  is  a  mere  temporary  incident  in  their  professional  career,  and 
who  consider  the  work  mainly  from  the  constructive  stand- 
point, without  much  attention  to  those  larger  economic  ques- 
tions which  it  is  the  purpose  of  this  volume  to  discuss,  and  to 
which,  in  well-conducted  work,  the  mere  constructive  details 
should  be  wholly  subordinate.  But  as  the  inexperienced  young 
man  can  only  gauge  the  inportance  of  various  work  by  the  at- 
tention which  he  sees  paid  to  it  by  his  superiors,  he  is,  as  it 
were,  pushed  by  others  into  an  error  which  it  is  difficult  for  him 
to  avoid  at  best  ;  for  he  will  soon  note  that  the  assumption  and 
practice  of  the  world  is,  that  whoever  is  fit  to  design  the  struc- 
tures of  a  railway  is  thereby  fitted,  without  further  study  or 
preparation,  to  design  the  railway  as  a  whole.  In  fact,  this 
vicious  principle  is  in  very  many  instances  pushed  to  the  ab- 
surd extreme  of  entrusting  engineers  of  inferior  capacity  with 
the  location  of  railways,  and  only  seeking  for  a  higher  grade 
of  skill  when  the  design  of  the  cheaper  man  is  to  be  embodied 
in  construction.  The  error  in  so  doing  is  the  same  in  kind 
and  in  degree  as  if  it  were  assumed  that  whoever  was  fitted  to 
build  a  house  was  fitted  to  design  one.  The  mental  qualities 
and  special  training  needed  are  much  the  same  in  each  case,  but 
the  two  kinds  of  work  are  distinct,  and  skill  in  one  does  not 
argue  skill  in  the  other. 

Nevertheless,  railways  must  be  built,  and  fortunately  there  is 
a  bright  side  as  well  as  a  dark  side  to  the  picture.  There  is 
indeed  a  pitiable  waste  resulting  from  the  conditions  outlined  : 
such,  to  mention  a  simple  and  readily  comprehended  example,  as 
has  resulted  from  the  location  of  the  entire  railway  system  of 
the  prairie  States  of  the  West, — taking  it  as  a  whole  and  neglect- 
ing the  many  individual  exceptions, — where  the  fatal  ease  wath 
which  an  air-line  may  be  run  from  almost  anywhere  to  any- 
where, by  using  heavy  enough  grades,  has  brought  the  average 
train-load  lower  than  in  the  rugged  regions  of  the  East,  and 
caused  perhaps  a  greater  percentage  of  utterly  needless  waste, 


INTRODUCTION. 


and  a  more  discreditable  aggregate  of  thoroughly  bad  location, 
than  in  any  other  considerable  region  of  the  world  ;  and  in  view 
of  such  facts,  the  distorted  pre-eminence  given  by  engineers, 
and  by  those  who  teach  them  and  employ  them,  to  the  pettiest 
details  of  how  to  build  the  separate  works  which  make  a  railway, 
to  the  neglect  of  the  larger  questions  of  where  to  build  and 
when  to  build,  and  whether  to  build  them  at  all,  has  in  it  some- 
thing at  once  astounding  and  discouraging.  But  in  a  larger 
view  this  is  in  no  way  surprising.  It  is  but  the  common  result 
of  man's  attempts  at  solving  every  serious  problem  which  does 
not  admit  of  exact  and  positive  solution,  like  a  problem  in 
geometry,  but  contains  such  indeterminate  elements  that  to 
solve  it  perfectly  is  given  only  to  Omniscience.  In  all  such 
cases  mankind  in  general  shirks  the  issue,  or  jumps  at  a  solu- 
tion in  the  rudest  way,  as  is  seen  not  only  in  the  work  of  engi- 
neers, but  in  that  of  farmers  and  legislators  and  merchants, 
physicians  and  builders.  Compared  with  the  dismal  failure 
which  so  many  men  make  in  every  one  of  these  callings,  the 
work  of  engineers  in  laying  out  railways  shines  by  comparison. 
For  after  all,  the  fact,  if  it  be  a  fact, — as  in  a  rude  way  it  is, — 
that  between  waste  in  construction  and  waste  in  operation  and 
waste  from  inaccessibility  to  possible  patrons,  it  takes  about 
twice  as  great  expenditure  of  capital  and  labor  as  it  need  to 
afford  existing  transportation  facilities — this  really  means  no 
more  than  that,  instead  of  realizing  ninety  per  cent  of  the  ad- 
vantages which  might  be  gotten  from  George  Stephenson's  inven- 
tion, as  is  reasonably  possible,  only  some  seventy-five  or  eighty 
per  cent  is  actually  realized.  The  great  world  declines  to  take 
much  interest  in  such  a  trifling  waste  as  this,  being  accustomed 
to  much  greater  waste  in  many  things,  and  having  something  of 
that  large  indifference  to  waste  which  pervades  all  nature.  Nor 
would  it  be  worth  while  here  to  insist  on  it  for  the  mere  sake  of 
pointing  out  that  it  exists,  but  solely  to  point  out  that,  as  the 
location  of  railways  is  the  one  department  of  engineering  in 
which  waste  on  a  gigantic  scale  is  possible  from  probable  eri'ors 
of  judgment,  and  as  it  is  likewise  the  one  department  of  engi- 


3  INTRODUCTION. 


neering  in  which  no  natural  check  exists  against  such  errors,  it 
is  fitting  that  engineers  should  prepare  themselves  for  it  with 
especial  care,  at  least  to  the  extent  of  acquiring  an  adequate 
conception  of  the  number  and  magnitude  of  the  errors  into 
which  they  may  fall. 

Much  of  the  success  of  any  one  in  any  kind  of  work,  and  especially 
in  work  subject  to  the  peculiar  difficulties  of  that  we  are  considering, 
depends  upon  the  spirit  in  which  it  is  undertaken.  If  it  be  true,  as  it 
unquestionably  is,  that  no  one  ever  attained  great  success  in  any  walk  of 
life — or  certainly  in  no  intellectual  calling — who  found  no  other  nor 
higher  pleasure  in  doing  that  well  which  was  given  him  to  do  than  in 
the  money  or  the  glory  which  he  might  get  from  doing  it,  it  is  certain- 
ly much  more  true  in  a  calling  where  those  ordinary  stimuli  work  very 
imperfectly  or  not  at  all,  and  in  which  one  is  often  called  upon  to  do  the 
direct  contrary  of  what  will  win  him  credit  from  the  thoughtless  and 
superficial.  The  desire  to  do  good  work  for  its  own  sake  is  then  the 
only  real  guarantee  that  good  work  will  be  done  ;  for  although  a  kindly 
Providence  has  given  the  latent  power  to  do  bad  work  of  this  kind  to 
every  human  being  with  a  tolerably  observant  eye  and  intelligence 
enough  to  lay  up  bricks,  most  assuredly  the  power  to  do  good  work  will 
not  come  by  nature.  The  author,  therefore,  feels  that  he  need  make  no 
apology  to  those  young  men  who  may  honor  him  by  studying  this 
volume,  for  offering  them  one  page  at  least  of  true  wisdom,  in  the  state- 
ly periods  of  one  of  the  greatest  thinkers  of  our  or  any  age ;  which  he 
does  in  the  belief  that  they  will  find  its  study  more  profitable  than  that 
of  many  pages  in  this  or  any  other  text-book,  since,  if  they  have  studied 
it  to  some  purpose,  they  are  at  least  assured  the  most  permanently  grati- 
fying of  all  success — the  consciousness  of  having  done  one's  best : 

"  I  look  on  that  man  as  happy,  who,  when  there  is  question  of  suc- 
cess, looks  into  his  work  for  a  reply— not  into  the  market,  not  into 
opinion,  not  into  patronage.  In  every  variety  of  human  employment, 
in  the  mechanical  and  in  the  fine  arts,  in  navigation,  in  farming,  in  legis- 
lating, there  are  among  the  numbers  who  do  their  work  perfunctorily, 
as  we  say,  or  just  to  pass,  and  as  badly  as  they  dare,— there  are  the  work- 
ingmen,  on  whom  the  burden  of  the  business  falls,— those  who  love 
work,  and  love  to  see  it  rightly  done,  who  finish  their  task  for  its  own 
sake ;  and  the  state  and  the  world  is  happy  that  has  the  most  of  such 
finishers.  The  world  will  always  do  justice  at  last  to  such  finishers  :  it 
cannot  otherwise.     He  who  has  acquired  the  ability  may  wait  securely 


INl^ROD  UCTION. 


the  occasion  of  making  it  felt  and  appreciated,  and  know  that  it  will  not 
loiter.  Men  talk  as  if  victory  were  something  fortunate.  Work  is  vic- 
tory. Wherever  work  is  done,  victory  is  obtained.  There  is  no  chance, 
and  no  blanks.  You  want  but  one  verdict :  if  you  have  your  own,  you 
are  secure  of  the  rest.  And  yet,  if  witnesses  are  wanted,  witnesses  are 
near.  There  was  never  a  man  born  so  wise  or  good,  but  one  or  more 
companions  came  into  the  world  with  him,  who  delight  in  his  faculty 
and  report  it.  I  cannot  see  without  awe,  that  no  man  thinks  alone,  and 
no  man  acts  alone ;  but  the  divine  assessors  who  come  up  with  him  into 
life,  now  under  one  disguise,  now  under  another,  like  a  police  in  citi- 
zens' clothes,  walk  with  him,  step  for  step,  through  the  kingdom  of 
time. 

"  What  is  vulgar,  and  the  essence  of  all  vulgarity,  but  the  avarice  of 
reward  ?  'Tis  the  difference  of  artisan  and  artist,  of  talent  and  genius, 
of  sinner  and  saint.  The  man  whose  eyes  are  nailed,  not  on  the  nature 
of  his  act,  but  on  the  wages, — whether  it  be  money,  or  office,  or  fame, — 
is  almost  equally  low."  * 

The  true  moral  to  be  drawn  from  such  glittering  generalities  is  not 
that  if  a  man  does  not  succeed  the  world  is  not  doing  justice  to  him  ; 
for  the  chances  are  a  hundred  to  one  that  it  is  meting  him  out  exact 
and  equal  justice,  and  that  unless  he  wipes  out  that  delusion  from  his 
mind  and  sets  about  correcting  his  deficiencies,  it  will  continue  to  do  so 
in  the  same  way  :  nor  is  it  that  a  man  should  neglect  that  reasonable  care 
for  his  own  welfare  which  is  every  man's  duty,  nor  that  he  should  submit 
to  imposition,  nor  continue  very  often,  for  very  long,  to  render  something 
for  nothing :  In  this  utilitarian  age  there  is  little  danger  that  it  will  be 
so  interpreted.  But  the  author  has  seen — or  thinks  he  has  seen — so 
many  young  men  doing  permanent  injury  to  their  own  future  by  letting 
$150  a  month  fill  up  the  whole  arc  of  their  horizon,  that  he  has  seized 
his  chance,  while  he  has  them  foul,  to  inflict  a  little  advice.  He  grants 
it  is  against  the  laws  of  the  game,  and  stops. 

We  will  now  proceed  with  our  legitimate  subject,  and  endeavor  not 
to  depart  from  it. 

*  Ralph  Waldo  Emerson  :  **  Essay  on  Worship." 


PART   I. 


ECONOMIC    PREMISES. 


"  The  location  of  a  railroad  is  giving  it  its  constitution.  It  may  be 
sick,  almost  unto  death,  with  accidents  of  construction  and  manage- 
ment, but  with  a  good  constitution  it  will  ultimately  recover." 

— D.  H.  AiNSWORTH. 


PART  I. 
ECONOMIC  PREMISES. 


CHAPTER  I. 


THE    INCEPTION    OF    RAILWAY    PROJECTS,  AND    CONDITIONS    GOVERN- 
ING   IT. 

1.  When  a  railway  is  projected,  and  while  its  construction 
is  still  in  doubt,  the  most  important  and  most  doubtful  ques- 
tion of  all  is  one  which  does  not  admit  of  any  general  discussion 
or  analysis  :  Whether  or  not  to  build  the  line  at  ALL.i^The 
decision  of  this  question  is  not  within  the  legitimate  sphere  of 
an  engineer's  duties,  acting  as  such  ;  and  hence  it  should  not  be 
permitted  to  confuse  or  affect  his  mind  during  the  subsequent 
process  of  preparing  the  line  for  construction.  For  the  general 
question  of  whether  or  not  to  build  the  line  at  all  is  one  of 
finance  and  busmess  judgment  al^ne,  to  be  settled  by  a  more  or 
less  exact  or  visionary  estimate  of  the  available  capital  for  con- 
struction, the  probable  gross  and  net  receipts,  and  the  resulting 
direct  and  indirect  advantages  to  the  projectors,  with  the  final 
conclusion  that — 

(i)  There  is  (or  is  not)  sufficient  need  of  a  railway  to  give  a 
fair  return  on  the  expenditure  of  a  certain  gross  amount  in  con- 
structing it;  and 

(2)  That  this  gross  amount  can  (or  cannot)  be  raised. 

This  conclusion  is  not  necessarily  expressed  by  a  definite  sum 
in  advance — in   fact  it   is  very  rarely  so  expressed  ;  but  such  a 


14  CHAP.   I.— INCEPTION  OF  RAILWAY  PROJECTS. 

conclusion  is  in  effect  reached,  although  often  in  a  very  vague 
form,  whenever  it  is  decided  to  proceed  with  construction. 

2.  Neither  does  it  follow  that  the  deciding  motive  is  direct 
pecuniary  profit  ;  for  the  line  m'ay  be  of  great  value  to  the  in- 
ventors and  the  public,  and  yet  never  pay  such  profit.  In  fact, 
the  railway  system  of  the  world,  taken  as  a  whole,  and  especially 
that  of  the  United  States,  has  been  only  very  moderately  profit- 
able in  any  direct  form  ;  owing  not  so  much  to  mistakes  of  judg- 
ment pure  and  simple,  as  to  the  very  large  proportion  of  lines 
which  have  been  built  simply  to  increase  the  value  of  land,  to 
afford  local  transportation  facilities,  to  bring  traffic  to  the  main 
line,  and  similar  purposes.  Yet  the  resulting  gain  to  the  com-  ) 
munity,  from  these  indirect  advantages  alone,  has  been  vast  be 
yond  computation  ;  so  much  so  that,  although  the  lines  on  which 
projectors  have  lost  money  have  been  many,  there  have  been 
few  or  none  which  have  involved  a  positive  loss  to  the  commu 
nity  as  a  whole,  excepting  some  of  those  which  have  merely 
paralleled  other  lines. 

3.  A  certain  number  of  lines,  also,  are  built  for  more  or  less 
illegitimate  and  irregular  purposes:  to  sell  out  to,  or  sometimes, 
one  may  fairly  say,  to  black-mail  other  lines  ;  to  make  profit  on 
the  construction  ;  as  means  of  warfare  against  other  lines  ;  etc., 
etc.  Nevertheless,  even  with  such  irregular  enterprises,  as  cer- 
tainly in  all  other  cases,  the  same  general  law  holds  :  It  is  the 
plain  interest  of  the  constructors,  in  all  cases,  to  obtain  as  good  a 
road  as  they  can  for  the  money,  and  to  build  it  on  business  prin- 
ciples ;  to  spend  what  they  have  to  spend  to  the  very  best  advan- 
tage, and  to  spend  no  more  than  they  are  obliged  to  spend  to 
build  the  line  at  all  in  safe  operating  condition,  unless  the  addi- 
tional expenditure,  and  not  simply  the  expenditure  as  a  whole,  is 
clearly  a  good  investment. 

4.  From  the  point  of  view  of  this  volume,  therefore,  all  rail- 
ways are  legitimate  enterprises,  and  their  construction  is  gov- 
erned by  the  same  general  economic  laws.  These  laws,  vital  to 
the  successful  conduct  and  outcome  of  such  enterprises,  seem- 
ingly very  plain  and  simple,  but  frequently  neglected  or  forgot- 


CHAP.    I.— INCEPTION  OF  RAILWAY  PROJECTS.  15 

ten,  may,  as  respects  the  question  of  whether  to  build  the  line  or 
not,  be  summarized  as  follows  : 

5.  (i)  Railways  are  not  undertaken  unless  they  are  expected 
to  be  profitable,  not  to  the  general  public,  nor  to  other  parties"^ 
in  the  near  or  distant  future,  nor  to  those  who  lend  money  on 
them,  but  to  those  who  at  first  control  the  enterprise.  If  the  means 
in  hand  be  not  sufficient  for  the  projectors  to  complete  the  road 
for  operation  and  to  control  its  operation  afterwards,  the  result 
to  them  is  usually  complete  loss.  Remembrance  of  this  fact 
becomes  the  more  important  because  the  available  means  (the 
great  bulk  of  which  is  borrowed  money)  are  almost  always  over- 
rated, and  the  demand  upon  them  underrated. 

The  logical  order  of  procedure  in  the  case  of  any  new  enter- 
prise— which  is,  first,  to  determine  whether  or  not  the  project  is 
a  sound  one,  and  to  be  carried  out  ;  and,  secondly,  to  make  the 
necessary  studies  as  to  the  manner  of  carrying  it  out — is  not  (£^ 
necessarily  followed  in  order  of  time  :  often  it  cannot  be,  for  the 
final  decision  as  to  the  former  often  depends  on  the  results  of 
the  latter,  or  on  unknown  future  events.  Nevertheless,  although 
subsequent  events  may  cause  a  revision  of  such  assumptions, 
the  mere  initiation  of  the  study  of  details  implies  a  pro-for7?ia 
conclusion,  that  the  project  as  a  whole  is  a  wise  one  if  wisely 
carried  out,  and  can  only  fail  by  bad  judgment  in  details.  This 
premise  must  be  from  the  beginning,  therefore,  under  all  circum- 
stances, the  basis  of  the  engineer's  action.     From  this  it  follows  : 

6.  (2)  No  increase  of  expenditure  over  the  unavoidable  mini- 
mum is  expedient  or  justifiable,  however  great  the  probable 
profits  and  value  of  an  enterprise  as  a  whole,  unless  the  increase 
can  with  reasonable  certainty  be  counted  on  to  be,  in  itself,  a 
profitable  investment.     Conversely, 

(3)  No  saving  of  expenditure  is  expedient  or  justifiable,  how- 
ever doubtful  the  future  of  the  enterprise  as  a  whole,  when  it  can 
with  certainty  be  counted  on  that  the  additional  expenditure  at 
least  will,  at  the  cost  for  the  capital  to  make  it,  be  in  itself  a 
paying  investment. 

For  if  the  project  as  a  whole  be   an  unwise   one,  the   projec- 


1 6  CHAP.    I.— INCEPTION  OF  RAILWAY  PROJECTS. 

tors  will  lose  their  money  in  any  case  ;  but  an  additional  expendi- 
ture which  adds  more  value  to  the  property  than  it  costs  will,  at 
the  worst,  decrease  their  loss,  and  may  turn  the  scale  by  prevent- 
ing any  loss.  Doubtful  projects  least  of  all  can  afford  to  have 
their  future  imperilled  by  reckless  economies.  Nevertheless 
the  following  should  be  remembered  : 

7.  (4)  No  expenditure  is  wise,  however  otherwise  profitable, 
which  endangers  the  successful  completion  of  the  enterprise 
with  the  funds  on  hand  or  known  to  be  available. 

For  the  property  then  becomes  worthless  to  the  projectors,, 
however  valuable  it  may  become  to  others.  Successful  comple- 
tion, moreover,  includes  much  more  than  the  laying  of  the  track. 
It  includes  the  equipment,  the  terminal  facilities,  the  endurance 
of  thin  traffic  and  of  imperfect  exchange-traffic  facilities  until 
the  normal  business  of  the  line  has  been  fully  attained — always 
a  matter  of  time.  Therefore,  as  few  roads  are  even  sure  of  ob- 
taining the  capital  which  they  think  is  necessary  for  the  above 
purpose,  we  have  the  following  : 

8.  (5)  Expenditures  of  any  kind  on  new  projects  are  rarely 
wise,  however  otherwise  profitable,  which  can  be  postponed 
without  any  very  serious  loss,  however  sure  to  involve  some  loss 
if  all  goes  as  well  as  is  expected  ; — such  as  costly  works  which 
can  be  avoided  by  temporary  lines,  or  by  less  durable  but  cheaper 
structures,  complete  provisions  for  traffic  which  is  yet  in  the 
future,  and  elaborate  shops  and  buildings. 

On  the  other  hand,  economies  which  permanently  handicap 
the  line  with  inferior  works  or  alignment,  or  which  place  it  un- 
der a  permanent  disadvantage  in  seeking  for  business,  such  as 
using  over-light  rails,  keeping  away  from  towns  to  save  right-of- 
way  expenses,  heavy  grades,  etc.,  are  the  first  which  should  be 
avoided,  but  are  often  the  first  which  are  resorted  to,  for  rea- 
sons more  fully  discussed  in  Chapters  XXII.  and  XXIII. 

9.  The  profit  on  a  railway  property  depends,  firsts  on  the 
judgment  shown  in  selecting  the  region  through  which  it  is  to 
be  built ;  and,  secondly,  on  the  skill  with  which  the  line  laid  down 
in  it  is  adapted  to  be  of  the  greatest  use  to  the  greatest  number 


CHAP.    I.— INCEPTION   OF  RAILWAY  PROJECTS.  ly 

of  people  (giving  large  gross  revenue)  at  the  smallest  cost  for 
the  service  rendered  (giving  small  operating  expenses).  The 
first  is  distinctively  the  province  of  the  projectors  ;  the  last  is 
distinctively  the  province  of  the  engineer.  Which  is  most  im- 
portant it  would  be  needless  to  inquire,  but  certainly  the  last,  in 
this  sense  at  least,  that,  if  it  be  well  done,  any  errors  in  respect 
to  the  assumed  need  for  a  railway,  although  they  may  be  un- 
fortunate, can  rarely  be  ruinous  ;  while  it  has  again  and  again 
been  proven  that  if  good  judgment  be  not  shown  in  the  details 
of  the  route  and  expenditure,  no  merely  constructive  skill  of  the 
engineer,  nor  excellence  of  judgment  in  selecting  a  locality,  can 
save  the  project  from  disaster. 

10.  All  the  preliminary  questions  of  probable  profit  and  loss 
involved  in  the  decision  to  build  a  line  of  some  kind  over  some 
given  general  route  being  supposed  to  be  finally  settled  and  dis- 
posed of,  and  the  construction  of  the  road  definitely  determined 
on  (if  the  expectations  as  to  cost  of  construction  and  available 
means  are  realized),  the  province  of  the  locating  engineer  and 
the  proper  subject-matter  of  this  volume  begins. 

We  are  now  done  altogether  with  all  considerations  as  to 
whether  the  future  of  the  company  as  a  whole  will  be  prosperous 
or  otherwise,  and  as  to  whether  the  probable  aggregate  profits 
or  cost  of  the  road,  either  per  mile  or  in  gross,  will  be  large  or 
.small,  and  it  is  the  duty  of  the  engineer  to  neglect  them  abso- 
lutely in  laying  out  his  work,  considering  only  the  effect  of  his 
decisions  upon  these  three  items  : 

1.  The  difference  in  gross  receipts  which  will  or  may  result 
from  choosing  one  or  another  line. 

2.  The  difference  in  operating  expenses  which  will  or  may 
result  from  choosing  one  or  another  line,  one  or  another  gra- 
dient, one  or  another  limit  of  curvature,  etc. 

3.  The  difference  in  annual  interest  charge  which  will  or 
may  result  from  the  differences  in  cost  of  construction  caused 
by  differences  in  the  above  details. 

The  latter  should  be  computed,  of  course,  at  the  rate  or  rates 
2 


1 8  CHAP.    I.— INCEPTION  OF  RAILWAY  PROJECTS. 

of  interest  which  money  actually  costs  or  will  cost  his  company. 
This  is  supposed  to  be  known  to,  and  remembered  by,  the 
engineer  ;  and  is  the  only  fact  connected  with  the  present  condi- 
tion or  future  prospects  of  the  finances  of  his  company  which 
should  legitimately  influence  his  decisions. 

11.  Not  unfrequently  this  rate  of  interest  cannot  be  consid- 
ered uniform,  but  must  be  assumed  to  increase  very  rapidly 
with  the  amount  invested  ;  and  not  unfrequently  the  rate  of 
interest  which  should  properly  be  assumed  will  verge  upon  the 
infinite.  It  is  always  more  likely  to  be  underrated  than  over- 
rated ;  whereas  prudence  requires  that  the  reverse  should  be 
the  case. 

But  however  great  or  small  the  amount  and  cost  of  the  avail- 
able capital,  although  our  decisions  themselves  will  vary,  yet  the 
methods  by  which  these  decisions  are  reached  will  not  vary  ;  for 
even  in  such  an  extreme  case  as  when  the  cost  of  more  capital 
than  is  absolutely  essential  is  infinitely  great,  we  are  simply 
permanently  reduced  to,  and  compelled  never  to  vary  from,  what 
should  be  the  a  priori  basis  for  construction  with  which  the  con- 
struction of  every  line  is  entered  upon, — however  prosperous  the 
company,  however  large  the  probable  traffic  and  profits, — because 
no  more  than  this  is  implied  in  the  mere  decision  to  build  the 
road,  which  is  : 

That  excepting  when  and  as  specific  reasons  to  the  contrary  appear., 
the  cheapest  line  is  to  be  built  over  which  it  is  physically  possible  to  carry . 
the  probable  traffic  with  proper  safety  and  speed.,  using  to  this  end  any 
grades  and  curves  and  length  of  lijie  which  ?nay  be  most  conducive  to  this 
end  only — and  never  abandoning  it  by  increasing  the  expenditure.,  unless 
the  investment — not  the  investment  as  a  whole,  for  the  line  as  a 
whole,  but  each  particular  investmeftt  for  each  particular  purpose  at 
each  particular  point — will  be  in  one  way  or  ajiother  profitable  i?i  itself. 

12.  In  other  words,  reduction  of  first  cost  to  the  lowest  pos- 
sible point  is,  in  logical  or  economic  order,  the  first  considera- 
tion ;  although  therefore  not  by  any  means  either  the  most 
important  or  the  governing  consideration.  That  this  is  so  is 
easilv  seen,  however  often  forgotten.     It  is  not  only  business-like 


CHAP.    I.— INCEPTION   OF  RAILWAY  PROJECTS. 


19 


common-sense  for  the  investors  and  their  servants,  but  it  is 
sound  political  economy  for  the  community  as  a  whole.  It  does 
not  mean  nor  imply  cheap  and  shabby  construction.  It  simply 
means  an  avoidance  of  waste,  either  in  saving  money  or 
spending  it.  It  simply  means  a  recognition  of  the  fact  that 
every  dollar  and  every  day's  work  which  goes  into  the  ground 
and  does  not  bring  something  out  of  it,  makes  not  only  the  indi- 
vidual but  the  whole  community  the  poorer.  The  welfare  of  all 
mankind,  as  well  as  of  investors  in  the  enterprises  which  employ 
engineers,  depends  upon  the  skill  with  which  the  investment  in 
its  constructive  or  manufacturing  enterprises  (destruction  of 
existing  capital)  is  kept  small,  and  the  productive  or  earning 
power  (creation  of  new  capital)  is  made  large.  The  difference 
between  the  two  is  the  so-called  "profit"  (net  addition  to  exist- 
ing capital),  which  goes  indeed  into  the  control  of  those  who 
created  it  by  perceiving  the  (supposed)  opportunity  or  necessity 
and  using  their  own  means  at  their  own  risk  to  supply  it ;  but  it 
is  not,  therefore,  for  the  true  interest  of  any  person  or  class  to 
make  it  less  by  increasing  the  investment,  for  otherwise  there  is 
a  waste  which,  as  it  benefits  no  one,  indirectly  injures  all.  Not 
even  the  laborer  who  uses  up  a  portion  of  the  wasted  capital  is 
really  the  gainer;  for  if,  on  the  one  hand,  the  capital  spent  {i.e., 
destroyed)  for  construction  or  plant  be  needlessly  large,  although 
the  poor  man  gains,  for  the  time  being,  wages  which  he  would 
not  otherwise  receive  from  that  particular  enterprise,  yet  it  is  as 
if  he  were  paid  wages  to  turn  a  crank  which  ground  no  grist — 
his  time  and  his  work  go  for  naught.  If  he  spend  half  his  time 
in  this  way  he  must,  in  the  long-run,  do  two  days'  work  for  the 
wages  of  one — a  condition  which  is  nearer  to  existing  in  railway 
enterprises  than  is  always  realized  or  admitted. 

Comparison  of  the  condition  of  laborers  in  countries  and  ages  where  human 
labor  is  economized  (reduced  to  a  minimum  for  each  separate  service)  and 
where  it  is  not,  fully  establishes  this  important  economic  truth,  as  to  which 
many  false  notions  prevail. 

13.  On  the  other  hand,  if  the  proper  margin  of  profit  has 
been   reduced  by  reckless    and    costly  economies,  no  one  gains 


20  CHAP.    I.— INCEPTION  OF  RAILWAY  PROJECTS. 

even  the  semblance  of  benefit,  while  both  the  projectors  and  the 
patrons  of  the  enterprise  are  heavy  losers — the  projectors  in 
money,  the  patrons  in  convenient  service. 

These  two  vital  truths,  therefore,  which  directly  result  from 
what  has  preceded,  should  never  be  forgotten  :  that  because  a 
line  will  have  oris  expected  to  have  a  prosperous  future — because, 
perhaps,  it  is  to  be  built  by  the  State  for  great  reasons  of  state, 
or  for  any  other  reason  will  have  plenty  of  money  in  the  treasury, 
there  is  therefore  no  justification  in  that  fact  alone  for  making 
it  a  costly  road  as  well. 

On  the  other  hand,  no  road  is  so  poor  that  it  can  afford  ta 
economize  when  certain  additional  expenditure  will  be  clearly 
very  profitable.  If  it  is  clearly  understood,  or  believed  for  good 
reason,  that  a  given  additional  investment  will  certainly  pay  lo 
or  15  or  25  or  50  per  cent,  as  the  case  may  be,  it  may  almost  be 
said  that  the  poorest  company  can  find  ways  and  means  for 
obtaining  the  capital,  if  the  facts  be  properly  and  clearly  pre- 
sented. 

14.  The  temptation  to  err  by  neglecting  these  axiomatic 
laws — which  is  always  present  with  every  one  in  laying  out  a 
railway — becomes  especially  difficult  to  guard  against  under  two 
circumstances  of  frequent  occurrence  : 

First,  when  a  line  of  light  traffic  is  to  be  carried  through  an 
inherently  difficult  country,  so  that  the  cost  of  construction  must 
in  an}^  case  be  large.  The  tendency  to  look  on  a  slight  per- 
centage of  increase  in  cost  as  a  trifling  matter,  although  it  may, 
nevertheless,  involve  an  expenditure  out  of  all  proportion  to  the 
real  advantage  secured,  is  very  strong,  very  difficult  to  avoid, 
rarely  or  never  avoided  altogether.     Per  contra  : 

15.  Secondly,  when  a  line  of  comparatively  heavy  traffic  is  to 
be  carried  through  a  region  offering  small  natural  difficulties,  a 
dangerous  tendency  arises  of  an  opposite  character; — a  tendency 
to  unduly  exaggerate  the  importance  of  a  large  percentage,  and 
yet  small  aggregate  of  increased  cost.  This  tendency  is  especi- 
ally probable  and  dangerous  when  means  for  construction  are 
limited,  or  when   the  margin  of  profit  on  the   enterprise   as   a 


CHAP.    I.— INCEPTION  OF  RAILWAY  PROJECTS.  2 1 

whole  is  liable  to  be  small :  a  fact  which  should  not  be  per- 
mitted to  exercise  any  influence  whatever,  except  through  its 
reflex  effect  on  the  rate  of  interest  on  capital.  The  most  usual 
and  most  unfortunate  form  which  an  error  of  this  kind  can  take 
is  the  adoption  of  unduly  high  gradients  to  effect  a  really  trifling 
economy.  The  railways  of  the  Western  United  States,  as  al- 
ready noted,  have  suffered  greatly  from  this  cause. 

The  most  experienced  and  cautious  man  cannot  free  himself 
wholly  from  these  too  grave  errors  ;  the  inexperienced  engineer 
or  projector  should  therefore  be  continually  on  his  guard  against 
them. 

16.  It  has  seemed  essential  thus  to  lay  down  certain  prelimi- 
nary generalities  as  to  what  should  be  the  attitude  of  mind  of 
a  locating  engineer,  because  he  is  often  unconsciously  and  im- 
properly guided  in  his  actions  by  the  mere  bald  feeling  (whether 
justified  or  not  does  not  matter)  that  his  company  is  very  rich  or 
very  poor,  and  that  he  can  spend  or  must  save  accordingly. 
Supposing  him  to  enter  upon  the  work,  therefore,  with  that 
most  important  of  all  preliminaries,  a  correct  appreciation  of 
the  proper  basis  for  decisions,  the  problem  for  which  he  is  prop- 
erly responsible,  when  selecting  a  route  for  a  railway  whose 
construction  has  been  determined  on,  may  be  again  subdivided 
thus  : 

First,  and  by  very  much  the  most  important,  is  the  selection 
of  the  general  route  between  the  two  established  termini,  or,  as 
very  often  happens,  the  selection  of  one  or  both  termini  as  well. 

Secondly  comes  the  adaptation  of  the  line  in  detail  to  the 
topographical  conditions  which  exist  along  the  route  selected. 

17.  The  question  of  general  route  is  commonly  settled  by  the 
RECONNAISSANCE,  which  for  this  reason  must  be  classed  as  by 
far  the  most  important  duty  of  the  engineer  in  charge,  and  the 
one  for  which  it  is  most  essential  that  he  should  qualify  himself 
properly,  which  he  can  only  do  by  learning  to  estimate  and  give 
due  relative  weight  to  all  those  circumstances  which  have  or 
may  have  a  bearing  upon  the  future  of  the  property,  as  well  as 


22  CHAP.    I.— INCEPTION  OF  RAILWAY  PROJECTS. 

to  judge  of  the  physical  possibilitfes  of  the  route  in  question. 
Otherwise — if  he  is  qualified  merely  in  the  latter  respect — his 
danger  is  a  double  one :  that  he  will  give  undue  weight  to 
purely  engineering  questions  as  against  commercial  and  pecuni- 
ary advantages  ;  or,  vice  versa,  that  the  desire  to  reach  such  and 
such  a  town  or  make  such  and  such  a  connection  may  work  in- 
jury to  the  property  considered  as  a  v^hole. 

The  reconnaissance,  in  the  broad  sense  here  given  to  the 
term,  viz.,  the  selection  of  the  entire  route  between  termini,  or 
even  in  cases  of  the  termini  themselves,  is  rarely  left  entirely 
to  the  engineer  or  to  any  one  person.  But  by  whomsoever  de- 
cided, there  is  the  same  danger  of  error  from  attaching  undue 
importance  to  some,  at  the  expense  of  other,  governing  con- 
siderations. 

18.  The  art  of  correctly  discerning  in  advance,  by  merely 
ocular  examination,  assisted  only  by  maps  and  a  few  portable 
instruments,  the  physical  possibilities  and  probable  cost  of  a 
projected  or  possible  railway  route,  and  of  making  the  most  ad- 
vantageous selection  from  the  possible  routes  (which  are  always 
numerous)  for  further  instrumental  examination,  is  sometimes 
supposed  and  stated  to  be  a  sort  of  ''natural  gift,"  dependent 
upon  an  "eye  for  country,"  and  to  be  acquired  only  and  exclu- 
sively by  practice. 

As  with  most  popular  impressions,  there  is  a  foundation  of 
truth  in  this.  Certain  natural  qualifications  and  a  considerable 
amount  of  practice  are  essential.  Nevertheless,  the  acquirement 
of  reasonable  skill  and  competency  for  the  discharge  of  this 
most  responsible  of  all  duties  connected  with  laying  out  a  rail- 
way is  only  to  a  limited  degree  dependent  upon  practice  alone, 
or  increased  by  long  practice,  and  is  hardly  dependent  at  all 
upon  any  peculiar  "  natural  gift,"  other  than  a  natural  gift  for 
close  observation,  and  for  care  in  observing,  collecting,  and  re- 
membering those  facts  which  are  or  may  hereafter  be  important 
— qualities  which  are  apt  to  be  useful  for  other  purposes  as  well. 
There  are  certain  general  rules  and  methods  to  be  observed,  and 
certain  general  dangers  to  be  avoided,  which  can  be  laid  down 


CHAP.    I.— INCEPTION   OF  RAILWAY  PROJECTS.  23 

almost  as  certainly  as  if  the  art  of  reconnoitring  were  an  exact 
science,  and  which,  if  they  be  mastered  in  advance, — not  simply 
by  reading  them,  but  by  acquiring  a  habit  of  observation  and  of 
applying  them  to  hypothetical  instances, — will  enable  the  young 
engineer  of  very  limited  experience  to  go  into  the  field  better 
guarded  against  error  than  by  long  years  of  field  practice  alone  ; 
for  the  latter,  in  location,  as  in  most  other  matters  which  re- 
quire something  more  than  the  mechanical  application  of 
methods  learned  by  rote,  is  quite  as  apt  to  confirm  erroneous 
opinions  as  to  inculcate  good  ones.  The  first  necessity  is  to 
form  correct  and  definite  ideas  as  to  what  a  railway  should  be, 
what  kind  of  a  railway  we  are  to  build,  what  are  the  conditions 
which  contribute  most  to  its  prosperity,  and  to  what  extent  they 
so  contribute,  in  order  that  the  reconnoitring  engineer  may  be 
prepared  to  form  on  the  instant  an  approximately  correct  idea, 
not  only  as  to  what  he  can  do,  but  as  to  what  he  ought  to  do,  in 
any  given  case,  and  to  decide  which  of  two  incompatible  ends 
should  be  sacrificed  to  the  other,  and  what  approximate  sum 
represents  the  difference  in  value  between  them.  Otherwise  the 
experienced  and  inexperienced  man  alike  are  in  imminent  dan- 
ger of  failing  even  to  discern  or  consider  what  are  really  the 
most  promising  possibilities — not  from  lack  of  an  "  eye  for  coun- 
try" or  training  in  the  field,  but  from  wrong  ideas  of  expe- 
diency. 

19.  It  necessarily  results  from  the  preceding  that  the  re- 
connaissance is,  of  all  his  duties,  the  one  which  the  responsible 
engineer  in  charge  should  personally  discharge,  and  never  un- 
der any  circumstances  delegate,  in  part  or  whole,  to  less  expe- 
rienced subordinates,  where  the  final  decision  may  be  seriously 
affected  thereby. 

The  greater  portion  of  this  volume  will  be  devoted  to  the 
presentation  of  data  as  to  the  first  and  most  important  of  the 
duties  connected  with  the  reconnaissance  and  subsequent  sur- 
veys, determining  what  ought  to  be  done  ;  afterwards  con- 
sidering the  comparatively  simple  matter  of  how  to  do  it. 

20.  To  reach  entirely  correct  decisions  as  to  what  ought  to 


24  CHAP.    I.— INCEPTION   OF  RAILWAY  PROJECTS. 

be  done  requires,  it  is  plain,  that  we  should  not  only  have  a 
correct  idea  of  the  nature  of  a  railway  corporation's  finances  and 
of  railway  traffic,  but  that  we  should  foresee  exactly  the  volume 
and  sources  of  the  future  traffic,  and  the  details  and  probable 
amount  of  the  future  operating  expenses,  as  well  as  in  part  of 
the  future  revenues  ;  for  the  larger  the  probable  traffic,  the  more 
perfectly  adapted  to  its  cheap  handling  can  we  afford  to  make 
every  detail  of  the  line  ;  the  larger  the  probable  revenue,  the  less 
will  the  burden  be  felt  of  paying  interest  on  present  expendi- 
tures, etc.,  etc. 

21.  This  we  cannot  do.  To  foresee  such  details  perfectly  is 
impossible.  To  foresee  them  in  any  degree  we  are  obliged  to 
do  that  most  hazardous  thing — to  look  forward  to  and  "dis- 
count" the  future  ;  to  make — and  act  upon — what  is,  after  all, 
nothing  more  than  a  guess  at  the  probable  course  of  future 
events.  To  foresee  the  future  with  adequate  exactitude  even  in 
the  simple  case  of  improvements  on  an  old  road  is  difficult,  al- 
though we  have  a  definite  past  to  guide  us.  In  the  case  of  a  new 
road  it  is  still  more  difficult  to  approximate  to,  and  still  less  pos- 
sible to  reach,  an  exact  and  positive  result  ;  but  nevertheless, 
especially  in  any  country  where  railways  already  exist,  estimates 
of  the  financial  importance  of  doing  or  not  doing  certain  things 
can  always  be  made,  by  proceeding  on  correct  principles  and 
using  proper  care,  which  shall  be  a  sufficient  guide  for  location, 
and  hence,  whe^.  made,  should  always  be  carefully  followed  in 
preference  to  mere  "judgment"  and  guesswork  pure  and  sim- 
ple. The  uncertainty  as  to  the  exact  requirements  to  be  ful- 
filled by  the  works  when  completed  is  a  disadvantage,  indeed, 
which  cannot  be  escaped  ;  but  the  more  difficult  it  is  to  reach 
absolute  correctness,  the  greater  need  we  have  of  some  guide 
which  shall  reduce  the  unavoidable  guesswork  to  its  lowest 
terms,  and  so  save  us  from  the  manifold  hazards  which  result  from 
not  only  guessing  at  facts,  but  at  the  effect  of  those  facts.  What- 
ever care  we  use,  we  can  never  attempt  with  success  to  fix  the 
exact  point  where  economy  ends  and  extravagance  begins  ;  but 
what  we  can  do  is    to  establish   certain    narrow  limits   in    either 


CHAP.  I.  — THE   INCEPTION   OF  RAILWAY  PROJECTS.      25 


direction,  somewhere  within  which  lies  the  truth,  and  anywhere 
outside  of  which  lies  a  certainty  of  error.  Due  judgment  and 
caution  require  that  we  should  do  so  ;  and  this  is  what  we  do 
effect  when  we  make  as  careful  an  estimate  as  possible  of  the 
details  of  the  problem  and  accept  the  final  result  as  an  absolute 
:guide. 

The  following  three  tables  (i  to  3),  while  containing  data  otherwise  useful,  and 
to  which  we  shall  have  occasion  to  refer,  bring  out  vividly  the  enormous  indi- 
rect benefits  of  railways,  which  have  much  to  do  with  the  construction  of  many 
lines  otherwise  profitless,  as  notably  in  Canada  and  Mexico,  where  the  govern- 
ment has  (very  properly  and  wisely)  paid  heavy  subsidies  to  secure  the  con- 
struction of  otherwise  profitless  lines.  The  same  has  been  true  to  a  large  ex- 
tent in  the  United  States,  both  as  respects  the  general  government.  States,  and 
private  individuals  and  corporations.  Nearly  all  the  increase  in  the  valuation^' 
of  the  United  States  since  1850,  as  shown  in  Table  2,  may  be  said  to  be  due  in 
directly  to  railways,  since  without  their  aid  a  much  greater  valuation  than  ex 
isted  in  1850  would  have  been  impossible. 

Table  1. 
Estimated  Total  Wealth  of  the  United  States. 

[Abstracted  from  U.  S.  Census,  1880,  Report  of  H.  Gannett,  Special  Agent.] 


:) 


Items. 


Railways  and  equipment. 
Farms 


Residence  and  business  real  estate,  including  water- 
power  

Telegraph,  shipping,  and  canals 

Live-stock,  farming  tools,  and  machinery 

Household  furniture  and  personal  clothing,  etc 

Mines  and  quarries,  including  6  mos.  average  output 
estimated  as  on  hand 

Three  fourths  of  annual  product  of  agriculture,  manu- 
factures, and  importations,  estimated  as  on  hand 

Churches,  schools,  and  public  buildings  not  taxed 

Specie , 

Mechanics'  tools  and  miscellaneous , 


Total  wealth  of  United  States,  June,  1880. 


Total 
Amount, 
=  1. 000. 000. 


5,536 
10,197 

9,881 

419 

2,406 

5,000 

781 

6,160 

2,000 

612 

650 


43,642 


Per  cent. 


12.69 
23-37 

22.64 
.96 

5-51 
611.46 

1.79 

14. II 
4-58 
1.40 
1.49 


Note. — Including  the  mileage  which  was  under  construction  at  the  time  of  the  census, 
-and  money  spent  on  abandoned  grading,  there  may  have  been  the  equivalent  of  some 


26     CHAP.  I.  — THE  INCEPTION  OF  RAILWA  V  PROJECTS. 


Table  2. 

Valuation  per  Head  and  Total  True  Valuation  of  each  State  of  the 
United  States  since  1850,  by  Decennial  Periods. 

[Abstracted  from  Vol.  VII.  of  1880  Census.     The  valuations  preceding  1870  include  shares  as 
personal  property,  so  that  much  of  the  apparent  falling  off  is  fictitious.] 


True  Valuation  per  Head. 

Total  True  Valuation,  i  ~  1,000,000. 

1850 

I860 

1870 

1880 

1890 

1850 

I860 

1870 

1880 

1890 

Maine 

210 
326 
294 

577 
546 
420 

303 
479 
389 
662 

%\ 

555 
794 

7I2« 

1403 
1366 
1441 

787 
1046 

909 
1471 
1447 
1251 

123 
104 

92 

''A 
■56 

190 
156 
122 
815 
135 

444 

348 
253 
235 
2132 
297 
775 

1 

2623 
400 
779 

New  Hampshire.. 
Vermont       

Massachusetts 

Rhode  Island 

Connecticut 

Average 

396 

596 

1055 

1152 

1129 

1862 

4040 

4978 

New  York  

New  Jersey 

Pennsylvania 

Delaware .    ... 

349 
409 

313 
230 

475 
696 
487 
412 

1483 
1038 
1081 
111 

1241 
1154 
1154 
928 

1080 

200 

722 

21 

1843 

468 

1417 

46 

6501 

941 

3808 

97 

6308 

1305 

4942 

136 

Average 

325 

518 

1095 

iiiq 

2023 

3774 

11,345 

12,691 

Maryland   

Dist.  of  Columbia. 

376 

J-303 
261 
431 
370 
261 
296 
377 
452 
248 
190 
201 
307 

549 
547 

497 
361 
779 
611 
521 
514 
767 
850 
605 
504 
445 
576 

824 
,963 
J334 
I431 
243 
295 
226 
235 
202 
253 
445 
194 
323 
396 
457 

895 

'7l 
566 
329 
323 
393 
445 
339 

518 
356 
457 
547 

219 
14 

[     431 

227 

288 

335 

23 

228 

228 

234 

53 

40 

201 

302 

377 
41 

793 

646 
73 

602 

365 
219 

644 
127 
J      410 
(      191 
261 
20S 
268 
44 
202 
209 
323 
159 
156 
498 
604 

837 
220 
707 
350 
461 
322 
606 
120 
428 
354 

286 
705 
902 

West  Virginia 

North  Carolina.... 
South  Carolina — 

Florida 

Alabama    .... 

Mississippi 

Louisiana 

Texas 

Arkansas 

Tennessee 

Kentucky 

Average 

310 

552 

388 

506 

2823 

6285 

4304 

7505 

Ohio 

255 
205 
183 
150 

510 
392 
509 
343 

839 
755 

607 

1013 
850 

1043 
965 

505 
203 
156 
60 

1194 
529 
872 

257 

2235 

1268 

2122 

719 

?1? 

3210 

1580 

Illinois       

Michigan  . 

Average 

iq8 

439 

759 

968 

924 

2852 

6344 

9709 

Wisconsin 

Minnesota 

138 

123 
201 

353 
304 
366 
424 
292 
317 

666 
521 
601 
746 

563 

866 
1014 
1059 
720 
763 
851 

42 

24 
137 

274 

52 

247 

501 

31 

9 

702 
229 
718 
1285 
189 
69 

"39 
792 
1721 
1562 
760 
385 

Missouri  

Kansas  

Nebraska 

Average 

154 

343 

603 

879 

203 

1114 

3192 

6359 

Dakota 

Montana 

Wyoming 

Colorado 

84 

223 

395 
737 
770 
508 
341 

873 
1022 
2596 
1235 

410 

5 

21 

6 
15 

7 
20 

31 

118 

.    40 

54 

240 

49 

New  Mexico 

Average 

84 

223 

550 

1227 

5 

21 

79 

501 

Arizona 

Utah 

87 

*38i 
234 

139 

"483 
551 

356 
186 
437 
566 

567 

1014 
792 
890 
82s 
882 



5 
6 

6 

6 

29 

i 

7 
14 
52 

41 
114 

29 
62 

IS4 

Idaho 

Washington 

Oregon 

Average 

391 

422 

881 

41 

89 

400 

Nevada  

California 

239 

547 

733 
1 140 

2506 

1553 

22 

""208 

31 

639 

156 
1343 

Average  U.  S. . . 

308 

514 

780 

870 

7,136 

16,160 

30,069 

43,642 

Miles  of  Rai 

way  (i 

840,  2, 

3i8)... 

9,021 

30,635 

52.914 

93,340 

CHAP.  I.  — THE  INCEPTION  OF  RAILWAY  PROJECTS.      27 

95,000  miles  in  the  country,  indicating  that  make  the  average  value  placed  on  it  a  little  less 
than  $60,000  per  mile.  This  corresponds  closely  with  the  aggregate  of  stock  and  bonds 
per  mile  (Table  32),  but  it  represents  value  and  not  cost,  and  the  latter  has  probably  not 
been  over  $35,000  to  $40,000  per  mile  in  cash,  which  would  make  the  actual  cost  of  the 
railways  is  not  over  71^  to  8  per  cent  of  the  national  wealth.  Yet  at  least  three  quarters  of 
the  enormous  aggregate  may  be  said  to  be  the  direct  result  of  railways,  since  without  them 
it  could  never  have  existed.  In  other  words,  every  dollar  of  cash  invested  in  railways  has 
on  an  average  added  $6  to  $8  to  the  national  wealth;  a  fact  which  has  had  much  to  do 
with  the  construction  of  railways  which  were  not  directly  profitable. 


Table  3. 
Railway  Capital  and  Public  Wealth  of  the  World. 

[Reconstructed  and  Revised  from  Mulhall's  "  Dictionary  of  Statistics."] 


United  States 

Canada 

Australia , 

United  Kingdom. . . 

France 

Germany , 

Russia 

Austria 

Italy 

Spain 

Portugal , 

Belgium 

Holland 

Denmark , 

Sweden  and  Norway 

Switzerland 

Turkey,  etc , 

Total  Europe 

Grand  Total 


Popu- 
lation, 


50,410 
4-340 
2.880 


34,650 

37,430 

45,260 

84,440 

37,830 

28,910 

16,290 

4,350 

5,480 

4,060 

1,960 

6,560 

2,810 

17,250 


312,990 
370,620 


Total 
Railway 
Capital. 
Millions. 


5,780 

349 
272 


3,740 

2,400 

2,270 

1,500 

1,286 

524 

383 

58 

296 

131 

49 

155 

160 

117 


13,069 
19,470 


Per 

Mile  of 
Railway. 

% 
55,300 
46,700 
50, 500 


203,000 

133,000 

102,300 

99,500 

100,300 

94,200 

79,600 

74,800 

109.200 

90, 300 

50,000 

32,000 

97,200 

64,600 


117,200 
84,700 


Per 

Inhabi- 
tant. 


% 

112 
83 

97 


117 
63 
49 
19 
34 
19 
24 
15 
53 
34 
24 
24 
58 
10 


39 
49 


National 
Wealth, 
Millions. 


% 
50,340 
3,160 
2,900 


42,300 

39,200 

30,700 

19,860 

19,000 

10,820 

7,620 

1,648 

5,720 

5.450 

1,720 

3,580 

1,502 

3,490 


192  600 
249,000 


Ratio  of 
Railway 
to  Total 
Capital. 


Per  cent. 

II. 4 

II. I 

9-3 


6.1 


7-1 
7-7 
6.5 
4.8 

5.1 
3.3 
5.3 
2.4 
2.8 

4.3 
10.7 

3-3 


6.7 

7.8 


The  above  statistics,  except  population,  are  mostly  for  the  year  1882.  Many  errors  and 
inconsistencies  probably  exist  in  this,  as  in  all  similar  estimates.  No  great  accuracy  is 
possible  in  them. 

According  to  Mulhali  the  wealth  of  Britain  has  more  than  doubled  in  the  past  40  years, 
and  quadrupled  in  70  years.  While  the  indirect  benefits  of  railways  have  been  far  less  in 
Europe  than  in  the  United  States,  it  is  tolerably  certain  that  at  least  40  per  cent  of  the 
present  wealth  of  Europe  would  not  exist  except  for  them. 


CHAPTER   II. 

THE    MODERN    RAILWAY    CORPORATION. 

22.  Modern  railway  corporations,  even  the  strongest  of  them, 
have  but  a  narrow  margin  for  mistakes.  It  is  important  that 
we  should  have  that  fact  clearly  before  the  eyes,  and  the  reasons 
why  it  must  be  so,  in  order  that  the  atmosphere  of  wealth  which 
surrounds  the  period  of  construction  may  not  beguile  us  into 
folly. 

The  origin  of  most  modern  railway  corporations  is,  in  its 
economic  aspects,  about  as  follows  :  A  certain  number  of  men 
conclude  that,  for  anyone  of  the  reasons  before  considered,  there 
is  sufficient  need  of  a  railway  in  a  certain  region  to  make  it,  when 
completed,  worth  more  than  it  has  cost  to  those  who  have  built 
it,  so  that  a  "  profit,"  or  creation  of  a  greater  value  than  the 
expenditure,  will  accrue  to  them. 

Ordinarily,  this  sanguine  expectation  is  at  least  so  far  justi- 
fied that  the  property  when  completed  is  worth  to  some  one,  in 
one  way  or  another,  all  or  nearly  all  it  has  cost,  although  there 
may  be  no  great  profits.  In  any  rapidly  growing  country,  like 
the  United  States,  the  general  rule — subject  to  numerous  and 
painful  exceptions — has  been  and  is  that  railway  properties,  like 
other  enterprises  of  the  kind,  tend  to  be  very  productive,  and  to 
eventually  rise  in  value  far  above  their  real  cost,  often  to  many 
times  their  cost. 

23.  For  this  reason  it  has  very  frequently  happened  in  the 
United  States  that  enterprises  have  appeared  to  be  of  so  sound 
a  character  that  they  have  been  almost  immediately  able  to 
borrow  on  mortgage  their  entire  capital  for  construction,  or 
even   a  still  larger  sum,  and  the  original  projectors  and  true 


CHAP.    II.— THE  MODERN  RAILWAY   CORPORATION.        29 

"  owners"  of  the  property  have  not  been  required  to  invest  any- 
thing whatever  in  the  property  themselves  beyond  their  original 
sagacity  in  initiating  the  enterprise — a  quality  which  has  its 
value  in  railway  business,  as  in  most  other  human  affairs.  In 
all  cases  they  can,  if  they  choose,  borrow  on  mortgage  whatever 
sum  they  can  make  capitalists  believe  is  or  will  be  the  minimum 
value  of  the  property.  Usually  they  not  only  choose,  but  are 
compelled  to  do  this. 

24=  The  original  projectors,  who  alone  appear  in  the  manage- 
ment of  the  enterprise,  and  who  alone  constitute  what  is  known 
as  "  the  Company,"  then  simply  make  good  the  deficiency,  if 
there  is  any  deficiency,  in  the  means  for  construction;  assuming 
what,  in  the  general  opinion,  is  the  whole  risk  of  the  enterprise. 
For  taking  this  risk,  as  well  as  for  their  services  in  initiating  and 
carrying  on  the  enterprise,  they  obtain  nothing  more  than  what 
may  be  called  the  speculative  interest,  viz.,  that  portion  which 
fluctuates  with  and  depends  solely  upon  the  skill  and  good  judg- 
ment with  which  the  property  has  been  originally  planned  and 
is  afterwards  managed;  which  may  be  wiped  out  in  a  moment 
or  may  become  very  valuable. 

25.  This  interest  is  in  modern  times  supposed  to  be  repre- 
sented by  the  stock  or  (in  England)  "  shares,"  although  the  line 
between  stock  and  bonds  or  mortgage  securities  is  not  always 
sharply  drawn.  The  proportion  which  the  stock  and  bonds 
bear  to  each  other  varies  greatly  in  different  parts  of  the-United 
States  and  of  the  world.  In  regions  where  capital  is  abundant, 
and  there  are  small  chances  of  either  great  loss  or  great  gain, 
those  who  believe  in  the  enterprise  and  would  be  willing  to  lend 
money  on  its  minimum  value  will  prefer  to  own  it  outright,  and 
few  or  no  mortgage  bonds  will  be  issued.  Such  is  the  case  in 
England  and  on  the  Continent.  In  a  country  where  the  future 
is  all  uncertain,  but  where  population  and  traffic  is  advancing, 
literally,  by  leaps  and  bounds,  and  where  the  future  is  so  "  dis- 
counted "  (as  it  is  all  but  inevitable  that  it  should  be)  that  lines 
are  built,  not  for  the  traffic  which  exists  but  for  the  traffic  which 
is  to  come,  the  opposite  conditions  will  all  but  inevitably  prevail. 


30        CHAP,   II.— THE   MODERN  RAILWAY  CORPORATION. 


The  bonds  themselves  will  then  partake  of  a  speculative  char- 
acter, and  will  involve  as  much  hazard  as  large  investors  can  be 
persuaded  to  consent  to.  Consequently  there  will  be  a  constant 
tendency  for  roads  to  be  "built  on  bonds,"  the  bondholders 
being  in  fact  sharers  in  the  speculative  risk,  but  to  a  less  extent. 
The  limits  of  doubt  as  to  the  future,  between  the  maximum  and 
minimum  value  of  the  property,  being  a  large  one,  they  know- 
ingly assume  a  portion  of  this  risk,  leaving  it  to  the  nominal 
''  Company"  to  manage  the  property,  and  trusting  that  they  will 
manage  it  as  skilfully  as  they  can,  as  their  own  sole  chance  of 
reaping  a  profit  for  themselves. 

These  latter  conditions  are  well  known  to  obtain  more  fully 
in  the  United  States  than  in  any  other  considerable  region  of  the 
world,  and  on  that  account  it  is,  and  not  primarily  from  differ- 
ence of  laws  or  business  habits,  that  the  railway  system  of  the 
United  States  has  been  built  to  so  much  larger  extent  than  else- 
where on  borrowed  capital  represented  by  bonds. 

26.  Under  conditions  involving  so  large  an  element  of  specu- 
lative uncertainty,  as  well  as  such  great  probabilities  of  ultimate 
profit,  many  abuses,  much  feverish  excitement,  many  deceptive 
exaggerations  both  in  good  faith  and  in  bad  faith,  much  gaining 
of  something  from  nothing,  many  cases  of  visionary  folly,  of  sad 
disappointment  and  of  deliberate  fraud,  are  all  but  unavoidable  ; 
yet  in  the  conditions  themselves  there  is  nothing  either  surpris- 
ing or  .reprehensible  or  avoidable.  We  have  seen,  in  a  much 
exaggerated  form,  the  same  causes  producing  the  same  effects 
in  the  oil  excitement  of  1863-5,  Y^^  ^hey  were  but  the  collateral 
evil  eftects  of  a  movement  in  itself  in  every  way  healthy  and 
normal,  and  they  ceased  with  the  period  of  rapid  expansion  and 
sudden  and  irregular  profits. 

So  with  the  organization  of  our  railways.  The  existing  con- 
ditions, with  all  their  collateral  evils,  are  in  the  main  healthy 
and  natural  ;  and  whether  good  or  bad,  cannot  be  expected  to 
materially  change  until  the  process  of  rapid  development  and 
advance  in  wealth  has  ceased,  which  will  not  probably  be  for 
many  decades.      Until   that   time  railways  will   continue  to   be 


CHAP.    II  — THE  MODERN  RAILWAY  CORPORATION.        3 1 

largely  built,  as  they  are  built,  on  bonds  and   faith  and   hope, 
with  a  narrow  margin  of  financial  safety. 

27.  It  is  often  claimed  that  the  existence  of  these  conditions 
is  an  evidence  and  result  of  a  greater  national  rashness  in  doing 
business,  but  this  is  true  only  to  a  limited  extent.  The  main 
reason  is  that,  owing  to  the  rapid  development  of  the  United 
States,  the  margin  of  positive  and  certain  value  has  seemed  to 
capitalists  to  be  larger,  and  the  minus  side  of  the  speculative  and 
dubious  element,  the  proper  allowance  for  possible  depreciation, 
has  appeared  to  be  less.  The  same  general  law  obtains,  and 
always  has  obtained,  throughout  the  world,  that  such  properties 
are  always  built  on  borrowed  money  up  to  the  limit  of  what  is 
regarded  as  their  positive  and  certain  minimum  value.  The 
risk  only,  the  dubious  margin  which  is  dependent  upon  sagacity, 
skill,  and  good  management,  is  assumed  and  held  by  the  Com- 
pany proper  who  control  and  manage  the  property. 

Thus  it  happens  that  in  America,  and  in  an  increasing  degree 
throughout  the  world,  the  nominal  "  Company,"  which  the  engi- 
neer and  all  other  officers  serve,  and  which  exercises  full  control 
over  the  entire  property  for  the  time  being,  although  in  theory 
it  is  the  real  owners  of  the  property,  is  not  such  in  fact.  All  it 
really  owns  is  a  contingent  interest  in  the  results  of  its  own 
sagacity  and  skill  in  creating  a  property  which  shall  be  in  fact 
worth  more  than  what  leading  capitalists  consider  its  j?imtmii??i 
probable  value.  Their  small  payment  for  this  contingent  inter- 
est (if  they  pay  anything  at  all)  is  precisely  equivalent  in  its 
nature,  although  less  objectionable  morally,  to  what  is  called  a 
"  margin"  on  stocks—  it  is  sufficient  only  to  cover  the  financial 
risk  of  the  enterprise,  or  the  difference  between  the  actual  and 
necessary  cost  and  the  general  estimate  of  the  minimum  value  of 
the  line  when  completed,  which  is  represented  by  various  forms 
of  bonds. 

28.  The  essential  truth  of  this  general  summary  is  not  de- 
creased by  the  fact  that,  to  be  entirely  correct,  it  should  take 
oote  of  many  apparent  anomalies  and  exceptions.  Thus  it  not 
infrequently  happens  that  the  issue   of  "  mortgage  bonds,"  and 


32        CHAP.    II.— THE  MOX>ERN-  RAILWAY  CORPORATION. 

even  the  cash  received  for  them,  is  alone  far  greater  than  the 
actual  investment,  and  still  more  frequently  that  a  large  propor- 
tion of  the  bonds  are  "  taken"  ("  convey"  the  wise  it  call)  and 
held  by  the  original  incorporators.  Usually,  in  such  instances, 
the  second  or  third  or  fifteenth  mortgage  bonds  are  in  reality 
the  stock,  and  represent  the  speculative  interest  dependent  upon 
management;  which  in  that  case  very  properly  controls  the  prop- 
erty, either  in  law  or  fact.  In  that  case  too,  when  the  property 
is  not  a  productive  one  and  a  necessity  arises  for  more  capital  to 
enable  it  to  hold  its  own,  some  new  device,  '^  prior  lien"  bonds 
or  what  not,  is  used  to  transfer  the  true  mortgage  interest, 
involving  no  risk,  to  new  parties,  in  lieu  of  those  who  originally 
held  it,  or  thought  they  did.  Per  contra,  when  the  property  has 
been  successful,  then  begins  the  process  of  "  watering,"  so  called, 
i.e.,  increasing  the  stock  or  bonds  by  new  issues  until  their  total 
amount  bears  a  nearer,  or  at  least  more  satisfactory  relation  to 
the  present  value  or  productive  capacity  of  the  property,  as  dis- 
tinguished from  its  original  cost.  There  have  not  been  wanting 
gross  frauds  and  impositions  in  this  practice,  as  is  not  unknown 
in  other  business  matters  ;  but  in  its  essence  it  is  an  entirely 
legitimate  and  proper  business  transaction,  in  the  nature  of  a 
capitalization  or  "salting  down"  of  realized  business  profit,  and 
belonging  as  justly  to  the  holders  of  the  property  as  the  corre- 
sponding rise  in  the  value  of  other  real  property.  A  certain 
argument,  whose  force  in  certain  individual  cases  is  universally 
recognized  by  intelligent  men,  can  be  made  against  the  reten- 
tion by  the  individual  of  all  such  "  unearned  increment,"  but  in 
the  general  judgment  of  mankind  the  argument  on  the  other 
side  is  immensely  stronger.  The  only  legitimate  distinction  in 
this  respect  between  railway  property  and  any  other  real  estate 
is  that  the  nature  of  its  origin  as  a  creature  of  the  State  justi- 
fies a  demand  that  its  monopoly  powers  shall  not  be  used  op- 
pressively, to  charge  more  than  a  fair  equivalent  for  service,  as 
measured  by  practice  elsewhere  or  on  other  kinds  of  traffic, 
under  similar  circumstances  ;  but  the  just  increase  in  value  of  a 
well-located  railway,  which  does  not  abuse  its  monopoly  powers 


CHAP.    II.— THE  MODERN  RAILWAY  CORPORATION.        33 

to  make  unjust  exactions,  is  fairly  the  property  of  the  owners, 
however  large,  unless  and  until  the  public  are  prepared  to  in- 
sure the  investors  a  certain  minimum  return  as  well  as  deny 
them  the  uncertain  maximum. 

It  may  be  added,  that  the  mortgage  or  bonding  process  is 
carried  on  to  a  greater  extent  in  railway  than  other  business, 
simply  because,  unlike  most  other  business  enterprises,  a  certain 


':2o,ooo,ooo 


Fig.  I. — Diagram  showing  the  Financial  Record  of  the  Lake  Shore  and  Michigan 
Southern  Railway  from  1870  to  1885. 


considerable  fraction,  but  only  a  fraction,  of  the  income  of  their 
property  is  in  the  nature  of  a  monopoly  which  no  conceivable 
circumstances  can  destroy. 

29.  The  annual  interest  on  these  various  forms  of  mortgage, 
together  with  fixed  rentals  of  leased  property,  which  are  of  the 
same  nature,  constitute  what  are  known  as  the  fixed  charges,^ 
by  which  a  large  proportion  of  net    revenue  is  always  absorbed 


34       CHAP.    II  — THE   MODERN  RAILWAY  CORPORATION. 


Operating-  Expensed, 

-1--f--T- 


on  the  most  prosperous  properties — very  frequently  nearly  the 
whole  of  it,  and  not  unfrequently  a  good  deal  more  than  the 
whole  of  it,  if  all  such  charges  were  paid. 

In  tables  immediately  following,  the  fact  that  these  are  the 
conditions  which  actually  exist  is  clearly  brought  out,  and  if 
they  were  more  generally  realized  by  engineers,  and  by  railroad 
officers  generally,  during  the  period  of  construction,  it  can  hardly 
be  doubted  that  it  would  lead  to  more  careful  study  of  the  art  of 
obtaining  the  utmost  possible  value  from  the  money  expended; 

but  there  are  few  men  who  are 
not   elated  and,  as  it  were,  in- 
toxicated by  having  their  pock- 
ets full  of  borrowed  money,  even 
when  the    responsibility  is   all 
theirown,and  on  so  small  a  scale 
that    its    length,    breadth,    and 
depth  can  be  readily  grasped. 
?        \       ^.       ^        °.  When  the  further  dansrer  is  add- 
ed  of  dividing  up  the  responsi- 
_    bility  among  a  dozen  or  more, 
each  of  whom  sees  millions  in 
5   sight,  which  in  his  eyes  are  "  the 
f/s^j       "f  Company's,"  and  not  the  Com- 
fits    79     /880     8/       8z     83      84      85  pany's   Creditors',   and  a  small 

Fig.  2.— Diagram  SHOWING  THE  Financial  Rec-  part  of  which  will  SufficC  for  all 

ORDOFTHR    MICHIGAN  CENTRAL    RaILROAD  (iN-  .  .  ^   ,     , 

cLUDiNG  THE  Canada  Southern),  1878-1885.  posslble  rcquiremcuts  of  his  de- 
partment, the  impulse  to  spend 
money  freely  may  well  become  too  great  for  average  human 
nature  to  resist  ;  so  that  the  enormous  sums  of  borrowed  money 
Aand/ed  during  construction  will  create  an  atmosphere  of  wealth 
leading  to  a  rash  improvidence,  which  has  been  the  chief  cause 
of  the  bankruptcy  of  many  lines.  As  the  engineer  has  the  first 
"  whack"  at  the  Company's  funds,  and  at  a  time  when  the  judg- 
ment of  the  coolest  men  is  most  likely  to  be  tossing  about  on 
the  dancing  waves  of  a  "boom"  at  its  very  height,  his  danger  is 
f)articularly  great ;  and    he  especially   should  realize    that    the 


CHAP.   II.— THE  MODERN-  RAILWAY  CORPORATION.       35 


RULE  with  new  American  railways  is,  and  must  continue  to  be, 
that  a  very  moderate  percentage  of  difference  in  either  the  first 
cost,  or  the  operating  expenses,  or  (above  all)  the  revenue,  means 
to  tlie  original  projectors,  whom  alone  he  serves  or  knows,  all 
the  difference  between  success  and  failure. 


l3--?0|     rrool       f2T35l      [2^89]        [2^       faTTgl       ISg?] 


UZ.S3    0  2.52 


IB7^      1875        76  77         78  79        J880       81  82.         83         S4        (885       86 

Fig.  3. — Diagram  showing  the  Financial  and  Traffic  Record  of  the  Chicago  &  North-. 
WESTERN  Railway,  1874-1886. 

[Figures  in  squares,  or  points  surrounded  by  squares,  give  the  receipts  per  ton-mile 
and  passenger-mile  ;  the  lower  figures  being  those  per  ton-mile.] 


In  Figs.  I,  2,  and  3  is  shown  graphically  how  very  small  is  the  margin  of 
profit  which  makes  the  difference  between  solvency  and  insolvency  even  in  the 


36       CHAP.   II.— THE  MODERN  RAILWAY  CORPORATION'. 

soundest  companies.  These  lines  have  not  been  chosen  as  specially  marked 
examples  of  the  ordinary  fluctuations,  but  on  the  contrary  are  naturally  very 
strong  properties— so  good  that  their  stock  has  ranked  for  years  together  among 
the  best  investment  securities.  Yet  out  of  the  millions  which  they  take  in 
yearly  it  will  be  seen  how  small  a  margin  is  left  over  for  distribution  to  the 
stockholders  in  many  years,  and  what  a  heavy  percentage  of  advantage  to  the 
stockholders  results  from  a  very  small  percentage  of  increase  in  the  gross  re- 
ceipts, or  of  decrease  in  the  operating  expenses  or  (in  much  less  degree)  fixed 
charges.  The  gain  of  all  gains  for  a  railway  to  secure  will  be  seen  to  be  addi- 
tional revenue. 

30.  In  fact,  the  situation  is  somewhat  worse  than  if  the  Com- 
pany merely  began  business  with  a  heavily  mortgaged  prop- 
erty owned  in  fee.  The  theory  that  the  Company  is  the  owner 
in  fact,  as  it  is  in  form,  of  the  entire  property,  and  has  simply 
placed  certain  mortgages  upon  it,  is  convenient  and  in  a  sense 
true ;  but  it  more  correctly  corresponds  with  the  real  facts  which 
prevail  in  the  United  States,  and  for  the  most  part  throughout  the 
world,  to  consider  that  the  mortgage  interest  itself  builds  and 
owns  the  real  property,  as  a  man  might  build  a  house  or  factory 
to  rent  to  others,  induced  thereto  by  the  allegations  of  the  man- 
aging Company  that  in  that  case  they  can  and  will  earn  and  pay 
a  fair  or  a  large  rental  on  the  property  from  the  profits  of  the 
business  which  they  propose  to  carry  on  with  the  property  and 
plant  furnished. 

31.  This  is  the  truer  manner  of  looking  at  the  facts,  both  be- 
cause the  "mortgage"  is  ordinarily  far  in  excess  of  the  mort- 
gaging value  of  the  property  as  property,  closely  approximating 
to  and  often  exceeding  its  cash  cost,  and  because  the  property 
itself  is  all  but  absolutely  worthless  except  for  the  one  particular 
business  which  it  was  built  to  carry  on,  so  that  the  loan  or  mort- 
gage involves  the  determination  that  the  property  on  which  the 
money  is  lent  is  worth  its  cash  cost  for  any  one  to  "operate,"  if 
the  managing  company  should  fail  to  do  a  profitable  business 
with  it.  And  as  the  full  cost  of  all  the  fixed  property  is  then 
always  (practically)  advanced,  and  frequently  the  cost  of  all,  or 
most  of,  the  portable  plant  (rolling  stock)  in  addition,  the  nomi- 
nal mortgage  interest  is  so  large  that  it  really  amounts  practi- 


CHAP.   II.— THE  MODERN  RAILWAY  CORPORATION.       37 

cally  to  an  ownership  interest  in  the  real  property  ;  and  all  that 
the  mortgage  interest  does  not  own  is  the  immaterial  franchise, 
which  necessarily  goes  with  the  property  when  and  if  they  as- 
sume control  of  it.  This  is  the  additional  security  which  makes 
the  nominal  mortgage  interest  a  real  one,  except  that  usually, 
the  operating  company  are  obliged  either  to  invest  some  money 
themselves  in  plant  to  borrow  the  rest  of  it,  or  to  throw  in  an 
interest  in  the  business  (stock)  in  order  to  persuade  outsiders  to 
build  the  plant.  Very  frequently, — in  fact, — usually,  individuals 
in  the  operating  company  (stockholders)  also  lend  money  (buy 
bonds)  for  the  erection  of  the  plant. 

32.  The  instances  where  the  original  projectors,  even  of  lines 
which  have  ultimately  proved  well  justified  and  highly  success- 
ful, have  been  ruined  by  depleting  their  means  too  rapidly  with 
unwarranted  or  deferable  expenditures,  and  have  been  compelled 
to  yield  their  control  of  the  property,  almost  on  the  eve  of  its 
success,  have  been  very  numerous.  A  single  instance,  selected 
almost  at  random,  of  the  startling  vicissitudes  to  which  such 
properties  are  subjected,  and  of  the  dangers  of  the  most  merito- 
rious enterprises  from  the  long  periods  of  depression  through 
which  they  usually  have  to  pass  soon  after  their  construction, 
and  from  the  scanty  means  of  the  original  projectors,  may  be  in- 
structive. 

33.  Within  a  few  years  after  its  construction,  what  has  since  become 
the  St.  Paul,  Minneapolis  &  Manitoba  Railway,  then  the  St.  Paul  &  Pa- 
cific, was  a  very  striking  example  of  such  reckless  management  of  rail- 
way investments. 

Its  construction  began  in  the  flush  times  of  1872-3.  Working  then 
318  miles,  it  earned  only  $630,000  gross  and  $166,000  net,  the  latter  being 
at  the  rate  of  only  $523  per  mile  of  road.  Its  debt  (exclusive  of  stock) 
was  then  over  $50,000  per  mile,  and,  no  interest  being  paid  on  any  part 
of  it,  a  receiver  was  appointed. 

In  1873-4  and  1874-5  the  net  earnings  were  still  less. 

In  1876-7,  an  extension  of  104  miles  into  the  Red  River  Valley  hav- 
ing been  completed,  the  net  earnings  were  nearly  doubled,  and  became 
$749  per  mile. 

By  1878,  although  the  bonds  of  the  Company  had   become   almost 


38       CHAP.    II,— THE  MODERN  RAILWAY  CORPORATION. 


worthless,  the  receiver  succeeded  in  completing  the  line  to  the  Dominion 
boundary,  in  time  to  save  a  large  land  grant,  and  the  better  days  of  the 
property  began  to  dawn  ; — five  years  too  late  for  the  original  projectors. 

A  new  company  was  then  organized,  purchased  the  line  at  foreclosure 
sale,  and  found  itself  the  possessor  of  the  422  miles  above  specified,  and 
143  miles  more,  with  a  bonded  debt  of  only  $7,266,000 — less  than  $13,000 
per  mile.  Then  first  the  land  grant  began  to  be  of  immediate  value. 
Immigration  was  flowing  in,  the  Canada  Pacific  was  building  beyond  it, 
wheat  began  to  rise,  and  a  property  which  had  been  almost  worthless, 
all  at  once  became  very  productive. 

The  boom  continued  until  1883,  and  its  progress  is  shown  in  Table  4. 

Table  4. 

Financial  History  of  the  St.  Paul,  Minneapolis   &   Manitoba 

Railway. 


Year. 

Miles. 

Earnings. 

Pass. 

Miles 
(Mil- 
lions). 

Fr'ght. 
Miles 
(Mil- 
lions). 

Land 
Sales. 
Acres. 

Aver'ge 
Rate, 

Cents 
per 
Ton. 

Divi- 
dends. 

Gross. 

Net. 

Per 

Cent. 

3^8 
318 
422 

$1,980 

S522 
749 

.... 

1876-77 

1879-80      

1,497 
1,497 
1,497 
1,497 

$4,471 
4.954 
7,159 
7,605 
5,992 
5.230 

$2,489 

934- 
190. 
341. 
340- 
395- 

268,700 

97.900 
203,300 
104,250 
83.900 
65,600 

2.88 
2.52 
1. 91 
1.79 
1.52 

1881-82 

1882-83     

3,573 
3.995 
3,282 

3,057 

54-4 
68.1 
53-5 
45.0 

6^ 
95^ 

188--84 

8 

1884-85 

6^ 

By  the  end  of  1883  the  road  was  earning  net  more  than  anyroad 
westward  of  Chicago  except  two  (the  Rock  Island  and  Chicago  & 
Alton),  and  the  boom  was  at  its  height.  The  real  surplus  in  the  last  two 
years  had  been  enough  to  pay  nearly  twice  as  great  dividends.  Its  lines 
were  well  placed,  and  almost  completely  secured  to  the  Company  the 
possession'  of  the  traffic  of  one  of  the  most  fertile  valleys  on  the  Con- 
tinent. 

Then  an  ebb-tide  set  in.  Immigration  and  the  price  of  wheat  fell  off, 
as  also  the  immense  traffic  from  the  construction  of  the  Canada  Pacific. 
A  competing  line  on  the  north  shore  of  Lake  Superior  was  opened. 
Rates  were  necessarily  made  much  lower,  and  for  the  two  additional 


CHAP.   II.— THE  MODERN  RAILWAY  CORPORATION.       39 

years,  which  alone  can  be  given  in  this  volume,  the  record  was  as  shown 
in  the  last  two  lines  of  Table  4,  the  contrast  between  which  and  the  last 
year  of  the  flush  period  is  notable. 

In  the  last  year,  in  spite  of  the  falling  off  in  prosperity,  which  had  in 
it  no  element  of  immediate  disaster,  bonds  to  the  amount  of  50  per 
cent  of  the  stock  were  "  sold  "  to  stockholders  for  10  cents  on  the  dollar, 
which  was,  of  course,  equivalent  to  a  dividend  of  some  45  per  cent, 
more  if  the  future  of  the  property  did  not  belie  its  promise.  From  the 
point  of  view  of  the  public  interest  there  was  no  danger  of  this.  Its 
future  was  magnificent  and  assured.  As  respects  the  individual  owners, 
great  as  had  been  their  profits  to  date  from  securing  control  of  this  for- 
merly bankrupt  property,  this  was  and  is  far  less  certain. 

34.  The  instructive  feature  of  the  example  is  that  even  now  (1885), 
failing  anyone  of  these  following  conditions,  ruin  or  serious  loss  of  all 
recent  investors  in  the  stock  of  property  would  be  near  at  hand : 

1.  The  fixed  charges  arp  only  $1358  per  mile,  whereas  double  that 
figure  or  even  more  would  be  more  usual.  At  the  latter  figure  a  com- 
bination of  many  causes  might  bring  the  net  earnings  below  it. 

2.  The  rapid  fall  of  rates,  which  otherwise  would  have  extinguished 
the  surplus,  was  met  by  important  improvements  of  the  main-line  grades, 
and  by  the  introduction  of  more  powerful  locomotives,  as  well  as  by  the 
natural  economies  resulting  from  heavier  traffic,  so  effectually,  that  in  the 
last  year  but  one  of  the  table  24  per  cent  more  freight  was  moved  with- 
out any  increase  of  engine  mileage. 

3.  The  revulsion  occurred  at  a  time  when  the  general  depression  of 
business  was  not  marked,  when  the  Company  was  not  embarrassed  by 
excessive  obligations  for  new  construction,  and  when  the  falling  off  in 
traffic  and  revenue  was  in  no  respect  panic-like.  Otherwise,  even  as 
sound  a  property  as  this  had  proved  itself  to  be,  had  it  entered  upon 
considerable  expenditure  for  new  construction  or  improvement,  based 
on  a  standard  conforming  to  the  present  large  earning  power  of  the  prop- 
erty as  a  whole  instead  of  the  probable  earning  power  of  the  additions, 
separately  considered,  might  well  have  found  itself  again  a  bankrupt. 

35.  That  such  contingencies  and  fluctuations  are  not  excep- 
tional, is  indicated  by  the  aggregates  of  railway  foreclosures, 
shown  in  Table  5,  which  in  1885  rose  to  the  aggregate  of  2880 
miles  with  $139,658,000  in  bonds  ($48,500  per  mile)  and  $120,- 
090,000  in  stock  ($41,700  per  mile)  or  $268,213,000  in  all  ($93,136 
per  mile)  the  bonds  alone  probably  representing,  as  is  so  com- 


40       CHAP,   II.— THE  MODERN  RAILWAY  CORPORATION. 


Table  5. 
Railway  Foreclosures. 


Year. 

Miles. 

Capital  Stock. 
I  =  1000. 

Funded  Debt. 
I  =  1000. 

Floating  Debt. 
I  =  1000. 

Total. 

I    =    lOCX). 

1881 

2,617 

668 

1,190 

714 

2,880 

$51,278 

20,751 

24,588 

12,894 

120,090 

$76,645 
23,999 
38,198 
i3,o6l 

139-658 

($10,000?) 

10,074 

2,482 

423 

8,465 

$137,923 
54.824 

65  268 

1882 

1881 

1884 

26.378 
268,213 

1885 

Total,  4  yrs. . . 

8,069 

$229,601 

$291,561 

$31,444 

$552,606 

Per  mile,  average 

$28,455 

$36,135 

$3,897 

$68,487 

Per  mile,  1885 

$41,697 

$48,499 

$2,940 

$93,136 

The  above  is  compiled  from  "  Poor's  Manual,"  1886.  It  is  unquestionably  full  of  errors, 
but  no  authentic  or  complete  figures  exist.  The  genejal  fact  that  the  bonds  and  stocks 
of  bankrupt  lines  run  a  good  deal  higher  than  those  for  solvent  lines  is  clear,  as  the  most 
serious  errors  are  probably  in  the  earlier  years. 

The  Commercial  ajtd  Financial  C/t?-onicle^  in  its  October,  1884,  Investors^  Supple- 
ment presented  a  valuable  table  showing  the  railway  companies  now  in  default  on  pay- 
ment of  interest  on  bonds.  Only  railways  in  the  United  States  are  included,  Mexican 
and  Canadian  lines  being  omitted,  and  only  the  particular  issues  of  bonds  are  taken  on 
which  default  is  made,  although  the  mileage  given  includes  all  operated  by  the  defaulting 
companies.  The  table  includes  all  companies  defaulting  during  the  period  covered,  which 
had  not  resumed  payment  in  full,  and  which  had  not  been  foreclosed  and  reorganized. 
The  totals  are  summed  up  in  the  following  table,  in  which  comparison  is  made  with  the 
defaults  of  1873-76 : 


Mileage. 

Amount  of 
Bonds. 

Total  defaults,  October,  1884 

15,986 

121,592 

13-14 

$315, 28-?, 000 

Entire  railroad  system  of  U.  S. ,  Jan.  i,  1884 

3,455,040,283 
9.12 

Total  defaults.  1873-1876 

74,096 


$783,967,665 
2,175  000  000 

Entire  railroad  system  Tan    i    1876       „ . . . 

Per  cent  of  defaults  to  total 

36.04 

Increase  in  mileage  and  bonds  during  five  years  pre- 
ceding Tan    I    1884     . .                               

39,818 
21,232 

$1,157,249,467 

*636,96o,ooo 

Increase  in  mileage  and  bonds  during  five  years  pre- 
ceding Jan.  I,  1876 

*  Estimated  at  $30,000  per  mile. 


CHAP.   II.— THE  MODERN  RAILWAY  CORPORATION.       4 1 

The  whole  number  of  companies  in  default  in  1884  was  only  42,  against  197  in  the 
former  period.  In  the  former  period  of  defaults,  about  20  companies  out  of  the  total  197 
that  were  embarrassed  were  old  railroads  that  were  well  established  and  once  had  a  pay- 
ing business.  In  the  later  period,  out  of  42  companies  named  in  the  table,  none  can  be 
fairly  said  to  have  had  a  well-established  and  paying  business  on  the  basis  of  their  present 
lines  and  existing  liabilities,  unless  such  companies  as  Erie,  Wabash,  and  Reading  be 
classed  in  that  category. 

On  British  railways,  which  are  subject  to  far  fewer  vicissitudes  than  those  of  the  United 
States,  the  average  dividend  of  4^4  per  cent  is  divided  approximately  as  follows, — United 
States  statistics  from  the  census  of  1880  being  added  for  comparison  : 


United  States. 

British. 

18.8     1 

16. 1  per  cent  pays 

no  dividends. 

i.o  "       "       " 

under  i  per 

cent 

10.2 

4.9  "       "       " 

"     2    " 

"            " 

9.2 

3.2  "       "       " 

"     3   " 

3-1 

7-3  "       "       " 

"     4   " 

2.5 

234  "       "       " 

"     5    " 

5-7 

21.7  "       "       " 

'•     6    ■•■' 

(i            «( 

6.5 

20.0  "       *•       " 

"     7    " 

((           «< 

6.5 

1.0  "       "       " 

"     8   " 

U                      i( 

7-4 

0.4  "       "       " 

U        g      u 

««             (( 

3-4 

0.4  "       "       " 

"   10   " 

3.9 

0.6  "       "       " 

about  15    " 

U                      i( 

While  exact  figures  on  which  to  base  a  judgment  are  not  available,  it  is  not  probable 
that  more  than  one  fourth  of  the  existing  mileage  of  the  United  States  has  escaped  fore- 
closure proceedings  or  default  on  bonds  necessitating  a  receivership.  Many  roads  which 
are  now  among  the  strongest  properties  have  been  through  such  difficulties  several  times 
in  their  earlier  history;  while,  on  the  other  hand,  many  others,  like  the  Denver  &  Rio 
Grande,  Philadelphia  &  Reading,  and  other  strong  properties  whose  future  seemed 
assured,  have  been  overtaken  by  disasters  resulting  in  great  part  from  the  intoxication  of 
long-continued  success.  So  that  the  properties  are  few  indeed — and  those  mainly  the 
ones  which  build  no  new  lines — of  which  it  can  be  predicted  with  any  certainty  that  they 
may  not  become  insolvent  in  the  next  period  of  serious  depression. 


Table  6. 
Estimate  of  Future  Railway  Construction  in  the  United  States. 

[Prepared  by  Edward  Atkinson,  of  Massachusetts,  for  various  groups  of  States  as  described 

on  next  page.! 


Group  of  States. 

Mileagre  still 

needed  from 

Jan.  I,  1881. 

19  years. 

Mileag-e  built 

from  Jan.  i, 

1881,  to  Jan., 

1885. 

4  years. 

Per  cent 

total  estimate 

built  in 

4  years. 

Mileag-e  still 
needed  before 

A.D.   IQOO. 

IS  years. 

Class  I 

Class  II 

36,236 

27,199 

34.472 

9652 

9,888 

8,597 
5.282 
8.351 
2,893 

5,857 

24 
I9i 
24 
30 

59 

27.639 
21,917 
26,121 

6.759 
4.031 

Class  III 

Class  IV 

Class  V 

Totals 

117,447 

30,980 

26.3 

86,467 

42       CHAP.    II.— THE  MODERN  RAILWAY  CORPORATION,. 


monly  the  case,  somewhat  more  than  the  actual  total  expendi- 
ture to  create  the  entire  property.  This  amounts  to  nearly  three 
per  cent  of  the  mileage,  and  over  four  per  cent  of  the  capitalized 
cost  of  the  entire  railway  system  of  the  country,  and  that  too  in 
a  year  which  was  in  no  respect  a  particularly  bad  one  finan- 
cially, as  will  be  seen  from  Table  5,  which  gives  similar  figures 
for  several  years  back. 

36.  The  fact,  illustrated  by  the  history  just  given  of  a  road 
in  tlie  far  West,  that  the  intoxication  of  realized  success  will 
lead  even  prosperous  companies  to  assume  dangerous  and  reck- 
less liabilities,  becomes  especially  important  in  view  of  the  fact 
that  in  the  future  a  large  portion  of  the  new  mileage  will  be 
constructed  by  such  lines.  A  carefully  studied  forecast  of  the 
probable  mileage  to  be  constructed,  by  Mr.  Edward  Atkinson, 
made  in  1881,  and  confirmed  as  a  moderate  and  cautious  esti- 
mate which  will  almost  certainl}^  be  exceeded  by  experience  up 
to  1885,  brings  out  this  fact  clearly,  in  addition  to  having  an  in- 
terest of  its  own,  and  is  given  in  Table  6. 

Description  of  Groups,  Table  5. 

Class  1.  consists  approximately  of  the  ii  States  lying  in  or  on  the  irregular  pentagon 
marked  out  by  Boston,  New  York,  St.  Louis,  Louisville,  Washington — estimated  to  have 
by  1900  07ie  mile  of  railway  pe?-  4  square  miles,  as  now  in  Massachusetts. 

Class  IL  consists  of  the  10  States  lying  immediately  to  the  north,  west,  and  south  of 
Class  L,  stretching  down  the  Atlantic  coast  to  Florida,  estimated  to  have  by  1900  one 
7nile per  8  sq.  7niles,  or  half  of  Class  I. 

Class  in.  includes  11  States  in  the  far  West  and  South,  with  one  mile  per  \6.sq. 
miles,  or  half  of  Class  H. 

Class  IV.  includes  the  5  States  of  Maine,  Nevada,  Colorado,  Oregon,  and  California, 
with  one  mile  per  32  sq.  miles,  or  half  of  Class  III. 

Class  V.  consists  of  Florida,  Dakota,  and  7  other  Territories,  with  one  mile  per  64  sq. 
miles. 

Total  United  States  mileage  when  estimate  was  prepared,  91,778;  estimated  total, 
1890,  209,225  miles.  This  estimate  assumes  an  average  future  construction  for  the  15 
years  after  1885  of  5,764  miles  against  an  average  of  7,745  miles  per  year  for  the  previous 
4  years.     The  estimate  is  almost  certain  to  be  largely  exceeded. 

Table  7. 
Progress  and  Extent  of  the  Railway  System  of  the  World. 

[Revised  from  Mulhall's  "  Dictionary  of  Statistics."] 


Miles  Open. 

Cost  (millions,  $). 

1840 

1850 

1860 

1870 

1880 

1850 

1860 

1870 

1880 

United  States... 
United  Kingdom 

Continent 

Canada,  etc 

2.818 

838 

1,074 

9,021 

6,621 

8,311 

538 

30,635 
10,433 
21,815 
4,228 

52,914 
15,537 
49,320 
12,339 

93,349 
17,945 
86,818 
31,804 

202 

1,166 

652 

34 

1,094 

1,685 

1,730 

243 

2,332 

2,572 

4,320 

860 

5,070 
3,640 
8,690 
2,010 

Total 

4.730 

130,110 

229,916 

2,144 

4,752 

10,084 

19,410 

-,, 

CHAP.   II.— THE  MODERN  RAIIWAY  CORPORATION.       43 


Table  8. 
Railways  of  the  World,  January  i,  1884. 

[From  Prof.  A.  T.  Hadley's  "  Railroad  Transportation,  its  History  and  its  Laws."] 


Miles. 

Capital  Invested. 

Per  Mile. 

140,000 

114,000 

11,600 

3.400 

6,500 

$8,400,000,000 

16,110,000,000 

775,000,000 

240,000,000 

325.000,000 

$60,000 

J^m-Qpe      . 

115,000 

66,000 

Africa.                . 

70.000 

50,000 

275,500 

$25,850,000,000 

$72,200 

Germany 

Great  Britain  and  Ireland 

France 

Russia 

Austria  and  Hungary 

Italy 

Spain 

Sweden  

Belgium 

British  India 

United  States 


Length, 
Jan.  I,  1884. 


22.300 

18,600 

18,500 

15.700 

12.800 

5.900 

5,100 

4.000 

2,600 

10.500 

120,000 


Per  cent 
Increase 

in 
5  years. 


5 
18 

7 
12 

13 
16 

14 

6 

20 

43 


Miles  of 
Road 
to  100 

sq.  miles. 


10.6 
15.2 

9 
o 

5 
5 
2 
2 

23 
o 


Miles  of 

Road  to 

10,000 

inhab. 


Cost 

per 

mile. 

Dollars. 


105,000 

204,000 

128.000 

80,000 

105,000 

92,000 

78,000 

30,000 

132,000 

66,000 

61,000 


Germany  . . . . 
Great  Britain. 

France   

Russia 

Austria. ..... 

Italy 

Spain 

Sweden.  .... 

Belgium 

British  India. 
United  States 


1882 
1882 
1881 
1881 
1882 
1882 
1880 
1S81 
1881 
1883 
1883 


Equipment  per  100  miles. 


Locom.     Pass.  cars.    Freight 


51 
76 
46 
40 
30 
29 
26 
16 
72 
24 
22 


95 
232 
105 
c;o 
62 
88 

77 
36 

139 
65 
21 


1,081 
2.298 
1.207 

775 
716 
510 
468 
401 
1,840 
436 
663 


Pass. 

Moved 
(Millions). 


224 

655 
180 

33 
47 
34 
15 
7 
57 
65 
313 


Tons 

Moved 

(Millions). 


198 

291 

93 

14 

70 

II 

9 

5 

37 

19 

400 


Comparison  with  Table  10  and  others  will  show  that  there  is  considerable  uncertainty 
in  these  figures.  It  should  be  remembered  that  American  rolling-stock  is  much  heavier 
and  larger  than  foreign,  and  that  the  average  distance  over  which  each  passenger  or  ton  is 
moved  is  far  greater. 


44       CHAP.   II  — THE  MODERN  RAILWAY  CORPORATION. 


Table  9. 

Progress  of  American  Railway   Construction  by   Groups   of   States, 

AND  OF  Foreign  Railway  Construction. 


1850 

1855 

1860 

1865 

1870 

1875 

1880 

5,977 
13,865 
2,005 
7,803 
7,008 
21,964 

22,259 

6,582 
5,886 

1885 

Six  New  England  States 

2,508 
2,807 

395 
1,620 

415 
1,256 

20 

3,469 
4,849 
624 
3,294 
1,523 
4,173 

394 

40 
8 

3,660 

5,841 
865 
5,111 
3,726 
8,684 

2,380 

23 

3,834 
7,594 
945 
5,228 
3,901 
9,646 

3,201 

503 
233 

4,494 
9,709 
1,282 
6,094 
5,135 
13,177 

9,506 

1-583 
1,934 

5,638 
12,639 
1,816 
7,047 
6.240 
18,879 

14,903 

3,966 
2,968 

6,310 
16,973 

2,566 
11,127 

9,675 
27,101 

31,527 

13,734 
9,954 

New  York,  New  Jersey,  Penna.. 
Delaware,  Maryland,  W.Virginia 
Virginia,  N.  Ca.,  S.  Ca.,  Ga.,  Fla. 
Alabama,  Miss.,  La.,  Tenn.,  Ky.. 

Ohio,  Michigan,  Indiana,  Illinois. 

Wisconsin,    Minnesota,     Dakota, 
Iowa,  Nebraska,  Kan.,  Mo 

Indian  Ten,  Arkansas,  Texas, Col- 
orado, Wyoming,  Montana 

Pacific  States  and  Territories. . . . 

Total  United  States 

9,021 

18,374 

30,635 

35,085 

52,914 

74,096 

93,349 

128,967 

The  above  was  compiled  from  the  tables  in  various  issues  of  Poor's  "  Manual,"  which 
are  full  of  numerical  errors.     These  have  been  corrected  as  far  as  possible. 

Foreign  Countries. 


1840 

1845 

1850 

1855 

1860 

1865 

1870 

1875 

1880 

1884 

Great  Britain 

France 

838 
271 
340 

2,536 

551 

1,429 

6,621 

1,879 

3-747 

38 

8,335 
3,459 
5,138 
1,218 

10,433 
5,900 
7,212 
2,173 

13,289 
8,477 
9,105 
2,231 

15,537 
10,904 
12,136 
2,679 

16,658 
12,339 
17,317 

4,899 

17,933 
14,839 
20,900 

6,887 

18,851 
19,243 

Germany 

22,812 

Canada 

9,571 

Total  Mileage  of  Railway  Constructed  and  in  Operation  in  the  United 
States,  for  each  Year  from  the  Beginning  of  Railway  Construction. 


1830. 
1840 
1850 
1860. 
1870 
1880. 


0 

1 

2 

3 

4 

5 

6 

7 

8 

23 

95 

229 

380 

633 

1,098 

1,273 

1,497 

1,913 

2,818 

3,535 

4,026 

4,185 

4,377 

4,633 

4,930 

5.598 

5-996 

9,021 

10,982 

12,908 

15.360 

16,720 

18,374 

22,016 

24,503 

26,968 

30,635 

31,286 

32,120 

33,170 

33,908 

35,085 

36,801 

39,250 

42,229 

52,9M 

60,293 

66,171 

70.268 

72,385 

74,096 

76,808 

79,088 

81,717 

93,349 

103,145 

"4,713 

121,454 

I   5-379 

128,967 

2,302 

7.365 
28,789 
46,844 
86,463 


ANNUAL   INCREASE. 


1830. 
1840. 
1850. 
1860. 
1870. 
1880. 


72 

134 

151 

253 

465 

175 

224 

416 

516 

717 

491 

159 

192 

256 

297 

668 

398 

1,656 

1,961 

1,926 

2,452 

1,360 

1,654 

3,642 

2,687 

2,465 

1.846 

651 

834 

1,050 

738 

1,177 

1,716 

2,449 

2,979 

6,070 

7,379 

5,878 

4,097 

2,117 

1,711 

2,712 

2,280 

2,629 

6,876 

9,796 

11,568 

6,741 

3,825 

3,588 

389 
1,369 
1,821 
4,615 
4,746 


CHAP.   II.— THE  MODERN  RAILWAY  CORPORATION.       45 


Table  10. 

Mileage  of  American  and   European  Railways,  with  Total  Cost  of 
Construction  and  Average  Cost  per  Mile. 

[Rearranged  and  recomputed  from  the  Revue  Generale  des  Chemins  de  Fer,  1886.] 


Country. 


Miles. 


Cost. 
Millions. 


Av.  Cost 

Per  Mile. 


Sq.  Miles  per 
Mile  Ry. 


Per  Cent 
Increase, 
One  Year. 


United  Kingdom. 


Belgium 

France 

Germany 

Austro-Hungary . 


Switzerland. 

Spain 

Portugal 

Russia 

Italy 

Holland 

Sweden  ... . 

Denmark 

Norway 


18,864 


16,578 
21,785 
12,603 


1.795 

4.550 

927 

14,226 

5.871 

1,406 

3.975 

926 

970 


$3,895- 


334-45 
2,232.20 
2,248.40 

1,279.80 


442.26 
90.  II 
,382.30 
554-50 
127-34 
59-34* 
37-00 
33-51 


$206,490 


177,420 
134,640 
103,210 


103,000 
97,200 
97,200 
97,168 
94,448 
90,918 
41,563 
39,961 
34,548 


Eng....  4.4 
Scot...  10.3 
Ire 13.0 


6.5 
4.2 
II. I 
9-4 
14.7 
24.0 


Aus . . . 
Hung. 


9.2 

38-3 

37-9 

130-5 

18.5 

9-7 

41.7 

13.0 

127.0 


2.03 
1.29 

2.0I 

1.91 
2.13 
2.05 
2.07 
2.98 
3-12 

3-04 
3.66 
3-30 
4.98 
5-72 
4.86 

3.21 

I.  12 
1.80 

1-97 


Germany  in  detail — 

Prussia 

Bavaria 

Saxony 

Wurtembufg 

Baden 

Alsace-Lorraine 

Other  German  States  .. 


106,361 

12,636 

2,833 

1,434 

968 


3,096 


$12,901.19 

1,309.40 
268'.  39 

149-35 
110.95 
99.70 

310.61 


$121,300 

103,620 
94,728 
104,150 
113,140 
121,880 

100,328 


32-9 

10.2 
9-4 
4-4 
8.4 
7.0 


3-07 

2.13 
1.76 
2.36 
2.24 
1.95 

1.96 


Total  Germany 

Minor  European  Countries- 

Bosnia  and  Hertzegovina 

Bulgaria 

Finland 

Greece 

Luxemburg 

Roumania 

Turkey 


21,785 

Kilos. 

370 

222 

1,181 

22 

366 

1,503 

1,173 


4.837 


(some  3,000 


miles). 


87.0 
179.0 
196.0 
1800.0 
4-4 
53  9 
III. 5 


5-14 
14-55 
2.92 
147.00 
0.97 
5-73 
7-54 


*  There  is  an  error  in  this  sum,  which  should  be  about  $100,000,000  greater — 150.66. 

The  last  three  columns  are  taken  (converting  metric  into  English  units)  from  the 
Statisque  des  Chemins  de  Per  de  r Europe,  1882.     Vienna,  1885. 

According  to  other,  and  perhaps  more  authentic  figures,  the  railways  of  Great  Britain 
have  cost  $205,842  per  mile  of  road  ;  the  Belgian  State  Railways,  $123,986 ;  for  the  French 
railways,  $124,642  ;  for  the  German  State  Railways,  $105,204;  the  German  private  roads, 
$71,877;  the  Austro-Hungarian  roads,  $104,420.  The  cheapest  system  of  Europe  is  the 
State  Railways  of  Finland,  $30,102 ;  the  other  Russian  railways  stand  at  $82,244,  against 
$63,250  per  mile  for  the  railways  of  the  United  States. 

The  whole  cost  of  the  railways  of  the  world  has  been  more  than  $24,000,000,000,  which. 


46       CHAP.    II.— THE  MODERN  RAILWAY  CORPORATION. 

however,  is  only  about  $24  per  inhabitant.  In  this  country  the  expenditure  has  been 
about  $133  per  inhabitant;  in  Great  Britain,  $107;  in  Germany,  $47;  in  France,  $57;  in 
Austria-Hungary,  $33;  in  Italy,  $19;  in  Belgium,  $41;  in  Sweden,  $25;  in  Spain,  $29; 
in  Russia,  $14 ;  in  Canada,  $89. 

In  France  and  Germany  railways  pay  about  5  per  cent  on  the  capital  invested,  as  an 
average  ;  in  Great  Britain,  4  to  41^  ;  in  all  Europe  and  in  the  United  States,  about  4  per 
cent. 

Table  11. 

Extreme  Fluctuations  in  Price  of  the  Stocks  of  Various  Companies 
OF  Great  Natural  Strength. 
The  lowest  points  in  times  of  depression  (distinguished  by  an  1)  and  the  highest  price 
in  times  of  activity  (distinguished  by  an  h)  are  alone  noted,  except  that  in  the  last  column 
is  given  the  price  in  November,  1886.  The  list  has  been  selected  almost  at  random, 
regardless  of  their  actual  financial  status,  to  include  the  more  prominent  companies  which, 
from  the  nature  of  their  traffic  or  other  strategic  advantages,  might  naturally  be  expected 
to  be  (as  for  the  most  part  they  are)  least  subject  to  erratic  fluctuations  of  value. 


Company. 


New  York  Central 

Erie   

Pennsylvania 

Baltimore  &  Ohio 

Central  of  New  Jersey. . . 

Boston  &  Albany 

Lake  Shore 

Michig^an  Central 

Canada  So 

Pittsburg  &  Ft.  Wayne. . . 

Chicago  &  Alton 

Ch.,  Burlington  &  Q 

Ch.,  Milw.  &  St.  P 

Ch.  &  N.  Western 

Ch.,  Rocklsl.  &P 

111.  Central 

Atchison, Topeka  &  St.  F. 
Denver  &  Rio  Grande — 

Central  Pacific 

Union  Pacific 

Louisville  &  Nashv 

New  York,  N.  H.  &  Hartf . 
No.  Pacific 


1878.      1879.     1880.      1881.      1882.      1883.     1884.     1885.     1886. 


I103M 
17% 


I75 
1  129 

158^ 
I38 
I85 
166% 

1271^ 
132^ 
198% 

l72-% 


I61H 
I35 
I153M 


181% 


I16 


11155% 


I96 


I1204 
h     ■ 


1152% 
1 11 14034 
'I1210 
I1112 
hi75^ 
I1135M 
111303^ 

h  go 
h.  142 
I1156 
111823^ 
h i2o34 
I1136 


hi  463^ 

52% 

16i^hii3M 

1  63         llI02% 

h  174        1  79 
11190 


11150% 


11150^ 


liioo% 
I168 
h54% 


1263^ 


16834 
hi85 


1119:^ 
1  118 
1  107 


18i^ 


liio 

159^ 


I28 


81% 
19^ 

191^ 

I165 

I31 

I169 

150% 

l46>^ 
1  23 
h  142 

I1140 
11138^ 
164% 


I105 
h.140 
h89^ 
14% 
1263^ 
h  62% 
1  22 
11204 
I131M 


114% 


197 

0634 

96 

64% 
145 
1433^ 
1403^ 

95 
120 
128 

i33J^ 
96 

33H 

m 


^9H 


The  above  extremes  are  in  many  cases  brought  about  temporarily  only  by  the  machi- 
nations of  speculators.  In  many  cases  permanent  changes  in  the  nature  of  the  company 
have  also  had  great  influence.  On  the  other  hand,  these  fluctuations  of  stock  are  far  less 
than  the  fluctuations  in  the  productiveness  for  the  time  being  of  the  properties  represented 
by  them,  for  the  price  of  a  stock — neglecting  the  mere  momentary  fluctuations  of  a  few 
points  forced  for  the  sake  of  a  "  turn"— is,  at  the  most,  merely  this  :  It  is  the  speculators' 
estimate  of  what  permanent  investors  feel  for  the  time  being  to  be  the  permanent  aver- 
age value  of  the  stock.  For  there  are  always  large  holders  who  keep  in  mind  the  average 
value  of  the  property  during  good  times  and  bad  times  alike,  and  who  will  buy  or  sell  in 
quantities  large  enough  to  immediately  affect  the  price  if  they  think  it  is  falHng  below 
the  present  worth  of  its  future  chances,  all  uncertainties  included. 


CHAP.  II.— THE  MODERN  RAILWAY  CORPORATION.       47 

Table  12. 
Rolling  Stock  Per  Mile  in  the  United  States  and  British  Colonies, 


Name  of  Railway. 


New  England  States,  1883 

Middle  States,  1S83 

Southern  States,  1S83 

Western  States,  1883 

Pacific  States,  1883 

Canadian  Pacific,  1885 

Intercolonial  of  Can., Halifax  to  Quebec,  1884 

Indian,  5  feet  6  inches  gauge 

India,  metre  gauge,  1884 

Ceylon  Government,  1883 

Mauritius  Government,  1884 

Queensland  Government,  1882 

New  South  Wales  Government,  18S1 

Victorian  Government,  1882 

South  Australia  Government,  1881 

New  Zealand  Government,  1883 

The  Cape  Government,  1882 

Average  of  totals   


Per  100  Miles  of  Railway  Open. 


Loco- 

Passenger 

Freight 

motives. 

Cars. 

Cars. 

28.76 

48.31 

635-9 

41-93 

45.34 

1714-5 

13-32 

12.06 

283.2 

16.23 

13-74 

483-4 

9-63 

12.06 

191. 8 

10.9 

10. 1 

276.2' 

19.2 

28.4 

513-3' 

27.2 

66.5 

512.2 

20.4 

69.2 

369-7 

31.8 

95-6 

296.1 

40.9 

131-8 

500.5' 

7-9^ 

II. 6 

112. 8 

23-4 

53-2 

487.1 

16.8 

33-6 

2QI.6 

13.6^ 

22.1 

344-9 

15.0 

42.7 

453-2 

23-4 

41.2 

374-8 

19.86 


590-5 


1  Only  partially  open  for  traffic.  2  Opened  about  1876. 

3  Freight  traffic  heavy  during  crop  season.  ^ 

4  Report  states,  "  We  have  been  extremely  short  of  engines  all  through  the  year." 

5  Report  states  that  more  locomotives  are  required. 

Condensed  from  a  paper  on  "The  Laying-out,  Construction,  and  Equipment  of  Rail- 
ways in  Newly-Developed  Countries,"  by  James  Robert  Mosse,  M.  Inst.  C.E.,  in  Trans- 
actio7is  Inst.  C.E.,  1886.     See  also  Table  8. 


CHAPTER   III. 

THE     NATURE     AND     CAUSES     CONNECTED     WITH     LOCATION     WHICH 
MODIFY    THE    VOLUME    OF    RAILWAY    REVENUE. 

37.  With  the  invention  of  the  railway  began  a  new  industry 
— the  MANUFACTURE  OF  TRANSPORTATION.  Transportation,  in- 
deed, existed  before  its  invention,  just  as  cotton  cloth  existed 
before  the  invention  of  modern  machinery,  but  it  was  in  each  case 
mainly  produced  on  a  small  scale  by  each  consumer  for  his  own 
use  and  his  immediate  neighbors'.  With  the  invention  of  the 
railway  first  began  the  manufacture  of  transportation  for  sale  on 
a  large  scale  and  by  modern  processes. 

38.  A  railway  corporation  such  as  has  been  just  considered 
— the  typical  modern  corporation — exists  for  this  purpose.  It 
finds  itself,  on  completion  of  its  works,  in  possession  of  a  certain 
piece  of  improved  real  estate,  of  certain  buildings  and  fixed 
machinery  (the  track),  and  of  certain  tools  and  machines  (the 
rolling-stock)  for  the  manufacture  of  its  commodities,  together 
with  certain  establishments  (the  locomotives  and  car-shops)  for 
the  maintenance  and  repair  of  its  machine-tools,  which  the  extent 
of  its  business  requires.  In  many  instances  it  has  not  a  dollar's 
worth  of  ownership  interest  in  all  this  costly  plant,  excepting  a 
portion  of  the  minor  machinery,  but  simply  controls  it  at,  in  ef- 
fect, a  fixed  rental  (interest  and  other  fixed  charges).  All  that  it 
really  owns  is,  commonly,  a  portion  of  the  business  or  franchise  ; 
and  this  latter  has  likewise  been  hypothecated,  or  pledged,  in 
the  mortgage  bonds  as  security  for  the  payment  of  its  rent 
charges.  As  this  business  has,  from  the  nature  of  railway  busi- 
ness, assurance  of  always  amounting  to  a  certain  minimum  at 
least,  this  franchise  alone  has  a  value  as  security  which  no  ordi- 
narv  business  would  have,  and  in  a  rapidly  growing  country  its 


CHAP.    III.— CAUSES  MODIFYING  VOLUME   OF  REVENUE.   49 

existence  enables  all  or  nearly  all  of  the  actual  cost  of  the  entire 
premises  and  plant  to  be  borrowed,  or  rented,  from  others. 

On  the  premises  so  rented,  the  corporation  carries  on,  for  its 
own  benefit,  the  business  of  manufacturing  and  selling  transpor- 
tation, so  to  speak,  at  wholesale  and  retail,  in  lots  to  suit  the 
purchasers.  Since  it  owns  the  business  only,  and  has,  as  a  cor- 
porate body,  no  interest  or  ownership  in  the  property  itself,  it 
will  be  clear,  and  should  be  fully  realized,  that  all  its  interests 
are  limited  to  the  narrow  debatable  ground  which  lies  between 
doing  the  best  possible  and  doing  the  worst  possible  with  the 
property  in  hand,  which  is  in  all  ordinary  cases  simply  lent  to 
them  for  an  annual  consideration. 

39.  Now,  continuing  the  parallel,  which  will  perhaps  help  to 
enforce  the  truths  required,  and  referring  only  to  sales  of  trans- 
portation, or  revenue  :  if  a  manufacturing  compan}^  in  such  cir- 
cumstances should,  in  planning  its  works,  so  plan  them  as  to  cut 
itself  off  from  disposing  of  certain  lines  of  goods  which  it  manu- 
factures, or  should  place  its  retailing  establishments  (stations)  at 
inconvenient  points,  it  is  clear  that  it  would  have  seriously  hand- 
icapped itself,  even  if,  perchance,  justifiably.  This  a  railway 
company  does  when,  b}^  failing  to  run  close  to  any  accessible 
towns,  it  is  prevented  from  furnishing  them  with  transportation, 
or  is  so  far  away  that  sales  are  inconvenient.  If  it  strives  to 
shorten  its  line  it  is,  for  certain  parts  of  its  traffic,  trying  to  sell 
\^^^  yards  of  its  goods,  at  a  certain  ^v\ce  per  yard,  in  order  to  save 
the  cost  of  its  manufacture  ;  forgetting  that  by  the  same  act  it 
also  loses  the  selling  price  and  hence  the  profit  on  them.  If,  on 
the  contrary,  it  builds  an  over-long,  or  crooked,  or  otherwise 
objectionable  line,  it  is  in  effect  fitting  itself  to  produce  only  an 
inferior  article,  which  will  command  a  lower  price. 

40.  The  force  of  this  parallel  is  still  further  and  greatly 
strengthened  if  we  remember  that,  with  much  that  is  similar, 
there  is,  in  one  respect,  a  momentous  and  broad  distinction 
between  the  seller  of  transportation  and  the  seller  of  most  other 
commodities.  The  production  or  partial  production  of  trans- 
portation is,  from  the  necessity  of  the   business,  considerably  in 

4 


50   CHAP.   III.— CAUSES  MODIFYING  VOLUME   OF  REVENUE. 


excess  of  the  amount  sold,  and  its  cost  bears  a  very  irregular 
ratio  thereto.  Every  time,  for  example,  a  passenger  train  starts 
out,  there  is  "manufactured,"  so  to  speak,  several  hundred  pas- 
senger trips.  If  they  be  not  sold,  they  cannot  be  stored  away  on 
the  shelf  for  the  next  day's  trade,  like  the  remnants  of  a  lot  of 
dry-goods.  They  are  simply  wasted  and  thrown  away.  It  is 
with  the  railway  much  as  if  tradesmen  were  compelled  to  cut  a 
new  piece  of  each  kind  of  goods  each  day  and  then  throw  away 
the  part  remaining  unsold  each  night.  We  should  probably 
under  such  circumstances  observe  a  conspicuously  greater  zeal 
even  than  now  exists  for  regulating  and  increasing  sales,  so  as 
to  sell  the  whole  of  every  piece  of  goods  ;  whatever  price  the 
remnants  might  bring  being  so  much  clear  gain. 

41.  To  a  greater  or  less  degree,  but  always  to  a  very  impor- 
tant degree,  the  conditions  here  suggested  exist  with  respect  to 
every  part  and  kind  of  railway  traffic.  We  see,  therefore,  how 
vital  and  peculiar  is  the  interest  of  railways  in  neglecting  no 
consideration  which  by  ever  so  little  affects  its  revenue.  It  is 
on  slight  differences  of  traffic  and  revenue  that  the  corporation 
grows  rich  or  poor. 

Granting,  therefore,  that  no  probable  effect  upon  traffic  and 
revenue  which  may  or  can  occur  from  the  decisions  reached  in 
the  original  location  should  be  neglected,  it  will  be  obvious,  as 
already  hinted,  that  such  effects  are  possible  from  any  one  of  the 
following  causes  : 

42.  I.  The  Length  of  the  Line. — Even  slight  variations 
therein  are  very  certain  to  affect  the  revenue,  as  well  as  the 
expenses  ;  because  all  local  rates,  except  by  special  contract,  are 
nominally  fixed  by  the  mile,  and  all  through  rates  (those  shared 
in  by  two  or  more  companies)  are,  without  exception,  divided 
according  to  distance  hauled,  although  not  necessarily  in  exact 
ratio  thereto. 

Up  to  a  certain  point,  therefore,  varying  in  almost  every  case, 
the  gross  revenue  certainly,  and  the  net  revenue  frequently,  will 
be  increased  by  a  longer  line,  as  well  as  the  operating  expenses. 
But  if  the  process  be  carried  too  far,  the  traffic  will  be  overbur- 


CHAP.   III.— CAUSES  MODIFYING  VOLUME   OF  REVENUE.    5 1 

dened,  discouraged,  and  decreased.  The  questions  thus  raised 
will  be  separately  discussed  in  Chapter  VII.,  on  Distance.  It  is 
one  of  extreme  importance. 

Such  effects  on  revenue  may  also  occur  from — 

2.  The  comparative  weight  allowed  to  securing  way 
TRAFFIC,  the  quantity  which  may  be  expected,  and  the  sacrifices 
which  may  or  must  be  made  to  reach  certain  additional  traffic 
points.     Also, 

3.  Allied  to  the  latter,  is  the  question  of  how  near  to  run 

TO    CITIES,    towns,     AND    OTHER     SOURCES    OF     TRAFFIC,    which    are 

already  upon  the  line,  and  how  much  the  traffic  and  revenue  will 
be  thereby  affected. 

4.  Still  other  similar  questions  arise  in  connection  with 
BRANCH  LINES  :  whether  to  build  a  branch  at  all,  or  take  the 
main  line  through  the  given  point ;  whether,  if  a  branch  be  de- 
cided on,  the  connection  should  be  made  at  this  or  that  point, 
there  being  often  much  choice,  and  the  decision  governed  by 
commercial  considerations  to  an  unusual  extent,  or  at  least  by 
very  different  laws  from  those  which  might  govern  the  laying 
out  of  lortger  lines,  owing  to  the  shortness  and  isolation  of  most 
branches. 

5.  All  of  these  questions  together  arise  on  a  grand  scale  in 
the  laying  out  of  great  systems  of  railway  at  once  or  in  the 
connection  of  a  number  of  isolated  lines  into  a  single  system,  as 
happens  with  increasing  frequency  in  modern  times. 

In  a  certain  sense,  indeed,  every  line,  even  nominally  inde- 
pendent, and  no  matter  how  short,  is  a  part  not  only  of  one  but 
perhaps  of  several  great  systems  of  roads.  On  this  account,  and 
because  of  the  great  importance  of  the  questions  which  arise  in 
connection  with  the  laying  out  of  branch  lines  and  systems,  a 
separate  chapter  (XXI.)  is  devoted  hereafter  to — not  a  general 
discussion,  for  that  is  impossible — but  to  the  presentation  of 
certain  suggestions  intended  to  illustrate  the  laws  which  govern 
their  solution.  Much  of  the  chapter  referred  to  has  likewise  a 
direct  bearing  on  the  remainder  of  this  chapter. 

43«  It  is  unfortunate   that  the  very  great  and  often  decisive 


52    CHAP.   III.— CAUSES  MODIFYING  VOLUME  OF  REVENUE. 

effect  which  differences  of  location  may  have  upon  the  revenue 
of  railways  is  not  susceptible  of  more  exact  analysis,  for  it  is- 
very  often,  in  properly  conducted  work,  a  consideration  of  such 
importance  as  to  sink  differences  of  engineering  details  into 
insignifieance.  The  most  that  can  be  done  is  to  lay  down  with 
all  possible  care  the  general  principles  which  govern  this  effect, 
with  the  caution  that  the  very  difficulty  of  determining  exactly 
what  weight  shold  be  given  to  it  creates  too  great  a  tendency  to 
neglect  it  altogether. 

44.  The  traffic  of  railways  is  often  spoken  and  thought  of 
as  for  the  most  part  a  monopoly.  In  a  certain  sense,  of  a  cer- 
tain small  part  of  its  traffic,  this  is  true,  as  already  noted,  to  the 
extent  that  there  is  a  certain  fraction  of  the  traffic  of  all  railways 
which  no  folly  can  destroy  or  throw  away.  But  in  a  larger  sense, 
the  traffic  of  any  and  all  railways  is  only  to  a  very  limited  ex- 
tent a  monopoly  of  such  nature  that  to  secure  it  the  Company 
has  nothing  more  to  do  than  to  put  up  its  buildings,  and  station 
a  man  at  the  receipt  of  customs.  The  selling  of  transportion  is 
governed  to  a  very  large  extent,  whether  there  be  nominal  com- 
petition or  not,  by  the  same  laws  which  govern  the  selling  of 
any  other  commodity;  and  these  laws  require  that  the  railway 
company,  like  any  one  else  with  something  to  sell,  shall  consult 
the  convenience,  and  even  sometimes  the  unreasonable  whims,. 
of  the  buyer,  if  it  would  sell  its  goods  to  him. 

45.  For  only  a  small  proportion  of  the  traffic  of  any  railways 
is  in  the  strict  sense  of  the  term  necessary  traffic,  which  must 
come  to  it  anyway,  under  all  circumstances.  The  amount  of 
such  traffic  is  measured,  when  a  railway  system  is  first  coming 
into  existence,  by  the  stage-coach  travel  as  respects  passenger 
business,  and  by  the  carting  on  the  common  roads  as  respects 
freight  business.  Under  the  stimulus  which  the  bare  existence 
of  any  kind  of  railway  facilities  gives  to  the  development  of  any 
country,  the  volume  of  this  strictly  necessary  travel  is  no  doubt 
increased  many-fold.  Nevertheless  no  railway  is  so  prosperous 
and  so  favorably  situated  that  it  would  not,  in  literal  truth, 
starve  to  death  on  it.     The  traffic  would  be  so  very  greatly  de- 


CHAP.   II L— CAUSES  MODIFYING  VOLUME   OF  REVENUE.    53 

■creased  that  on  most  lines  it  would  not  be  possible  to  run  the 
trains  at  all.  Neglecting  altogether  the  traffic  which,  as  respects 
any  one  company,  is  not  necessary,  because  it  has  a  choice  of 
routes,  and  one  line  has  to  fight  for  it  with  others,  a  very  large 
proportion  of  the  business  of  the  railway  system  as  a  whole  is 
made  up,  as  respects  passenger  business,  not  only  of  pleasure 
travel  pure  and  simple,  but  of  travel  which  is  more  or  less  a  mat- 
ter of  whim  or  of  fancied  or  partial  necessity;  and  even  as  respects 
freight  business,  of  freight  which  will  not  be  shipped  except  un- 
der reasonably  favorable  circumstances,  especially  by  any  one 
route,  or  shipped  only  at  a  lower  rate  :  so  that  the  rates  must  be 
solely  fixed,  not  by  the  cost  of  the  service,  but  by  the  price  it 
will  bear  without  discouraging  traffic. 

46.  It  will  be  evident  therefore  that,  since  we  have  already 
seen  the  vital  importance  to  railways  of  making  the  largest 
possible  sales  of  their  wares,  and  since  a  large  part  of  their 
sales  are  of  such  nature  that  they  may  be  easily  discouraged  and 
prevented,  any  failure  to  facilitate  traffic  to  the  utmost  is  a  se- 
rious matter.  The  question  of  encouraging  or  discouraging 
traffic  by  the  facilities  offered  will  depend  in  the  main,  no  doubt, 
upon  the  manner  of  operating  the  road  after  it  has  opened;  yet 
in  one  respect  at  least  (postponing  for  the  present,  as  noted,  the 
discussion  of  the  first,  fourth,  and  fifth  considerations  above)  it 
is  possible  in  the  beginning  to  ^^xiOM'^Xy  and  permanefitly  ^^^oX 
the  future  traffic  of  the  line  :  viz.,  by  going  on  the  principle, 
which  has  often  been  followed  in  the  practice,  that  "  if  the  rail- 
way DOES  NOT    GO    TO    THE    TRAFFIC,  THE    TRAFFIC  WILL    COME    TO 

THE  RAILV/AY."  This  argument  is  sometimes  gravely  advanced 
in  support  of  the  plea  that  it  is  of  no  particular  importance 
whether  the  line  pass  through  a  town  or  a  mile  or  two  off 
from  it,  because  in  either  case  the  line  will  get  "  all  the  business 
there  is."  From  the  very  fact  that  there  is  a  grain  of  truth  in 
this  plea  lending  a  certain  support  to  that  cheapest  of  all 
ways  of  saving  money, — and  perhaps  saving  a  little  distance 
and  curvature  at  the  same  time, — keeping  the  line  off  all  land 
which  is  worth  any  considerable  price,  it  is  important  that   it 


54   CHAP.   III.— CAUSES  MODIFYING  VOLUME   OF  REVENUE, 

should  be  fully  realized  why  it  is  a  dangerous  and  fallacious 
argument. 

47.  It  is  particularly  easy  to  see  that  the  argument  is  both 
dangerous  and  fallacious  when  there  is,  or  is  liable  to  be,  com- 
petition for  the  traffic,  or  any  part  of  it,  as  may  be  said  to  be 
always  the  case,  at  least  potentially,  in  the  United  States.  In  that 
case,  the  only  safe  rule  is,  that  any  considerable  difference  in  haul 
to  the  station  or  in  any  other  convenience  to  the  public  will  al- 
most wholly  destroy  the  possibility  of  profit  from  the  traffic  to  be 
competed  for,  even  if  a  portion  be  secured.  For  it  might  be 
proved  by  many  instances  that  it  requires  but  a  very  slight  dif- 
ference in  the  convenience  of  access  to  practically  destroy  all 
equality  of  competition.  Except  for  the  very  numerous  in- 
stances of  entire  neglect  of  this  danger  it  would  hardly  seem 
necessary  to  speak  of  the  matter  at  all  ;  for  it  is  evident  that,  as 
respects  freight  traffic,  rates  must  in  the  long-run  be  made 
equal,  not  simply  from  station  to  station,  hwl  from  the  door  of  the 
consignor  to  the  door  of  the  consignee :  in  other  words,  all  additional 
cost  for  cartage  or  switching  service,  and  something  more  as 
compensation  for  the  trouble  (usually  a  very  considerable  addi- 
tion), must  be  borne  by  the  railway  before  it  is  in  a  position  to 
compete  at  all.  As  respects  passenger  traffic,  to  a  certain  class 
ot  long-trip  travel  such  minor  differences  are  of  less  importance, 
but  there  is  a  considerable  fraction  even  of  long-trip  travel  on 
which  they  have  a  recognized  and  important  influence  ;  and  de- 
vices of  all  kinds — free  omnibuses,  more  or  less  open  concessions 
on  rates,  etc.,  etc. — are  required  to  counteract  what  may  have 
been  a  mere  oversight,  or  bit  of  indifferent  negligence,  in  the 
original  laying  out  of  the  line. 

48-  Let  us  imagine  an  instance  which  has  frequently  hap- 
pened already,  and  still  more  frequently  will  happen  :  A  num- 
ber of  good-sized  towns,  ten  to  fifty  miles  apart,  served  by 
two  competmg  lines  ;  one  of  them  coming  appreciably  nearer 
to  the  average  centre  of  population  than  the  other.  It  is  abun- 
dantly established  by  experience  that  m  such  a  case  the  favored 
line  can  by  a  moderate  amount  of  effort — which  may  be  counted 


CHAP,   III.— CAUSES  MODIFYING  VOLUME   OF  REVENUE.    55 

on  with  some  certainty — not  simply  cripple,  but  almost  destroy, 
its  rival's  local  traffic.  For  "  to  him  that  hath  shall  be  given," 
with  short-hand  traffic  especially.  If  one  line  start  with  any  ad- 
vantage, that  very  fact  will  tend  to  increase  it.  It  will  have  a 
better  reputation.  It  can  offer  better  facilities.  The  tendency 
of  the  traffic  of  all  kinds  will  be  to  concentrate  itself  upon  it — 
just  as  water  always  seeks  the  level  point,  however  little  lower  it 
may  be.  Even  when  a  railway  can,  or  thinks  it  can,  count  on 
permanent  immunity  from  competition,  it  should  naturally  fol- 
low from  what  has  proceeded  that  it  is  still  exceedingly  dangerous 
to  put  the  public  to  permanent  inconvenience  and  expense  under 
the  false  idea  that  "  it  will  cost  the  Company  nothing."  Under 
the  best  of  circumstances  there  will  always  be  some  loss;  and  the 
slighest  addition  to  receipts,  which  might  have  been  secured  but 
is  not,  would  have  gone  almost  in  gross  to  swell  the  surplus. 
The  slight  additional  trouble  and  expense  to  shippers  of  all 
freight,  and  the  horse-car  and  cab  fares  of  passengers,  must  be 
paid  for  sooner  or  later,  in  one  form  or  another,  by  the  corpora- 
tion, if  in  no  other  form  than  in  a  decrease  of  traffic.  It  is  not 
true  that  nothing  which  will  still  leave  rates  at  so  much  a  mile, 
without  immediately  affecting  them  at  this  or  that  non-competi- 
tive point,  is  of  importance  to  the  Company  or  has  effect  upon 
its  revenue. 

49.  The  universal  law  of  trade  ultimately  obtains  with  sales 
of  transportation  as  of  everything  else.  The  selling  price,  the 
amount  sold,  and  the  profit  realized  on  all  articles  of  bargain 
and  sale  is  ultimately  regulated  by  the  quality  of  the  article  and 
the  price  the  consumer  is  willing  and  able  to  pay,  and  this  again 
is  greatly  affected  even  by  trifling  differences  of  convenience. 
We  may  see  this  illustrated  every  day  by  the  difference  in  price 
of  the  same  article.at  fashionable  and  unfashionable  stores  ;  and 
even  when  there  is  but  one  point  at  w^hich  a  certain  desired  ar- 
ticle can  be  bought,  it  is  a  truth  universally  admitted  among 
business  men  that  minute  differences  in  the  price  or  the  quality 
of  the  article,  or  in  convenience  of  access  to  the  place  of  sale,  do 
have  a   material  influence  on   the  volume  of  sales,  especially  if 


56    CHAP.   III.— CAUSES  MODIFYING  VOLUME   OF  REVENUE. 

such  articles  as  are  to  be  sold  in  great  numbers  to  the  general 
public.  That  precisely  the  same  argument  applies  to  railways 
can  be  denied  only  by  asserting  that  the  patronage  of  a  railway 
is  strictly  a  matter  of  necessity — a  pure  monopoly,  except  as 
competed  for  by  another  railway  ;  but  this,  even  if  it  were  true 
of  the  greater  portion  of  traffic,  would  certainly  not  be  true  at  all 
of  the  remaining  fraction,  and  it  is  ordinarily  this  remaining 
fraction  which  alone  makes  the  business  of  operating  the  prop- 
erty worth  carrying  on  by  the  company  controlling  it  :  for  let  us 
suppose  that  by  systematic  negligence  at  several  points  in  the 
original  laying  out  of  a  line  a  corporation  should  succeed  in  af- 
fecting its  gross  yearly  revenue  so  much  as  one  per  cent.  It 
would  represent  certainly  five  to  ten  per  cent,  and  very  possibly 
one  hundred  per  cent,  of  the  value  of  the  franchise  owned  by  the 
corporation,  which  is  usually  all  they  do  own,  and  sometimes  a 
good  deal  more. 

50.  If  it  should  seem  improbable  that  any  possible  error  of 
this  kind  could  so  affect  revenue,  it  must  be  admitted  that  it  is 
difficult  and  in  fact  impossible  to  produce  statistical  proof,  nor 
would  such  proof,  even  if  produced  for  one  locality,  be  applicable 
elsewhere;  but  a  striking  example,  among  many,  of  the  natural 
effect  of  such  reckless  neglect  may  be  found  at  the  town  of 
Springfield,  Ohio.  A  dispute  about  a  trifling  sum  (about 
$50,000)  of  town  aid  to  the  Atlantic  &  Great  Western  Railway, 
now  the  New  York,  Pennsylvania  &  Ohio  Railroad,  caused  the 
manager  of  the  road  to  run  the  line  two  or  three  miles  from  the 
town — and  this  with  a  slight  increase,  if  anything,  in  the  dis- 
tance, curvature,  and  cost.  This  town  has  since  become,  as  even 
then  was  probable,  one  of  the  best  shipping  points  in  the  State; 
and,  purely  in  consequence  of  its  inconvenient  location,  the 
Atlantic  &  Great  Western  secures  only  an  inconsiderable  frac- 
tion of  this  traffic,  both  freight  and  passenger.  Its  annual  loss 
of  net  revenue  is,  beyond  all  question,  considerably  larger  than 
the  whole  sum  originally  in  dispute;  and  the  disadvantage  was 
so  serious  that,  very  recently,  arrangements  to  run  into  the 
town  over  another  line  were  made  at  heavy  cost,  while  still 
leaving  the  line  at  an  immense  disadvantage. 


CHAP.   III.— CAUSES  MODIFYING  VOIUME   OF  REVENUE.    5/ 

51.  In  this  occurrence  there  is  nothing  exceptional,  even  in 
degree.  There  is  hardly  a  town  of  any  importance  in  the 
United  States  in  which  some  one  of  the  lines  running  to  it  has 
not  done  precisely  the  same  thing  ;  so  that  it  is  known  of  all 
men  to  be  at  grave  disadvantage  in  respect  to  some  portion  of 
its  natural  traffic,  whether  long-haul  and  short-haul,  and 
whether  passenger  and  freight.  That  natural  and  not  unreason- 
able trait  of  human  nature  embodied  in  the  homely  proverb, 
"  Give  a  dog  a  bad  name  and  hang  him,"  then  comes  in  to  inten- 
sify this  disadvantage.  This  in  turn  begets  a  poverty  of  means, 
which  begets  a  poverty  of  service,  which  still  further  increases, 
and  justifies  on  rational  grounds,  what  may  have  been  in  the 
beginning  a  rather  unreasonable  popular  prejudice;  and  the  end, 
in  all  probability,  is  a  receivership.  It  will  be  found,  on  looking 
over  a  list  of  roads  which  have  failed  in  this  way,  that,  almost 
without  exception,  they  are  those  which  merely  skirt  the  edges  of 
the  towns  which  they  nominally  reach. 

52.  The  effect  on  short-haul  traffic  of  negligence  of 
this  kind  is,  as  already  hinted,  far  more  serious  proportionally 
than  in  the  case  of  longer  haul — not  only  because  it  is  far  more 
likely  to  drive  the  traffic  to  other  lines,  when  such  exist,  but  be- 
cause it  is  far  more  likely  to  have  the  still  further  effect  of  de- 
stroying a  portion  of  the  potential  traffic  completely.  The 
longer  the  journey  or  the  haul,  evidently,  the  less  effect  will  any 
trifling  inconveniences  have,  and  the  proportional  as  well  as  ab- 
solute loss  will  naturally  be  less  at  small  towns  than  large  ones — 
especially  than  at  very  large  ones  where  there  is  a  regular  and 
established  suburban  traffic.  Nevertheless  no  town  is  so  small 
that  the  short-haul  local  traffic  is  not  materially  affected  by  tri- 
fling difference  of  convenience  of  access.  Differences  which 
■originate  in  the  subsequent  management  of  the  operating  de- 
partment, better  cars,  time,  meals,  train  employees,  surer  con- 
nections, etc.,  may  have,  it  has  been  admitted,  relatively  much 
more  effect  than  a  mere  difference  in  convenience  of  access  to 
the  station;  but  the  latter,  unlike  the  former,  cannot  be  cor- 
rected at  any  time,  and  in  trips  of  ten  to  twenty  or  fifty  or  even 


58    CHAP.   III.— CAUSES  MODIFYING  VOLUME   OF  REVENUE. 

one  hundred  miles,  the  mere  fact  that  the  station  is  (or  is  not) 
convenient  for  taking  and  leaving  the  train  is  alone  enough  to 
have  a  powerful  influence  upon  the  number  of  such  trips,  es- 
pecially in  bad  weather,  but  to  an  important  extent  in  all 
weather,  with  the  weaker  three  quarters  of  the  population  at 
least. 

53.  In  very  much  less  degree  even  the  volume  of  non-com- 
petitive FREIGHT  SHIPMENTS  is  similarly  affected;  besides  the 
fact  that  it  must  be  assumed,  for  reasons  already  stated,  that  the 
rates,  in  the  long-run  and  in  some  direct  or  indirect  form,  will 
certainly  be  affected  likewise.  Sooner  or  later,  in  one  form  or 
another,  the  railway  will  be  compelled  to  make  concessions 
equivalent  to  paying  for  the  cost  and  annoyance  of  cartage  on 
much  of  its  traffic,  and  lose  altogether  more  than  enough  to  pay 
for  carting  the  whole  of  it.  There  is  no  clearer  moral  than  this 
to  be  drawn  from  recent  railway  history. 

54.  It  is  also  unmistakably  evident  from  recent  history  that  it 
is  impossible  to  maintain  more  than  a  reasonable  ratio  of  dispro- 
portion in  rates  between  competitive  and  non-competitive  rates, 
and  between  rates  on  one  class  of  freight  and  another,  even  for 
those  classes  of  freight  which  do  not  seem  to  be  affected  by  any 
immediate  cause  tending  to  have  this  effect.  A  clear  indication 
of  the  existence  of  this  law  may  be  found  in  Tables  93-5.  It  is 
now  too  well  known  and  generally  admitted  to  require  more  pre- 
cise evidence. 

55.  There  is  one  peculiar  phase  of  the  question  of  running  by 
A  TOWN  TO  SAVE  DISTANCE  which  may  be  more  appropriately  con- 
sidered in  this  connection,  as  illustrating  what  has  preceded, 
than  in  the  chapter  on  Distance. 

Let  us  suppose,  to  take  definite  figures,  that  we  have  run  by  a 
town  of  ten  thousand  inhabitants  in  order  to  save  a  deviation  of 
five  miles  from  an  air  line,  involving  a  loss  of  a  mile  or  two  of 
distance.  As  we  have  already  seen  in  part,  and  shall  more  fully 
see  (Chap.  VII.),  the  railway's  revenue  account  suffers  heavy  loss 
due  to  the  decreased  mileage  on  .most  of  its  local  and  through 
business,  competitive  and  non-competitive.     Per  contra^  its  ex- 


CHAP.   III.— CAUSES  MODIFYING  VOLUME   OF  REVENUE.    59 

pense  account  is  decreased  indeed,  but  in  very  much  less  ratio. 
The  probabilities  are  very  strong  that  there  will  be  a  net  loss  to 
the  revenue.  This  might  well  be  borne  if  it  meant,  as  in  ordi- 
nary cases,  simply  a  reduction  of  the  transportation  tax  upon 
the  traveller  or  shipper  of  freight,  but  how  stands  it  with  the 
latter?  They  save,  indeed  (in  the  case  of  local  traffic  only,  but 
not  in  the  case  of  through  traffic),  the  two  or  three  cents  per 
mile  which  the  railway  loses,  owing  to  its  shorter  line  ;  but  they 
lose  the  entire  direct  cost  of  cartage  or  switching  charges  on 
their  freight  and  carriage,  express  or  horse-car  fares  for  their 
own  conveyance,  besides  suffering  an  annoyance  and  inconveni- 
ence in  both  cases  which  they  will  surely  estimate  at  a  good 
round  sum:  In  money,  when  by  the  existence  of  competition  they 
are  able  to  throw  the  whole  of  both  of  these  losses  on  the  rail- 
way which  seeks  their  patronage  from  a  distance  ;  in  refusal  of 
patronage,  except  under  great  concessions  or  the  compulsion  of 
necessity,  when  through  absence  of  competition  they  cannot 
otherwise  shift  the  burden  from  their  own  shoulders. 

Thus,  under  any  possible  conditions,  in  such  a  case  there  is  a 
triple  loss:  The  tax  on  the  public  is  greater,  the  receipts  of  the 
railway  are  less  per  passenger  or  ton,  and  the  number  of  pas- 
sengers or  tons  is  decreased. 

66.  The  net  losses  might  be  estimated  something  in  this  way, 
assuming  the  town,  say,  to  be  in  Ohio : 

Loss  TO  THE  Railway. 

Loss  of  traffic  per  head,  by  being  5  miles  instead  of  i  from  centre  of 
population  (say  40  per  cent :  Table  13),  on  a  natural  revenue  per 
head  of  $10,  or  $100,000  from  the  town $40,000 

Loss  of  revenue,  due  to  one-mile  haul  on  $60,000  of  traffic — say  three 

per  cent i ,  800 

$41,800 
Per  contra  :  saving  of  expense  on  same,  at  40  per  cent  on  the  total  ex- 
penses, or  26f  (40  X  f)  per  cent  on  the  total  revenue ii,i4S 

Net  loss  to  railway $30,652 


60   CHAP.   IIL^CAUSES  MODIFYING  VOLUME   OF  REVENUE. 

Loss  TO  THE  Individual  Patrons. 

Expenses  of  reaching  the  railway  from  a  point  5  miles  off,  at  50  cents 

per  passenger  or  ton,  probably  about $25,000 

Less  saving  by  reduced  payments  to  the  railway,  as  above 1,800 

Net  loss  to  the  public $23, 200 

Destroyed  business,  which  the  public  would  have  been  glad  to  enjoy 
and  pay  for,  as  shown  by  experience,  and  which  hence  would  have 
been  worth  its  cost  to  them — say  one  third  of  the  40  per  cent  (as 
above)  of  $100,000,  the  rest  going  to  some  other  line 13,300 

Net  loss  special  to  the  public,  per  year $36,500 

Net  loss  special  to  the  railway,  per  year 30,652 

Aggregate  loss  to  the  community,  per  year $67,152 

Which  means  from  the  point  of  view  of  political  economy, 
and  as  a  plain  statement  of  a  fact  which  would  appear  in  the 
census  statistics,  that  the  capital  of  the  country  and  the  world 
is  less  than  it  otherwise  would  be  by  the  capital  sum  of  which 
$67,152  represents  the  interest,  or  (at  six  per  cent)  $1,119,200; 
the  whole  of  which  is  clear  loss,  by  which  no  one  is  benefited. 

57.  A  few  hackmen  and  expressmen  are,  indeed,  diverted 
from  working  elsewhere,  where  they  would  be  true  producers, 
into  earning  a  support  by  performing  what  might  have  been  a 
needless  service.  It  is  plain  that  by  this  diversion  they  are, 
individually,  neither  benefited  nor  injured,  so  that  they  simply 
do  not  enter  into  the  question  at  all,  even  from  the  point  of  view 
of  political  economy.  We  are  not,  however,  studying  political 
economy,  but  the  art  of  directing  private  investment  in  railway 
property  so  as  to  be  profitable,  not  primarily  to  the  general 
public,  but  to  the  projectors. 

Making  all  allowances  for  possible  errors  in  the  precise  fig- 
ures used  above,  it  represents  an  immense  loss  to  all  parties  from 
running  railways  by  towns  without  going  to  them,  so  far  as  the 
traffic  of  that  town  alone  is  concerned,  separately  considered. 
There  is,  however,  this  further  disadvantage  to  be  remembered  : 
if  we  lengthen   the  line  to  reach  a  town  we  necessitate  that  the 


CHAP.   III.— CAUSES  MODIFYING  VOLUME   OF  REVENUE.   6r 

whole  traffic  shall  be  hauled  over  this  extra  distance  in  order  to 
accommodate  the  traffic  of  one  town. 

58.  This  raises  the  general  question  of  the  value  of  distance, 
for  which  see  Chapter  VII.  It  need  only  be  premised  here,  what 
has  been  in  fact  already  said,  that  although,  as  a  mere  question 
of  political  economy,  the  cost  of  this  extra  haul  is  certainly  a  net 
loss,  conferring  no  added  value  on  the  service  rendered,  yet  to 
the  revenues  of  the  railway  only,  considered  as  a  private  enter- 
prise for  profit,  this  is  by  no  means  the  case,  since  there  is  always 
a  credit  as  well  as  a  debit  side  to  the  extra  haul.  It  is  not 
uncomimon  to  hear  engineers  speak  and  act,  indeed,  as  if  the 
extra  haul  were  a  mere  burden  on  the  traffic  :  which  would  be 
true  enough  if  railways  were  charitable  institutions  built  by 
moneyed  philanthropists  with  the  sole  purpose  of  serving  the 
public,  and  which  is  always  true  with  respect  to  that  consider- 
able fraction  of  traffic  on  which  neither  the  amount  nor  the  dis- 
tribution of  the  gross  rate  is  modified  by  the  distance.  But,  as 
matters  actually  stand,  it  may  be  rudely  stated  here  that,  as  the 
actual  cost  of  such  trifling  extra  haul  is  very  little,  the  net  effect 
of  such  deviation  for  such  a  purpose  is  ver)''  apt  to  have  a  favor- 
able effect,  if  any  (sometimes  a  decidedly  favorable  effect),  upon 
the  net  revenue  derived  from  the  entire  traffic,  independent  of 
that  from  the  particular  point  for  the  sake  of  which  the  devia- 
tion was  made,  as  well  as  upon  the  public  interest. 

For  one  most  important  reason  why  this  should  be  so,  see  Chapter  XXI. 

59.  It  is  true  that,  in  so  far  as  the  burden  upon  the  general 
traffic  may  be  increased,  there  is  a  tendency  to  compel  the  cor- 
poration to  reduce  rates  on  all  traffic  to  the  point  which  it  will 
bear,  instead  of  making  non-competitive  rates  strictly  according 
to  distance  ;  and  in  urging  that  a  railway  will  "get  something 
for  nothing"  out  of  extra  haul,  the  previous  claim  (par.  46  et seq.) 
may  seem  to  be  contradicted,  that  even  slight  burdens  on  traffic 
are  dangerous;  but  it  is  evidently  a  very  different  matter  for  a 
railway  to  take  measures  which  make  its  own  charges  on  all 
traffic   a   trifle   higher  to  relieve   a    part  of  it   from    other   and 


62    CHAP.   III.— CAUSES  MODIFYING  VOLUME   OF  REVENUE. 

heavier  burdens,  and  to  take  a  course  which  throws  a  heavy 
burden  on  its  own  traffic  and  on  its  patrons  as  well,  by  provid- 
ing facilities  for  a  lot  of  outside  parties — teamsters,  hackmen, 
and  horse-car  lines — to  extract  a  percentage  forever  of  the  total 
payments  which  the  traffic  has  to  bear. 

60.  Admitting,  therefore,  that  differences  of  location  may 
have  a  material  effect  on  the  revenue,  it  becomes  important  to 
remember  that,  as  we  have  already  seen,  as  small  a  difference  as 
one  per  cent  in  gross  revenue  will  ordinarily  represent  from 
three  to  six  per  cent  in  net  revenue,  and  from  six  to  twelve  or 
fifteen  per  cent  difference  in  profits  to  the  company  proper,  after 
their  rental  or  interest  charges  have  been  met,  even  in  the  most 
prosperous  companies,  and  from  that  up  to  many  hundred  per 
cent  in  those  less  favored.  Remembering  also  that  errors  in  the 
original  laying  out  of  the  line,  unlike  errors  in  subsequent  man- 
agement, are  mainly  irremediable, — a  kind  of  fixed  charge  for 
folly  forever, — it  will  be  seen  how  large  is  the  interest  of  the 
company  who  employ  and  pay  the  engineer  in  avoiding  all  errors 
of  the  kind,  and  how  particularly  important  it  is  that  no  possible 
difference  should  be  regarded  as  trifling  because  it  will  consti- 
tute a  trifling  part  of  the  total  receipts  or  expenses.  It  is  only 
a  small  fraction  of  that  total  which  ''the  company"  has  even  the 
hope  of  retaining  to  itself. 

When  the  cream  of  their  traffic,  the  profit  traffic,  is  lost 
to  them,  all  is  lost  ;  and  although  it  is  often  true  that  the  busi- 
ness sagacity,  or  lack  of  it,  with  which  the  enterprise  as  a  whole 
has  been  planned  will  overcome  all  that  the  engineer  can  do  to 
make  or  mar  it,  so  that  the  enterprise  will  succeed  or  fail  in  spite 
of  him,  yet  it  is  always  true  that  a  heavy  percentage  of  the 
surplus  or  deficit  which  alone  concerns  the  company  proper — - 
enough,  for  instance,  to  make  all  the  difference  betvv^een  a  great 
success  and  a  small  success,  or  a  great  failure  and  a  small  failure 
— is  strictly  dependent  upon  the  engineer  and  upon  those,  by 
whatever  name  they  may  be  called,  who  decide  with  him,  or  for 
him,  the  semi-engineering  and  semi-commercial  questions  which 
we  have  here  considered. 


CHAP.   III.— CAUSES  MODIFYING  VOLUME   OF  REVENUE.   63 

61.  Therefore,  with  an  end  so  important  before  us,  any  guide 
is  better  than  none,  in  order  that  we  may  reduce  the  unavoida- 
ble uncertainty  to  its  lowest  terms  ;  and  under  these  circum- 
stances a  rule  which  the  writer  has  formulated  as  a  sort  of  gen- 
eral average  to  estimate  exceptions  from  is  this  : 

As  A  MINIMUM  :  At  the  smallest  aiid  most  inert  non- competitive 
points  the  annual  loss  of  revenue  from  placing  the  station  at  a  distance 
from  town  may  be  taken  as  equivalent  to  10  per  cent  of  the  revenue  nat- 
urally originating  from  such  a  town,  with  the  station  in  any  given  loca- 
tion, for  each  additional  mile  that  the  station  is  moved  off  from  the 
centre  of  the  town. 

As  A  MAXIMUM  :  At  centres  of  considerable  manufacturing  or  com- 
mercial activity,  exposed  to  considerable  actual  or  potential  co??ipetition, 
a  fair  and  moderate  estimate  of  the  probable  loss  of  revenue  from  re- 
moving the  station  to  a  distance  will  be  2^  per  cent  of  the  revenue 
naturally  origi?iating  at  such  a  town,  for  each  additional  mile  that  the 
station  is  moved  off  fro7?i  the  centre  of  the  town  ;  and  this  is  frequently 
liable,  in  cases  of  very  sharp  competition,  to  amount  to  as  much  as  ^o 
per  cent  of  the  natural  revenue,  including  all  the  indirect  effects  of  such 
disadvantages. 

The  first  of  these  estimates  the  writer  has  considered  to  be 
applicable  to  such  towns  as  the  average  of  interior  Mexico.  It  is 
below  any  class  of  towns  in  the  United  States  or  Canada,  ex- 
cepting the  strictly  rural  regions  consuming  and  producing  little 
freight  shipped  by  rail.  The  last  is  a  fair  average  (varying  how- 
ever within  wide  extremes)  of  all  the  busier  towns  and  cities  of 
the  United  States. 

62.  The  causes  of  variations  are  : 

1.  Manufacturing  and  especially  mining  towns  are  usually 
heavy  shippers. 

2.  Towns  which  are  the  seats  of  special  industries  often  make 
payments  to  railways  out  of  all  proportion  to  their  apparent  size 
and  activity. 

3.  The  number  of  competing  lines  will  greatly  affect  the  pro- 
portion tributar}^  to  any  one  line. 

And  many  other  like  causes.     Nothing   definite  can  be  pre- 


64   CHAP.   III.— CAUSES  MODIFYING  VOLUME   OF  REVENUE. 

dieted  about  any  one  town  from  any  figures  in  this  chapter,  but 
•for  the  average  town  they  are  believed  to  be  fair. 

They  are  the  result  of  much  comparison  of  earnings  by  dif- 
ferent lines  at  large  and  small  towns  made  by  the  writer  at  dif- 
ferent times,  with  an  effort  to  estimate  the  true  cause  of  their 
disadvantages  ;  but  to  attempt  to  defend  them  in  detail,  except 
as  the  volume  as  a  whole  may  do  so,  would  occupy  too  much  space. 


Table  13. 

Estimated  Effect  on  Revenue  of  Removing  Stations  from  the  Centre 
OF  Population  of  Towns, 


Minimum. 
lo  per  cent  per  mile. 

Ordinary  Maximum, 
25  per  cent  per  mile. 

Miles. 

Difference. 
Per  cent. 

Per  cent. 

Difference. 
Per  cent. 

Per  cent. 

O 

100. 0 
90.0 
81.0 

72.9 
65.6 

59-0 
53-1 
47-8 
43 -o 
38.7 
34-9 

25.0 

18.75 
14.06 

10.55 
7.91 

5-94 
4.45 
3-34 
2.50 

1.87 

lOO.O 

75-0 

56.25 

42.2 

31-65 

23.74 

17.80 

13-35 

10.01 

7-50 

5.62 

Very  materially 
greater  under  certain 

circumstances, 

especially  with  sharp 

competition,  so  that 

a  difference  of  two  or 

three  miles  often 

means  the  loss  of 

nearly  the  whole 

traffic. 

I 

2    

3 

4 

5 

6 

7 

8 

9 

lO 

10 

9 

8 

7 
6 

5 
5 
4 
4 
3 

0 
0 

I 
3 
6 

9 
3 

8 

3 

8 

Av.   revenue 
per  head 
per  year. 

I  $2.00    to     $3.00 

$8.00     to     $15.00 

Column  I. — Average  distance  of  station  from  centre  of  population. 
Columns  2  and  4.— Loss  per  cent  of  total  natural  revenue  for  each  additional  mile  of 
distance. 

Columns  3  and  5. — Remaining  per  cent  of  natural  revenue  left  to  the  company. 

The  effect  of  this  rule  is  presented  numerically  in  Table  13, 
the  percentages  being  in  geometrical  ratio  to  each  other,  so  that 
any  number  in  the  column,  divided  by  the  first  or  second  or  third 
number  above  it,  gives  always  the  same  quotient. 

Under  this  table,  the  percentage  of  loss  for  each  additional 
mile  the  station  is  moved  away  is  the  same  under  all  circum- 


CHAP.   III.— CAUSES  MODIFYING  VOLUME   OF  REVENUE.    6$ 

Stances,  although  the  absolute  loss  is  much  less  as  the  distance 
increases. 

63.  The  above  rule,  it  should  be  repeated,  is  not  offered  as 
in  any  way  precise,  or  perhaps  even  safe.  Such  an  estimate 
must  always  remain,  for  the  most  part,  a  question  of  judgment. 
That  is  the  author's  judgment.  He  claims  no  more  solid  basis 
for  it  than  that  in  many  single  instances  there  has  been  an  actual 
difference  in  the  receipts  of  competing  lines  at  the  same  point, 
or  in  the  receipts  of  the  same  line  at  points  at  different  distances 
from  it,  but  otherwise  very  similarly  situated,  which  closely  cor- 
respond with  the  figures  given. 

64.  As  example  of  the  working  of  the  abo^  rule,  to  run  two 
miles  off,  instead  of  one,  from  the  centre  of  a  town  of  io,ooo 
people  would  involve  as  a  minimum  a  loss  of  g  per  cent  of  the 
natural  revenue  from  such  a  town,  or  from  $i8oo  to  $2700  per 
year.  If  the  town  were  an  active  business  place  this  might 
easily  be  several  times  this  amount,  and  if  competition  were 
a  factor  of  the  problem  it  would  be  very  certain  to  be.  If 
it  were  a  question  of  running  into  a  town  instead  of  a  mile 
away,  the  loss  would  also  be  liable  to  be  very  much  greater  than 
the  table  above  indicates,  since  the  stimulating  effect  of  better 
transportation  might  change  the  whole  character  of  the  town, 
besides  the  natural  effect  of  a  given  difference  of  distance.  The 
question  would  be  affected  likewise  by  the  character  of  the  ter- 
mini, etc.,  etc. 

65.  As  an  instance  from  actual  practice,  two  important  Mexi- 
can towns,  of  a  population  of  about  100,000  and  60,000  respec- 
tively, and  about  forty  miles  apart,  with  considerable  natural 
traffic  between  them,  were  left  distant  respectively  two  and  a 
half  miles  and  four  and  a  half  miles  from  the  nearest  point  of 
the  projected  line.  It  was  a  question  whether  to  bring  the  rail- 
way nearer  to  the  town,  in  which  case  both  stations  would  be 
half  a  mile  from  the  centre  of  population  : 

If  we  might  assume  the  above  minimum   to  be  correct,  the 
certain  loss  on  all  the  traffic  contributed  to  the  railwa)^  by  these 
5 


66   CHAP.    III.— CAUSES  MODIFYING  VOLUME   OF  REVENUE. 


towns,  and  not  simply  on  the  traffic  between  them,  would  be  an- 
nually— 

$200,000  X  0.09        =  $18,000 
120,000  X  0.344      =    41.280 

Total  ($120  per  day)  $59,280 

For  Mexican  towns,  in  their  present  condition  of  imperfect 
material  development,  this  is  possibly  large  enough;  but  for 
American  towns  of  equal  size  and  importance  it  would  almost 
certainly  be  far  too  low.  If  it  were  to  be  considered  as  solely 
affecting  the  passenger  traffic,  and  of  such  traffic  only  that  exist- 
ing between  the  f  wo  towns,  it  would  amount  to  the  loss  of  sixty- 
five  to  seventy  round  trips  per  day,  and  this  in  the  United  States, 
between  two  active  business  points  at  that  distance  from  each 
other,  would  be  far  from  an  exaggerated  estimate. 

It  would  in  such  a  case,  however,  be  extremely  erroneous  to 
■consider  only  the  traffic  between  the  two  points.  All  the  traffic 
originating  or  terminating  at  each  point  is  more  or  less  affected, 
the  importance  of  the  effect  decreasing  with  the  length  of  the 
haul.  The  freight  traffic  will  also  be  materially  affected,  in  some 
slight  degree  in  volume,  and  a  large  proportion  of  it  in  average 
rates,  for  reasons  already  pointed  out,  the  chief  of  which  is  that 
the  railway  sooner  or  later  pays  for  the  cartage. 

66.  Yet  all  these  arguments,  like  almost  everything  else  con= 
nected  with  the  laws  of  trade,  require  to  be  applied  with  great 
caution,  and  are  subject  to  many  exceptions,  such  as  these  which 
follow  : 

Towns  will  in  many  cases  move  to  the  railway,  if  the  railway 
does  not  come  to  the  town,  with  ultimate  benefit  to  all  parties 
concerned.  This  is  especially  common  and  probable  in  the 
United  States,  but  it  is  more  or  less  true  everywhere.  In  pro- 
portion as  the  population  and  traffic  may  be  expected  to  increase, 
the  importance  of  accommodating  the  line  to  that  which  already 
exists  becomes  less  and  less. 

Even  in  a  region  tolerably  well  settled,  but  heretofore  unde- 
veloped by  railways,  or  imperfectly  developed,  a  bold  neglect  of 


CHAP.   III.— CAUSES  MODIFYING  VOLUME   OF  REVENUE.   6/ 

existing  centres,  especially  those  of  minor  importance,  will  be 
exceedingly  apt  to  bring  them  sooner  or  later  to  the  railway  in- 
siead  of  losing  the  railway  their  traffic;  and  this  will  be  in  some 
cases,  where  other  lines  are  not  likely  to  compete,  the  more  apt 
to  follow  the  more  completely  such  points  are  left  out  in  the 
cold. 

Especially  when,  by  taking  a  central  line  between  two  subor- 
dinate centres  of  this  kind,  about  as  much  will  be  gained  from 
the  one  as  lost  from  the  other,  the  ultimate  effect  will  probably 
be  to  build  up  a  new  town  between  both,  affording  new  traffic, 
while  still  retaining  a  good  proportion  of  that  which  remains 
at  each  of  the  old  centres,  and  could  have  been  fully  secured 
from  one  of  them  only  by  wholly  neglecting  the  other;  thus  sub- 
stantially increasing  the  aggregate  traffic  of  the  line. 

This  amounts  to  saying  that  in  seeking  to  pass  through  the 
centre  of  the  population,  as  in  determining  the  centre  of  gravity, 
we  cannot  always  consider  one  body  alone,  but  must  consider 
several  as  constituting  one  composite  entity. 

67.  So,  too,  it  is  easily  possible,  in  laying  out  branch  lines  or 
the  parts  or  links  of  extended  systems,  to  be  so  over-anxious  to 
secure  some  trifling  advantages  of  local  traffic  as  to  seriously 
burden  and  cripple  other  and  much  more  important  interests,  or 
perhaps  lay  the  line  open  in  the  future  to  destructive  competi- 
tion. 

These  various  possibilities — co7i  as  well  2iS  pro — are  very  fre- 
quently the  most  important  of  those  which  fix  or  should  fix  the 
location  of  a  line.  Especially  in  easy  country  it  may  almost  be 
said  to  be  the  rule  that  these  will  be  important  enough  to  over- 
rule engineering  disadvantages  of  considerable  moment,  the  ex- 
tent of  which  latter,  therefore,  it  will  often  be  waste  of  time  to 
consider  ;  and  even  in  the  most  difficult  country  it  will  usually 
require  marked  and  decided  engineering  disadvantages  to  justly 
overbalance  any  considerable  advantages  as  respects  probable 
traffic  and  revenue. 

68.  The  question  of  the  location  of  termini,  and  its  effect 
upon  traffic,  is  really  closely  allied  to,  and  in  fact  a  part  of  the 


68    CHAP.   III.— CAUSES  MODIFYING  VOLUME   OF  REVENUE. 

general  question  of  how  near  to  bring  the  line  to  towns^  which 
we  have  just  been  discussing.  Nevertheless,  from  the  fact  that 
the  terminal  towns  are  usually  by  far  the  most  important  on  the 
line  and  likewise  the  most  costly  points  to  approach  closely,  sound 
business  judgment  is  violated  more  frequently  and  more  danger- 
ously at  such  points  than  at  points  along  the  line.  Had  it 
not  so  often  happened  that  lines  which  have  expended  mil- 
lions for  the  construction  of  long  lines  to  a  certain  place  have 
then  begrudged  or  failed  to  raise  the  necessary  additional  per- 
centage to  carry  their  line  into  it,  contenting  themselves  with 
hanging  on  to  the  skirts  of  the  town  somewhere,  where  they  can 
be  reached  by  horse-cars  or  hacks  and  drays,  it  would  seem  in- 
credible that  business  corporations  could  so  frequently  commit 
an  act  of  folly  which  can  fairly  be  paralleled  with  that  of  build- 
ing a  long  bridge  and  erecting  every  span  but  one — assuming, 
on  account  of  some  difficulty  with  foundations,  or  what  not,  that 
a  ferry  would  be  good  enough  for  that,  because  it  would  be 
"such  a  little  one."  The  lines  which  do  or  have  pursued  this 
course  will  be  found  to  be  those  which  figure  most  prominently 
in  the  list  of  bankrupt  corporations  ;  and  the  evidence  of  that 
fact  is  so  patent  to  any  one  who  will  take  a  list  of  such  and  study 
it  over,  that  it  is  needless  to  add  more  to  what  has  been  already 
said  than  to  note  the  great  sums  which  successful  properties  spend 
in  reaching  the  heart  of  great  cities  to  remedy  former  errors. 

69.  In  England  hundreds  of  millions  have  been  expended  for 
this  purpose,  and  tens  of  millions  at  the  smaller  towns  alone.  In 
America  we  are  far  more  backward  than  the  best  interest  of  the 
properties  requires  :  but  many  such  works  have  been  recently 
carried  through,  one  example  of  which  is  the  new  entrance  of  the 
Pennsylvania  Railroad  into  the  city  of  Philadelphia  ;  while  at 
New  York,  Boston,  St.  Louis,  and  other  cities  similar  improve- 
ments have  been  made  or  are  being  projected  on  a  lavish  scale. 
Certainly  it  has  never  been  questioned  that  the  Philadelphia  ter- 
minus was  an  expedient  investment,  and  we  may  be  sure  that  it 
was  not  undertaken  with  any  other  view  by  the  management  of 
the  company.     It  was  executed  almost  wholly  for  the  local  con- 


CHAP,   III. —CAUSES  MODIFYING  VOLUME   OF  REVENUE.   69 

venience  of  Philadelphia,  and  consisted  in  carrying  in  the  com- 
pany's tracks  on  an  elevated  structure  to  a  point  very  near  to 
the  centre  of  the  city.  It  was,  moreover,  an  expenditure  to  which 
the  company  was  not  driven  by  competition,  except  as  to  a  small 
part  of  their  traffic,  for  they  had  good  facilities  for  both  freight 
and  passengers  ;  facilities  as  conveniently  accessible  as  they  well 
could  be  by  horse-cars — that  ever-ready  excuse  for  neglecting  to 
bring  railway-stations  into  the  centre  of  population.  Some  in- 
crease of  space  was  indeed  desirable,  but  it  might  have  been  se- 
cured much  more  cheaply  in  other  ways,  had  the  company 
deemed  it  expedient. 

The  Philadelphia  improvement  cost  about  $4,590,000,  of 
which  about  half  was  for  land  only  ;  or  about  $5  per  head  of  the 
population  concerned,  the  interest  on  which  at  five  per  cent  is 
about  $225,000  per  annum,  or  twenty-five  cents  for  each  mian, 
woman,  and  child  of  the  population — a  sum  which  should  be 
largely  increased,  perhaps  doubled,  for  the  indirect  loss  on  in- 
vestments already  made,  and  from  operating  expenses  for  haul- 
ing the  whole  traffic  into  and  out  of  the  new  station,  to  which  the 
S5^stem  of  roads  centring  there  had  not  been  originally  adapted. 

It  is  to  be  presumed,  of  course,  that  the  value  of  this  improve- 
ment to  the  corporation  is  expected  to  be  considerably  more 
than  this.  Nor  does  such  expectation  seem  unreasonable  ;  for, 
independent  of  all  necessity  for  competition,  experience  at  other 
points  proves  that  it  w*ould  be  a  paying  investment,  from  its 
direct  and  indirect  effect  to  encourage  new  traffic. 

In  the  company's  report  for  1881  it  was  stated — 

"The  cost  of  this  work  is  already  having  a  marked  effect  on  the  develop- 
ment of  local  traffic  ;  and  it  is  believed  that,  in  addition  to  its  great  value  to 
through  and  competitive  business,  it  will  in  a  few  years,  by  its  promotion  of 
suburban  trains  reaching  the  park  and  other  portions  of  the  city,  and  its 
stimulus  to  the  traffic  before  referred  to,  fully  realize  all  that  was  contemplated 
at  the  time  of  its  original  construction." 

At  the  time  of  this  report  there  were  some  two  hundred  pas- 
senger trains  into  and  out  of  Broad  Street  Station  daily.  There 
are  now  about  fifty  per  cent  more. 


70   CHAP.   III.— CAUSES  MODIFYING  VOLUME   OF  REVENUE, 

70.  At  New  York  a  costly  improvement  was  carried  through 
at  the  joint  expense  of  the  city  and  the  New  York  Central  and 
Hudson  River  Railroad,  costing  some  $8,000,000,  in  order  to  per- 
manently insure  the  running  of  fast  trains  to  the  Grand  Central 
Station  at  Forty-second  Street,  which  will  probably  hereafter  be 
the  heart  of  the  population  patronizing  the  railway,  although  for 
the  present  it  is  rather  far  up-town.  The  then  existing  passen- 
ger station  at  Twenty-eighth  Street  was  abandoned,  in  part  on 
account  of  the  difficulties  and  expense  involved  in  securing  room 
at  that  point  for  the  immense  traffic  to  be  handled,  and  in  carry- 
ing the  line  to  it,  but  in  part  because  the  point  selected  was 
deemed  to  be  so  near  the  future  centre  of  the  city.  An  addi- 
tional passenger  station  (mainly  for  suburban  trains)  is  still 
maintained  on  the  west  side,  at  Thirty-second  Street,  as  are  also 
freight  stations  farther  down-town  on  both  the  east  and  west 
side,  to  and  from  which  cars  are  hauled  by  horses. 

71.  At  St.  Louis,  a  union  depot  for  all  the  railways  centring 
there  was  built  in  connection  with  the  great  St.  Louis  Bridge, 
the  whole  costing  some  $7,000,000;  while  there  is  hardly  a  city 
of  any  importance  where  smaller  improvements  of  the  kind 
are  not  projected  by  some  one  of  the  lines  reaching  it,  at  a 
largely  increased  cost  over  what  would  have  been  originally  nec- 
essary;— without  considering  in  this  statement  the  heavy  losses 
of  traffic  through  the  dubious  early  years  of  the  company's  his- 
tory which  have  enforced  such   improvements.     On    the  other 

.hand,  there  is  no  instance  on  record  where  adequate  terminal 
facilities  once  acquired  have  been  abandoned  for  others  more 
distant  and  less  valuable,  because  the  market  value  of  the  prop- 
erty was  greater  than  its  productive  value  in  the  hands  of  the 
company. 

72.  To  apply  the  same  ratio  of  expenditure  as  is  incurred  at 
the  larger  cities  to  smaller  places  might  not  in  many  cases  be 
safe  for  these  reasons  : 

First.  The  average  receipts  per  head  of  population  increase 
very  much  faster  than  the  population.  (See  Chap.  XXI.,  and  the 
various  tables  giving  revenue  per  head  of  population.) 


CHAP.   III.— CAUSES  MODIFYING  VOLUME   OF  REVENUE,   /I 

Secondly.  At  very  large  cities  like  New  York,  Philadelphia, 
Chicago,  and  Boston,  the  distinctly  suburban  traffic,  making 
daily  trips  at  commutation  rates,  is  a  large  element,  which  espe- 
cially requires  the  best  attainable  terminal  facilities  and  the 
largest  possible  saving  of  time. 

Table  14  gives  some  idea — in  part,  it  must  be  confessed,  a  deceptive  and 
imperfect  one — as  to  how  large  a  part  these  various  works  constitute  of  the 
total  cost  of  railways  of  the  first  class,  and  how  small  an  element  is  the  mere 
construction  to  sub-grade  between  stations.  See  also  Chapter  XXVI.,  on 
"Terminals." 

Table  14. 

Proportion  and  Amount  of  the  Various   Items  of  Cost  of  Road  and 

Equipment. 

New  York  Central  &  Hudson  River  Railroad,  1885,  953  miles  ;  amount  of  track,  2.85  times 
length  of  line  ;  and  in  less  detail  for  Pennsylvania  Railroad,  1257  miles. 


New  York  Central  &  Hudson  River. 

Pennsylvania, 

Items. 

Per 

Mile. 

Per 

Cent. 

Items. 

Per 

Mile. 

Per 
Cent. 

Grading  and  masonry 

Bridge 

Superstructure  

$22,000 

3,030 

32,500 

15,400 

15,740 

6,630 

1,617 

15,830 

3,160 

293 

18.9 

2.6 

27.9 

13-3 

13.6 

5-7 

1.4 

13.6 

2.7 

•3 

Construction 

Equipment 

Real  estate  and  telegraph . . 

Total 

$30,400 
19,300 
10,130 

50.7 
32.3 

Stations,  etc 

$59,830 

100. 0 

Land  and  land-damages — 

Stock  

$75,300 
53,500 

Passenger  cars 

Bonds 

.... 

Floating  Equipment 

The  Pennsylvania  owns  enormous  amounts 
of  the  securities  of  controlled  roads,  repre- 

Total  

$116,200 

100. 0 

sented  by  its  securities.     Its  policy  has  been 

Stock                     

93,800 
59,000 

.... 

to  defray  expenses  out  of  earnings  rather  than 

Bonds 

increase  capital  account. 

The  small  proportion  which  the  bare  cost  of  laying  down  the  track  bears  to  the  total 
investment,  on  lines  of  importance,  is  clear  from  the  above. 

Thirdly.  At  almost  all  points  in  the  United  States  the  proba- 
bilities of  future  growth  must  be  remembered,  which  will  some- 
times, as  at  New  York,  bring  a  point  which  is,  for  the  time  being. 


72    CHAP.   III.— CAUSES  MODIFYING  VOLUME   OF  REVENUE. 

considerably  outside  of  the  centre  of  population  into  the  very 
heart  of  it. 

Nevertheless,  no  town  is  so  small  that  the  considerations 
advanced  are  not  more  or  less  applicable  to  it,  and  the  usual  law 
of  development,  when  topographical  impediments  do  not  forbid 
it,  is  that  the  town  spreads  equally  in  all  directions,  its  centre  of 
gravity  remaining  unchanged,  as  in  the  case  of  London,  and 
measurably  of  Chicago,  Philadelphia,  and  other  cities  ;  in  which 
case  the  disadvantages  of  having  a  terminus  at  a  distance  from 
that  centre  do  not  decrease  with  time,  but  increase  in  direct  ratio 
to  the  population. 

73.  Although  the  impossible  task  of  definite  technical  analysis 
of  the  revenue  considerations  here  discussed  has  been  passed  by, 
it  is  hoped  that  enough  has  been  said  to  impress  upon  the  minds 
of  engineers  and  projectors  that  they  are  entitled  to  great,  if 
somewhat  indeterminate,  weight,  and  that  it  is  unsafe  for  any 
engineer  to  enter  upon  the  work  of  laying  out  a  railway  with  no 
more  thought  of  its  financial  future  than  a  vague  idea  that  the 
passenger  revenue  is  obtained  by  selling  tickets,  and  the  freight 
revenue  is  measured  by  the  sum  of  the  way-bills,  and  that  neither 
is  any  concern  of  his  ;  his  duty  being  simply  to  get  the  shortest, 
clieapest,  and  straightest  line, — the  phrase  has  almost  hardened 
iiuo  a  formula, — and  that  when  he  has  gotten  it  he  has  done  his 
whole  duty.  It  may  be  that  he  has,  but  it  does  not  follow  ;  and 
the  chances  are  good  that  he  will  have  not  only  completely  failed 
to  do  it,  but  will  have  involved  the  projectors  in  certain  ruin  ; 
because,  although  the  amount  by  which  the  revenue  can  be  mod- 
ified by  differences  of  location,  or  even  by  differences  in  the  sub- 
sequent management,  is,  as  a  rule,  only  a  small  percentage  of 
the  aggregate  revenue,  yet  it  is  this  small  percentage  alone  in 
which  the  original  projectors  have  a  property  interest  ;  that  por- 
tion of  the  revenue  which  goes  to  pay  fixed  charges  and  operat- 
ing expenses  being  in  no  sense  theirs. 

The  strength  of  the  argument  for  neglecting  no  effort  to 
reach  all  possible  sources  of  traffic  is  greatly  strengthened  by  the 
considerations  which  it  seemed  more  appropriate   to  discuss  in 


CHAP.   III.— CAUSES  MODIFYING  VOLUME   OF  REVENUE.    73 

Chapter  XXL,  but  which  have  a  very  direct  bearing  on  the  sub- 
ject-matter of  this  chapter. 

74.  That  the  effect  of  comparatively  slight  causes  to  influence 
revenue  has  not  been  exaggerated,  may  perhaps  be  proved,  as 
effectually  as  in  any  way,  by  a  trivial  incident  which  the  writer 
knows  to  be  authentic  : 

A  certain  railway,  for  competitive  reasons,  determined  that 
some  marked  improvement  in  its  eating  stations  must  be  made 
to  meet  the  competition  of  dining-cars  on  a  rival  line.  The  pro- 
prietor of  one  of  these  establishments,  therefore,  was  instructed 
to  make  certain  decided  improvements  in  the  appointments  of 
his  table,  and  in  the  character  and  quality  of  the  viands  provided, 
at  the  expense  of  the  company,  and  to  send  in  his  bills  from 
time  to  time  for  this  additional  expenditure.  The  bills  not  com- 
ing in,  although  the  desired  betterments  had  been  (with  some 
reluctance)  made,  and  with  results  very  gratifying  to  the  com- 
pany, the  proprietor  was  again  requested  to  send  in  his  bills  ; 
when  it  appeared,  on  inquiry  as  to  each  item  in  succession  for 
which  he  had  been  specifically  instructed  to  increase  his  expen- 
diture at  the  expense  of  the  company,  that  the  proprietor  was 
"satisfied  that  it  paid  him,"  or  that  it  was  "no  more  than  he 
ought  to  do,"  or  that  he  was  *'  well  enough  contented  as  it  was" 
— in  short,  that  he  had  no  bills  to  present. 

Such  an  incident,  the  details  of  which  were  precisely  as 
stated,  must  be  admitted  to  be  an  extraordinary  instance  of  the 
power  of  conscience  in  a  class  who- are  not  often  given  credit  for 
having  any,  but  it  is  also  a  proof  that  great  direct  advantages  to 
the  proprietor,  as  well  as  indirect  advantages  to  the  company, 
must  have  resulted.  To  fully  appreciate  its  bearing  upon  those 
semi-technical  questions  which  depend  more  or  less  on  the 
peculiarities  of  human  nature,  two  additional  facts  must  be 
remembered.     On  the  one  hand — 

T.  A  large  fraction  of  the  passengers  have  but  slight  reason 
to  choose  between  one  or  another  railway  before  beginnmg  their 
journey  ;  while,  on  the  other  hand, 

2.  The  journey  once  entered  on,  they  have  no  choice  what- 


74   CHAP.   III.— CAUSES  MODIFYING  VOLUME   OF  REVENUE. 

ever  as  to  where  to  take  their  meals,  but  to  take  such  meals  as 
are  set  before  them  at  the  appointed  stopping-places,  or  go 
hungry.  The  railway  restaurant  business  is  pre-eminently  non- 
competitive. 

If,  therefore,  a  trifling  improvement  in  meals,  which  had  never 
been  really  bad,  could  so  materially  affect  the  non-competitive 
business  of  a  railway  restaurant,  what  is  the  probable  effect  of 
the  same  and  other  slight  causes  on  the  traffic — especially  on  the 
receipts  from  that  considerable  class  who  travel  a  great  deal  by 
rail,  but  hardly  make  a  really  necessary  trip  more  than  two  or 
three  times  in  a  lifetime  ? 

With  this  attempt  to  solve  by  a  parable  an  essentially  inde- 
terminate problem,  we  pass  to  those  branches  of  our  subject 
which  are  often  of  less  real  importance,  but  which  admit  of  more 
definite  and  technical  treatment,  and  which,  perhaps  for  that 
reason,  are,  not  unnaturally,  too  often  the  only  ones  considered 
by  members  of  a  definite  and  technical  profession. 


CHAPTER    IV. 

THE   PROBABLE   VOLUME   OF   TRAFFIC,    AND   LAW    OF   GROWTH 

THEREIN. 

75.  It  having  been  once  determined  that  a  railway  is  to  be 
built  at  all  between  any  two  points,  with  the  consequent /r/;;/^- 
facie  corollary  that,  excepting  when  and  as  reasons  to  the  con- 
trary appear,  it  is  to  be  the  cheapest  line  over  which  trains  can 
be  run  with  due  safety  and  speed,  the  probable  nature  and 
volume  of  the  future  traffic  becomes  the  vital  question  ;  for  both 
the  revenue  and  the  operating  expenses  will  vary  in  close  ratio 
therewith,  and  only  to  increase  the  one  or  diminish  the  other 
are  we  justified  in  expending  more  money  than  proper  security 
in  handling  trains  requires.  The  more  the  traffic  of  a  railway 
the  larger  the  pecuniary  saving  from  a  given  betterment  in  the 
rate  and  distribution  of  gradients,  curvature,  or  distance — and 
the  more,  consequently,  the  justifiable  expenditure  to  effect  it  \ 
the  criterion  being  :  Will  a  certain  betterment,  which  is  not  an 
essential  for  the  safe  passage  of  trains,  save  the  company  more 
per  year  in  operating  expenses  (or  add  more  to  the  revenue,  in 
the  limited  class  of  problems  in  which  that  question  comes  in) 
than  it  will  add  to  fixed  charges  by  the  capital  expended  to  effect 
it?  If  it  will,  the  expenditure  and  betterment  should  be  made  \ 
if  it  will  not,  it  should  not  be  made. 

76.  To  determine  the  probable  volume  of  traffic  with  exactness 
is  of  course  impossible  ;  nor  is  it,  fortunately,  particularly  im- 
portant to  do  so,  if  we  make  a  reasonably  close  approximation  ; 
for  the  reason  elsewhere  discussed,  that,  with  a  judiciously  located 
Ime,  the  saving  by  adopting  a  poorer  line  than  one  naturally 
adapted  to  the  topography  is  ordinarily  not  so   great  that  any 


']6  CHAP.   IV.— PROBABLE  VOLUME   OF   TRAFFIC. 

probable  deficiency  in  the  estimate  of  traffic  would  permit  of  it; 
while,  on  the  other  hand,  the  cost  of  defying  the  natural  topo- 
graphical conditions  is  ordinarily  too  great  for  any  probable 
excess  in  the  estimate  of  traffic  to  permit  of  it  wrongly.  In  other 
words,  the  danger  lies  in  having  no  criterion,  or  in  a  false  per- 
spective as  to  the  relative  importance  of  various  ends,  or  in 
purely  arbitrary  decisions  based  on  no  investigation  whatever, 
rather  than  in  a  certain  percentage  of  error  in  our  criterion. 

All  that  we  need  to  do,  therefore, — all  that  will  have  any 
important  bearing  on  our  action,  as  experience  will  soon  teach, 
—is  to  bring  reasonably  near  to  each  other  the  maximum  and 
minimum  probabilities, — "  the  limits  of  error  in  either  direc- 
tion, somewhere  within  which  lies  the  truth  and  anywhere  out- 
side of  which  lies  a  certainty  of  error."  This  there  is  ordinarily 
no  difficulty  in  doing. 

77,  In  a  rude  way  it  can  be  done  at  once  by  any  one  at  all 
familiar  with  railroad  work.  We  know  at  once  whether  a  line  is 
more  likely  to  have  a  light  local  traffic  or  a  trunk-line  traffic.  It 
is  but  a  step  further  to  determine  with  very  approximate  exact- 
ness that  a  line  will  have  somewhat  more  traffic  than  this  or  that 
or  the  other  line  near  it,  or  similarly  situated  in  other  regions, 
and  less  traffic  than  as  many  others  ;  from  which  the  establish- 
ment of  a  mean  for  the  immediate  traffic  and  its  future  growth 
is,  with  some  knowledge  of  railroad  business,  a  simple  matter. 

78.  The  greatest  difficulty  in  making  such  estimates  is  ordi- 
narily the  fact  that  to  make  them  it  is  essential  to  estimate  and 
allow  for  the  probable  future  growth  of  traffic,  since  it  is  rarely 
the  case  that  a  railway,  especially  in  the  United  States,  is  built 
simply  and  only  to  accommodate  the  traffic  "in  sight,"  as  min- 
ers say.  On  the  contrary,  it  has  been  and  will  continue  to  be 
frequently  the  case  that  the  railway  is  relied  upon  not  only  to 
accommodate  but  to  create  a  great  part  or  the  whole  of  the 
traffic  for  which  it  is  built.  Even  when  the  population  of  the 
region  traversed  cannot,  as  it  can  in  most  parts  of  the  United 
States,  be  expected  to  rapidly  increase,  experience  has  shown 
that  if  the  surrounding  territory  has  heretofore  been  but  scantily 


CHAP.   IV.— PROBABLE  VOLUME   OF   TRAFFIC. 


77 


provided  with  railway  facilities,  (i)  the  traffic  of  the  first  few 
years  will  be  but  a  small  proportion  of  what  would  nominally  be 
expected  from  a  similar  population  elsewhere,  and  (2)   that  it 

Table  14i. 

Earnings  Per  Head  of  Population  and  Per  Mile  of  the  Railways  of 
THE  State  of  Iowa. 


Miles  of  Road. 

Population. 

Gross  Earnings. 

Year. 

Total. 

In- 
crease. 

Actual  or 

Estimated. 

I  =  1000. 

Per  Mile 
of  Road. 

Totals. 

Per  Mile 
Road. 

Per  Head 
Popula- 
tion. 

1862 

626 

653 
727 

27 
74 

778. 
If,. 

1,243 
1,271 
1,212 

2.89 

1863 

1,570,546 
2,553,699 

2,405 
3,512 

1864 

1865 

847 

120 

934- 

1,103 

3,871,783    i       4,572 

4.14 

1866 

1,060 
1,238 
1,448 
2,081 

213 
168 
220 
533 

+  986. 
t  1,038. 
t  1,040. 
t  1,142. 

930 

734 

550 

4,118,006           3,884 

5,867,501           4,778 

8,024,931           5,541 

10,409,950    1       5,002 

1867 

5:S 

9.12 

1868 

1869  

1870 

2,683 

602 

*  I. 194. 320 

445 

11,932,352 

4,447 

10.00 

1871  

3,160 
3^643 
3,728 
3,765 

1 

37 

+  1,231.600 
t  1,270.100 
+  1,309.800 
t  1,350.700 

389 
349 

352 
359 

1872 

1873 

1874 

1875  

3,850 

85 

*  1,393.000 

362 



1876 

3,939 
4,134 
4,157 
4,396 

89 
195 

23 
239 

t  1,436  500 
+  1,481.400 
t  1,527.700 
t  1.575.400 

360 
368 
359 

5-903 
5,587 

1877 

1878 

(24,550,000) 
(24,500,000) 

16.08 

1870 

1880 

4,977 

581 

*  1,624.615 

327 

(27,250,000) 

5,491 

16.80 

1881  

5,426 
6,337 
7,015 
7.249 

449 
911 
678 
234 

t  1,675.400 
t  1,727.7-0 
t  1,781.700 
t  1,837.400 

309 
272 
258 
253 

28,452,181 
32,023,966 
34,433,355 
35,735,272 

5,084 
5,607 
5,386 
5,481 

16.98 
18.54 

1882  .  . 

1883 

1884 

19-35 
19.46 

*  Actual.  t  Estimated. 

The  tendency  of  earnings  to  increase  about  as  the  square  of  the  population  tied  together 
by  convenient  means  of  transportation,  discussed  in  detail  in  Chapter  XXI.,  is  very  con- 
spicuous in  this  and  the  following  table. 


may  be  expected  for  the  first  few  years  to  have  an  abnormally 
rapid  growth.  Table  14  shows  this  clearly.  Even  in  a  com- 
paratively densely  populated  State  like  Massachusetts,  or  in  a 
country  like  England,  which  are  neither  growing  rapidly  in 
population  nor  ill  provided  with  existing  facilities,  experience 
has  shown  (Tables  15  and  16)  that  the  rate  of  growth  is  rapid 
enough  (from   5    to  8   per  cent  per  annum,  as  an  average)   to 


78 


CHAP.   IV.— PROBABLE  VOLUME   OF   TRAFFIC. 


Table  15. 

Earnings  per   Head   of   Population  and  Per  Mile   of   Road    of    the 
Railways  of  Massachusetts. 


Miles  of  Road. 

Population. 

Gross  Earnings. 

Year. 

Total. 

Per 
cent,  in 
Mass. 

Actual  and 

Estimated. 

I  =  1000. 

Per  Mile 
Road. 

Total 
(Thousands). 

Per  Mile 
Road. 

Per  Head 
Popula- 
tion. 

1845 

463 

97 

837- 

1,885 

$2,895 

$6,250 

$3-35 

^6      

622 

715 
787 
945 

96 

95 
94 
93 

882. 
909. 
937- 
965- 

1,542 
1,336 
1,265 
1,096 

3,642 
4,965 
5,406 
5,742 

5,850 
6,950 
6,890 
6,080 

4-23 
5-19 
5-43 

5-54 

Is::::::::::: 

49 

1850 

1,092 

92 

994. 

514 

992 

6,420 

5,890 

5-94 

1,142 
1,150 
1,164 
1,194 

91 

% 

88 

1,016. 
1,038. 
1,060 
1,083 

978 
1,003 
1,013 
1,024 

6,600 
6,886 
7,977 
8,696 

5,770 
5,990 
6,870 
7,300 

5-91 
5-95 
6.70 
7.04 

54 

1855 

1,281 

87 

1,107 

972 

9,077 

7.090 

7. II 

c6          

1,325 
1,351 
1,380 
1,380 

86 
83 

1,130 
1,155 
1,180 
1,205 

960 
972 
973 
993 

9,750 
9,094 
8,597 
9,771 

7,370 
7,360 
6,230 
7,080 

7.42 
6.69 
6.12 

S*::::::::: 

59 

6.75 

i860 

1,371 

82 

I,23i 

066 

1,033 

9,936 

7,260 

6.63 

61 

1,366 
1,386 
1,475 
1.486 

81 
81 
82 
83 

1,252 
1,273 
1,295 

1,317 

1,063 
1,080 
1,042 
1,070 

8,669 
9,655 
11,711 
14,981 

6,340 
6,960 
7,920 
10,100 

5-62 
6.09 
7.21 
9.78 

62 

65  

g ::.. 

1865 

1.500 

83 

1,340 

1,108 

17.459 

11,660 

11.04 

66 

67   

1,550 
1,612 
1,749 
I, .979 

84 

85 
85 

1,362 
1,385 
1,409 
1,433 

1,088 

1,076 

1,023 

930 

19,242 
19,444 
20,788 
22,495 

12,430 
12,100 
11,920 
11,380 

12.16 
12.17 
12  60 

68           

69 

13-35 

1870 

1,475 

1,457 

•351 

988 

13,220 

13.40 

2,098 
2,194 
2,365 
2,418 

1,601 
1,658 
1,735 
1,783 

1,487 
1,517 
1,548 
1,580 

930 
914 
962 
887 

27,186 
30,879 
34,930 
34.000 

12,950 
14,080 
14.800 
14.070 

13-94 
14.30 
15-38 
m.88 

73- •• 

74 

187; 

2,459 

1. 817 

1,612 

895 

31.495 

12,820 

14-35 

76       

2,479 
2,496 
2,492 
2,626 

1,837 
1,855 
1,850 
1,862 

1,645 
1,678 
1,713 
1,747 

896 
903 
927 
941 

29,856 
28,932 
28,003 

29,153 

12,070 
11,620 
11,250 
11,100 

13.48 
12.77 
12.15 
II  80 

78 

1880 

2,667 

1,893 

1,783 

.085 

945 

33,662 

12.640 

13-38 

81 

82               

2,755 
2,778 
2,783 
2,852 

1,928 
1,949 
1,953 
1,974 

1,820 
1,859 
1,897 

1,937 

944 
955 
974 
982 

35-936 
39.094 
41,636 
41,457 

13,070 
14.100 
15,010 
14,560 

13-85 
14.78 
15.40 
14.86 

83 

84 

The  actual  mileage  in  the  State  limits  is  not  given  previously  to  1870,  and  an  assumed 
percentage  has  been  used  to  determine  the  population  and  earnings  per  mile  of  road. 
From  1870  to  1884  the  earnings  per  head  are  computed  by  assuming  that  the  average 
earnings  per  mile  of  road  were  no  greater  inside  than  outside  the  State  limits,  which 
is  certainly  incorrect,  and  on  an  average  will  probably  make  the  earnings  per  head  ten 
to  fifteen  per  cent  too  small.     From  1861  to  1870  inclusive  the  total  earnings  within 


CHAP.   IV,— PROBABLE   VOLUME   OF   TRAFFIC. 


79 


constitute  an  element  which  might  be  legitimately  considered  in 
laying  out  a  new  line.  The  table  embodying  this  English  ex- 
perience is  very  instructive,  as  indicating  a  minimum  of  growth 
under  settled  conditions  which  no  large  section  of  this  country  is 
likely  to  fall  below  for  many  decades. 

In  all  but  the  rarest  instances,  it  would  be  absurd  to  claim 
that  no  allowance  should  be  made  for  future  growth  of  traffic, 
and  often  it  should  be  a  very  large  one.  Nevertheless,  while, 
theoretically,  large  allowances  for  this  future  traffic  are  almost 

Table  16. 
Growth  of  English  Railways  and  Railway  Traffic. 


Year. 

Miles. 

Capital. 

No.  of 

Double 
or  more. 

Single. 

Total. 

Total. 
I  =  $1,000,000. 

Per  Mile. 

1  =  $1000. 

Passengers. 
Millions. 

1855 

6,153 
6,690 

7,7" 
8,338 
8,898 
9,803 
10,239 

2,182 
3,743 
6,143 
7,038 
7,760 
8,130 
8,62s 

8,335 
10.433 
13,854 
15,376 
16,658 

17,933 
18,864 

1446. 
1692. 
2213-. 

2574- 
3061. 
3537- 
3892. 

173-4 
164.0 
166.6 
165.7 
183.8 
197.2 
206.1 

118  6 

I860 

163.4 
251.9 

336.5 
507.0 
603.9 
695.0 

1865 

1870 

1875 

1880 

1884 

Receipts. 

Per  Cent 
Oper- 
ating 

Expenses. 

Per  Cent. 
Net 

Year. 

Total. 
Millions. 

Per  Mile 
of  Road. 

Per 
Train 
xMile. 

Per  Cent  from— 

Receipts 
to 

Pass. 

Freight. 

Capital. 

1855 

104.6 
134.8 
174.4 
210.8 
286.3 
306.0 
328.8 

12,530 
12,930 
13,120 
13,570 
17,200 
17,040 
17,440 

cts. 
140.6 

131.5 
125.0 
124.4 

136.5 
127.2 
121. 3 

49-7 
47.1 
46.2 
42.8 
42.0 
41.5 
42.6 

so. 3 
50.9 
53-8 
53.5 
54-3 
54.6 
53-4 

47 
48 
48 
54 
51 
53 

I860 

1865 

4.19 
4.11 

1870 

1875 

1880 

4.38 
4.16 

1884 

Compiled  from  the  Board  of  Trade  returns. 


the  State  were  given  separately.  Previously  to  1861,  the  total  earnings  divided  by  the 
population  of  the  State  was  multiplied  by  the  assumed  per  cent  of  mileage  within  the 
State  limits  for  the  earnings  per  head.  The  compilation  for  the  years  preceding  1871  was 
abstracted  from  an  old  volume  of  the  Railway  Times. 

See  also  Tables  21  to  26,  83,  and  various  others  for  indications  as  to  growth  of  traffic. 


8o 


CHAP,   IV.— PROBABLE  VOLUME   OF   TRAFFIC, 


always  justifiable,  it  is  for  practical  reasons  so  exceedingly  dan^ 
gerous  as  to  amount  to  absolute  folly  for  an  average  American 
corporation,  even  of  the  more  prosperous  kind,  to  look  ahead  for 
more  than  from  three  to — at  most — ten  years  for  the  ''  rapidly 
increasing  traffic"  which  is  to  justify  an  increase  of  present 
expenditure  over  what  the  prospects  of  the  present  and  the  im- 
mediate future  will  justify. 

79.  Let  us  see  why  this  is  so.  The  theory  of  the  subject  is 
simple:  In  Table  i8  is  given  the  present  value  or  present  justi- 
fiable expenditure  to  save  $i  (or  one  unit  of  any  other  value) 
at  the  end  of  any  given  period  at  any  given  rate  of  interest;  that 
is  to  say,  the  sum  which,  if  placed  at  compound  interest  now, 
will  produce  $i  at  the  end  of  the  specified  period.  This  fact 
given,  it  logically  follows,  that  if  the  value  of  a  given  betterment 
for  a  given  immediate  traffic  be  $i,  the  present  value  of  the 
same  betterment  for  an  equal  traffic  which  is  to  exist  only  in  the 
future  will  be  that  sum  which  at  compound  interest  will  produce 
%\  when  the  assumed  traffic  comes  to  exist.  If,  for  example, 
we  expect  the  traffic  to  double  in  ten  years,  we  may  spend  for  a 
betterment  worth  %\  to  the  present  traffic,  $i  +  the  sum  which 
will  produce  $i  at  the  end  of  ten  years,  which  latter  is  at  7  per 
cent  (Table  18)  50.8  cents;  so  that  under  these  conditions  (which 
would  apply  to  most  new  American  lines)  we  should  be  war- 
ranted in  spending  50.8  per  cent  more  money  to  effect  given, 
betterments  than  we  would  for  the  traffic  "in  sight." 

Table  17. 


Value  of  $t 

PLACED  AT  Compound  Interest  for  a  Term  of  Years. 

With  Interest  at— 

Years. 

3 

per  cent. 

3^ 

percent. 

per  cent. 

4 
per  cent. 

5 

per  cent. 

6 

per  cent. 

8 

per  cent. 

10 

per  cent. 

I 
2 
3 
4 

7 
8 
9 

\2 

1.09 

1. 13 
1.16 
1. 19 

1.23 
1.27 
1.30 

\2 

1. 10 

1. 14 
1. 18 
1.22 

1.26 
1.30 
1-34 

1.03 
1.07 
I. II 

1. 15 
1. 19 
1.23 

1.27 
1.32 
1.36 

1.04 
1.08 
1. 12 

1. 17 
1.22 
1.27 

1.32 

1-37 
1.42 

1.05 
1. 10 
1. 16 

1.22 
1.28 
1.34 

1. 41 
1.48 
1-55 

1.06 
1. 12 
1. 19 

1.26 
1-34 
1.42 

1.50 
1.59 
1.69 

1.08 
1.26 

1.36 
1-47 
1.59 
1. 71 
1.85 
2.00 

1. 10 
1. 21 
1-33 

\$. 

X.77 

1-95 
2.14 
2.36 

10 

1-34 

1.38 

1.41 

1.48 

1.63 

1.79 

2.16 

2.59 

CHAP.   IV.— PROBABLE   VOLUME   OF   TRAFFIC, 


8i 


Table  17. — Continued. 
Value  of  $i  placed  at  Compound  Interest  for  a  Term  of  Years. 


With  Interest  at — 

Years. 

3 

per  cent. 

3^ 
per  cent. 

per  cent. 

4 

per  cent. 

5 
per  cent. 

6 

per  cent. 

8 

per  cent. 

10 

per  cent. 

10 

1-34 

38 

1. 41 

1.48 

1-63 

1-79 

2.16 

2.59 

II 

12 

13 

19 

1.38 
1-43 
1.47 

I-5I 
1.56 
1.60 

1.65 
1.70 
1-75 

43 
48 
53 

58 
63 
68 

74 
80 
86 

1.46 

1.62 
1.68 

1-73 
1.79 
1.86 
1.92 

1-54 
1.60 
1.67 

1.87 

1-95 
2.03 
2. II 

1.89 

1.98 
2.08 
2.18 

2.29 
2.41 
2.53 

1.89 
2.01 
2.13 

2.26 
2.40 
2-54 
2.69 
2.85 
3  03 

2.33 
2.52 
2.72 

2-94 
3-17 
3-43 

3-70 
4.00 
4-31 

2.85 
3.14 
3-45 

3-79 
4.17 
4.60 

5 -OS 

5-55 
6. II 

20 

1. 81 

93 

1.99 

2.19 

2.65 

3.21 

4.66 

6.72 

21 
22 
23 

24 
25 
26 

1? 

29 

1.86 
1.92 
1.97 

2.03 
2.09 
2.16 

2.22 

=:3l 

2 

2 
2 

2 

2 
2 

2 

06 
13 
20 
27 
35 

43 
51 
59 

2.06 
2.13 
2.21 

2.28 
2.36 
2.45 

2.53 
2.62 
2.71 

2.28 
2.37 
2.46 

2.56 
2.67 
2.77 
2.88 
3-00 
3-12 

2.79 
2.93 
3-07 

3-23 
3-39 
3.56 

3-73 
3-92 
4.12 

3 -40 
3-60 
3-82 

4-05 
4.29 
4-55 
4.82 
5. II 
5-42 

5 -03 
5-44 
5.87 

6.85 
7-39 

7-99 
8.62 

9-31 

8.94 

9-83 
10.81 

11.90 

13.08 
14.39 
15-83 

30 

2.43 

2 

68 

2.81 

3-24 

4-32 

5-74 

10.06 

17.41 

31 
32 
33 

34 
35 
36 

37 
38 

39 

2.50 
2.58 
2.65 

2.73 
2.81 
2.90 

2.99 
3-07 

3-17 

2 
2 
2 

3 
3 
3 

3 
3 

3 

96 

06 
16 
27 

% 

60 

2.91 
3.01 
3-II 

3-22 

3-33 
3-45 

3-57 

3-37 
3-51 
3-65 

3-79 
3-95 
4.10 

4.27 
4.44 
4.62 

5-00 

5-25 
5-52 
5.79 
6.08 
6.39 
6.70 

6.09 
6-45 
6.84 

7-25 
7.68 
8.15 
8.63 
9-15 
9.70 

10.86 
11.74 
12.67 

13.69 
14.78 
15.96 

17.24 
18.62 
20.11 

19-15 
21.06 
23-17 

25-48 
28.03 
30.83 

33.91 
37.30 
41.02 

40 

3.26 

3 

72 

396 

4.80 

7.04 

10.28 

21.72 

45.12 

42 

44 
46 
48 

3.46 
3.67 
3-90 
4-13 

3 
4 
4 
4 

97 
23 

52 
83 

4 
4 
4 

5 

24 
54 
87 

21 

5.19 
5.62 
6.07 
6.57 

8.56 

9-43 
10.40 

11.56 
12.98 

14-59 
T6.39 

25.33 

29-54 
34-46 
40.19 

54-59 
66.04 
79-90 
96.67 

60 

4.38 

5  15 

5 

58 

7. II 

11.47 

18.42 

46.88 

117. 0 

52 
58 

4.65 
4-93 
5-23 

5-55 

5-50 

6.27 
6.70 

5 
6 
6 

7 

98 
41 
87 

35 

8.99 
9-73 

12.64 
13-94 
15-37 
16.94 

20.70 
23-25 
26.13 
29.36 

54.68 
63.78 

141-5 
171. 2 
207.1 
250.5 

60 

5-89 

715 

7 

88 

10.52 

18.68 

32.99 

101.2 

303-1 

62 
68 

6.25 
6.63 

7.64 
8.15 
8.71 
9.30 

8 
9 
9 
10 

44 
04 
68 
37 

11.38 
12.31 

13-31 
14.40 

20.59 
22.70 

25-03 
27.60 

37.06 
41-65 
46.79 
52.58 

118. 0 
137-7 
160.6 
187-3 

366.7 
443-6 
536-7 
649-4 

70 

7.92 

9-93 

II 

II 

15-57 

30-43 

59.08 

218.5 

785-6 

8S 
90 

9.18 

10.64 

12.34 

14.30 

16.23 
19-13 

13 
15 
18 
22 

20 
68 
62 
II 

18.95 
23.05 
28.04 
34-12 

38  83 
49-56 
63-25 
80.73 

79.06 
105.80 
141-58 
189.47 

321.0 
471.6 
693 . 0 
1018. I 

1265. 
2036. 
3278. 
5277- 

100 

19.22 

26.55 

31 

19 

50.50 

131.50 

339-30 

2197.9 

13677- 

Formij 
amount  o 

la:  ^  =  (] 
f  $1  at  con 

apour 

K,  in 
din 

whi 
terest 

:hr 

=  rate  of  i 

nterest,  n 

=  numbei 

-  of  years, 

and  S  = 

82 


CHAP.   IV.— PROBABLE  VOLUME   OF   TRAFFIC, 


Table  18. 
Present   Justifiable   Expenditure  to  se- 
cure A  Return  of   $i  at  the  End  of 

ANY  Number  of  Years. 

Table  19. 
Saving  per    Annum   which 
WILL  IN  the  Aggregate 

AMOUNT     TO      $1     AT     THE 

End  OF  A  Term  of  Years. 

With   Interest  at — 

Years. 

With   Interest  at— 

Years. 

3 

per 
cent. 

4 

per 
cent. 

5 

per 
cent. 

6 

per 
cent. 

7 
per 
cent. 

8 

per 
cent. 

ID 

per 
cent. 

3 

per 
cent. 

4 

per 
cent. 

5 

per 
cent. 

6 

per 
cent. 

I 

2 

3 
4 

1 

9 

.971 
■943 
•9^5 
.888 
.863 
•837 
.813 
•789 
.766 

.961 

.790 
.760 
•731 
•  703 

•952 

.823 
•  783 
.746 

.711 
.677 
•645 

■943 
.890 
.840 

.792 
•747 
•705 
.665 
.627 
■592 

•935 

■'& 

•763 
•713 
.666 

.623 
.582 
■544 

.926 
-857 
•794 

.630 

.584 
•  540 
.500 

■751 

•  683 
.621 

■565 

%] 
.424 

I 
2 
3 
4 

% 

7 
8 
9 

1. 000 
•493 
.323 

•  155 
.130 
.112 
.098 

1. 000 
.490 
.320 

•235 
■  185 
•151 
.127 
.io8 
.094 

1. 000 
.488 
•317 
.232 
.181 
•147 
.123 
•  los 
.091 

1. 000 

•485 
•314 
.228 
.177 
•143 
.119 
.101 
.087 

10 

■744 

.676 

.614 

■558 

■  508 

•463 

•  386 

10 

.087  1  .083  1  .079 

.076 

12 

13 

14 
15 
16 

19 

.722 
.701 
.68r 

.661 
.642 
.623 

.605 
.587 
•570 

.650  1 

:£? 

•577 
•555 
•534 

•513 
■494 
•475 

.585 
•557 
■  530 

•505 
.481 
•458 

•436 
•415 
•396 

•527 
•497 
.469 

.442 
.417 
•394 

•371 
•350 
■330 

•475 
•444 
•415 
.388 
.362 
•339 

•317 

.296 
.276 

•  429 

•340 
•315 
.292 

.270 
■  250 
.232 

•351 
■319 
.290 

.264 
.240 
.218 

-t 
.164 

II 
12 
13 
14 

;i 

19 

.078 
.070 
.054 

.058 
•054 
.050 

.046 

■043 
.040 

.074 
.066 
.060 

•055 
.050 
.046 

.042 
•039 
.036 

.070 

.056 

.051 
.046 
.042 

•039 
•035 
•033 

.067 
.059 
•053 
.047 
•043 
•039 

■035 
.032 
.030 

20 

■554 

■456 

•377 

.312 

.258 

.215 

.149 

30 

•037 

•033 

.030 

.027 

21 
22 
23 
24 

25 
26 

27 
28 
29 

■537 
.522 
•507 
.492 
.478 
.464 
•450 
•437 
•424 

■439 
.422 
.406 

•390 
•375 
•  361 

•347 
•333 
.321 

•359 
■  342 
.326 

.310 

.268 
•255 
•  243 

•294 
•277 
.262 

.247 
•233 
.220 

.207 
.196 
■  i8s 

.241 
.226 
.211 

.197 
.184 
.172 

.161 
.150 
.141 

.109 
.184 
.170 

.158 
.146 
•135 
.125 
.116 
.107 

■135 
.123 
.112 

.102 
.092 
.084 

.076 
.069 
.063 

21 
22 
23 
24 
25 
26 

27 
28 
29 

•035 
•033 
.031 

.029 
.027 
.026 

.024 
.023 
.022 

.031 
.029 
.027 

.025 
.024 
.022 

.021 
.020 
.019 

.028 
.026 
.024 

.022 
.021 
.019 

.018 
.017 
.016 

.025 
.023 
.021 

.020 
.018 
.017 

.016 
.014 
.013 

30 

.412 

.308 

■  231 

.174 

•131 

.099 

•057 

30 

.021 

.018 

.015 

■  013 

31 
32 

33 
34 

I? 

39 

.400 
.388 
•377 
.366 
•355 
■345 

•335 
■325 
■316 

■% 

■274 

.264 

•253 
.244 

•234 
.225 
.217 

.220 
.210 
-200 

.IQO 
.181 
•173 
.164 

•157 
.149 

.164 
.146 

•  138 
.130 
.123 

.116 
.109 
.103 

.123 

•115 
.107 

.100 
.094 
.087 
.082 
.076 
.071 

:35 

.079 

.063 
.058 
•054 
.050 

.052 
.047 
•043 

•039 
.036 
.032 

.029 
.027 
.024 

31 
32 
33 
34 

11 

39 

.020 
.019 
.018  ■ 

.017 
.016 
.016 

•915 
.014 
.014 

.017 
.016 
.015 

.014 
.013 
.013 

.012 
.012 
.011 

.014 
.013 
.012 

.012 
.011 
.010 

.010 
.009 
.009 

.012 
.011 
.010 

.009 

■zi 

.008 

007 
.007 

40 

■307 

.208 

.142 

.097 

.067 

.046 

.022 

40 

.013 

.010 

.008 

.006 

42 
48 

.289 
.272 

■257 
.242 

•193 
.178 
.165 
.152 

.129 

.096 

.086 
.077 
.068 
.061 

.058 
.051 
.044 
•039 

•039 
•034 
.029 
.025 

.018  1 

•015 ! 

•013 

.010 

42 
44 
46 
48 

.012 
.011 

-QIO 
.009 

.009 
.007 

.007 
.007 
.006 
.005 

.006 
.005 
.004 
.004 

50 

.228 

.141 

.087 

•054 

•034 

.021 

.009 

50 

.009 

.006 

.005 

.003 

CHAP. 

IV.- 

-PROBABLE  VOLUME   OF 

TRAFFIC. 

83 

Table  18. — Continued. 

Present  Justifiable   Expenditure   to   se- 
cure A  Return   of   $i   at  the  End  of 
ANY  Number  of  Years. 

Table  19. — Continued. 

Saving  per  Annum   which 

WILL  IN  the  Aggregate 

amount    to    $i   at   the 

End  of  a  Term  of  Years. 

With  Interest  at— 

Years. 

With   Interest  at— 

Years. 

3 

per 
cent. 

4 

per 
cent. 

5 

per 
cent. 

6 

per 

cent. 

7 
per 
cent. 

8 

per 
cent. 

ID 

per 
cent. 

3 

per 
cent. 

4 

per 
cent. 

5 

per 

cent. 

6 

per 
cent. 

50 

.228 

141 

087 

054 

•034 

.021 

.009 

50 

.009 

006 

.005 

.003 

52 

^^ 

58 

•215 
.203 

130 
120 
III 

103 

079 
072 
065 

059 

048 

043 
038 

034 

.030 
.026 
.023 
.020 

.oi8 
.016 
.013 
.012 

.007 
.006 
.005 
.004 

52 

It 
58 

.008 
.008 
.007 
.006 

006 
005 
005 
004 

.004 
.004 
.003 
.003 

.003 
.003 

.003 
.002 

60 

.170 

095 

053 

030 

017 

.010 

.003 

60 

.006 

004 

.003 

.002 

62 
64 

68 

.160 
.151 
.142 

•134 

088 
081 
07s 
069 

049 
044 
040 
036 

027 
024 
021 

019 

.015 
.0x3 
.011 
.010 

.008 
.007 
.cx)6 
.005 

.003 
.002 
.002 
.002 

62 

% 

68 

.006 
.005 
.005 
.005 

004 
003 
003 
003 

.002 
.002 
.002 
.002 

.002 
.001 
.001 
.001 

70 

.126 

064 

033 

017      .009 

.004 

.001 

70 

.004 

003 

.002 

.001 

15 
85 
90 

.109 

.070 

053 

036 
029 

026 
020 
016 
012 

013 
009 
007 
005 

.006 
.004 
.003 
.002 

.003 
.002 
.001 
.001 

.001 
.000 

.OCX3 
.000 

11 

85 
90 

.004 
.003 
.003 
.002 

002 
002 
001 
001 

.001 
.001 
.001 
.001 

.001 
.001 
.000 
.000 

100 

.052 

020 

008 

003 

.001 

.000 

.000 

100 

.002 

001 

.000 

.000 

Table  20. 

Showing  the  Justifiable   Present  Expenditure  to  save  $i  per  Annum 
FOR  various  Terms  of  Years  at  various  Rates  per  Cent  for  Capital. 


Justifiable  Present  Expenditure  with  Interest  at — 

Term 

OF 

Years. 

3 

4 

5 

6 

7 

8 

9 

10 

per  cent. 

per  cent. 

per  cent. 

per  cent. 

per  cent. 

per  cent. 

per  cent. 

per  cent. 

I 
2 

$0 

I 

97 

91 

$0.96 

$0 

I 

n 

So.  94 
1.83 

So.  93 
1. 81 

So.  93 
1.78 

So  92 
1.76 

So 

I 

91 
74 

3 

2 

83 

2.78 

2 

72 

2.67 

2.62 

2.58 

2 

S3 

2 

49 

4 

3 

^o 

3-63 

3 

55 

3-47 

3-39 

3-31 

3 

24 

3 

17 

i 

4 
5 

58 
42 

4-45 
5-24 

4 

5 

11 

4.21 
4.92 

4.10 

4-77 

3-99 
4.62 

3 

4 

89 
49 

4 

79 
36 

7 

6 

23 

6.00 

5 

79 

5.58 

5-39 

5.21 

5 

03 

4 

87 

8 
9 

7 
7 

02 
79 

6.73 
7-44 

6 
7 

40 
II 

6.21 

6.80 

5-97 
6.52 

5-75 
6.25 

I 

53 
00 

5 
5 

34 
76 

10 

8 

53 

8. II 

7 

72 

7.36 

7.02 

6.71 

6 

42 

6 

M 

II 

9 

25 

8.76 

8 

31 

7.89 

7-50 

7.14 

6 

81 

6 

50 

12 

9 

95 

9-39 

8 

80 

8.38 

7-94 

7-54 

7 

16 

6 

81 

13 

10 

b4 

9.99 

9 

39 

8.85 

8.36 

7.90 

7 

49 

7 

10 

14 

II 
II 
12 

30 
56 

10.56 
II.  12 
11.65 

9 
10 
10 

90 

9-3° 
9.71 
10.  II 

8.75 
9. II 
9-45 

8.24 
8.56 
8.8s 

7 
8 
8 

79 
06 
31 

7 

7 
7 

37 
6i 
82 

17 

18 

13 

^3 

17 

75 

12.17 
12.66 

II 
II 

27 

69 

10.48 
10.83 

9.76 
10.06 

9.12 
9-37 

8 

8 

54 
76 

8 
8 

02 
20 

.      19 

14 

32 

13-13 

12 

09 

11.16 

10.34 

9.60 

8 

95 

8 

37 

30 

14 

88 

^3-59 

12 

46 

11.47 

10.59 

9.82 

9 

13 

8 

51 

84 


CHAP.   IV.— PROBABLE  VOLUME   OF   TRAFFIC. 


Table  20. —  Continued. 


Term 

Justifiable  Present  Expenditure  with  Interest  at— 

OF 

Years. 

3 

per  cent. 

4 

per  cent. 

5 

per  cent. 

6 

per  cent. 

7 
per  cent. 

8 

per  cent. 

9 

per  cent. 

10 

per  cent. 

20 

14.88 

13-59 

12.46 

11.47 

10.59 

9.82 

9.13 

8.51 

21 
22 
23 

24 

25 
26 

29 

15.42 

15-94 
16.44 

16.94 
17.41 
17. 88 

18.33 
18.76 
19.19 

14.03 
14.45 
14.86 

15.25 
15.62 
15.98 

16.66 
16.98 

12.82 
13.16 
13-49 
13.80 
14.09 
14-38 
14.64 
14.90 
15-14 

11.76 
12.04 
12.30 

12.55 
12.78 
13.00 

13.21 
13-41 
13-59 

10.84 
11.06 
11.27 

11.47 
11.65 
11.83 

11.99 
12.14 
12.28 

10.02 
10.20 
10-37 

10.53 
10.67 
10.81 

10.94 
11.05 
11.16 

9-29 
9-44 
9-58 

9.71 
9.82 
9-93 
10.03 
10.12 
10.20 

8.65 
8-77 
8.88 

8-99 
9.08 
9.16 

9.24 
9-31 
9-37 

30 

19.60 

17.29 

T5-37 

13-77 

12.41 

11.26 

10.27 

9-43 

31 

32 

33 

34 
35 
36 

39 

20.00 
20.39 
20.77 

21.13 
21.49 
21.83 

22.17 
22.49 
22.98 

1759 
17-87 
18.15 

18.41 
18.67 
18.91 

19.14 

19-37 
19.58 

15-59 
15.80 
16.00 

16.19 
16.37 
16.55 
16.71 
16.87 
17.02 

13-93 
14.08 
14.23 

14-37 
14.50 
14.62 

14.74 
14-85 
14-95 

12.53 
12.65 

12.75 
12.85 
12.95 
13.04 

13.12 
13-19 
13.26 

11-35 
11-43 
11.51 

11-59 
11.65 
11.72 

11.78 
11.83 
11.18 

10.34 
10.41 
10.46 

10.52 
10.57 
10.61 

10.65 
10. 6g 
10.73 

9.48 
9-53 
9-57 
9.61 
9.64 
9.68 

9.71 
9-73 
9.76 

40 

23.12 

19.79 

17.16 

15-05 

13-33 

11-93 

10.76 

9-78 

41 
42 

43 

44 
45 
46 

47 
48 
49 

23-41 
23.70 
23.98 

24.25 
24-52 
24.78 
25.03 
25.27 
25-50 

19.99 
20.19 
20.37 

20.55 
20.72 
20.89 

21.04 
21.20 
21.34 

17.29 
17.42 
17-55 
17.66 
17.77 
17.88 

17.98 
18.08 
18.17 

15-14 
15-23 
15-31 

15-38 
15-46 
15-52 

15-59 
15-65 
15-71 

13-39 
13-45 
13-51 

13-56 
13.61 
13-65 
13.69 
13-73 
13-77 

11.97 
12.01 
12.04 

12.08 
12. II 
12.14 

12.16 
12.19 
12.21 

10.79 
10.81 
10.84 

10.86 
10.88 
10.90 

10.92 
10.93 
10.95 

9.80 
9. 82 
9.83 

9.88 

9.89 
9.90 
9.91 

50 

25-73 

21.48 

18.26 

15-76 

13.80 

12.23 

10. q6 

9-92 

65 
70 

26.77 
27.68 
28.4s 
29.12 

22.11 
22.62 
23-05 
23.40 

18.63 
18.93 
19.16 
19-34 

16. x6 
16.29 
16.39 

13-94 
14.04 
14.10 
14.16 

12.32 
12.38 
12.42 
12.44 

11.01 
11.05 
11.07 
11.08 

9-95 
9-97 
9-98 
9-99 

75 

29.70 

23.68 

19.49 

16.46 

14.20 

12.46 

11.09 

9-99 

80 

85 
90 
95 

30.20 
30.63 
31.00 
31.32 

23.92 
24.11 
24.27 
24.40 

19.60 
19.68 
19-75 
19.81 

16.51 

16.58 
16.60 

14.22 
14.24 

14.26 

12.47 
12.48 
12.49 
12.49 

11.10 
11.10 
11.11 
11.11 

10.00 
10.00 
10.00 
10.00 

100 

31.60 

24-51 

19.85 

16.62 

14.27 

12.49 

11.11 

10.00 

Perpetuity. 

33.33 

25.00 

20.00 

16.67 

14.29 

12.50 

II. II 

10.00 

This  table  gives  simply  the  capital  sum  which  will — 

(i)  Return  $i  per  annum  in  interest  during  the  given  term  ;  and, 

(2)  Return  an  additional  sum  in  interest  each  year  which,  placed  at  compound  interest 

at  the  same  rate,  will  extinguish  the  principal  at  the  epd  of  the  given  term. 

At  10  per  cent  for  capital  it  is  worth  spending  but  twice  as  much  to  ensure  a  saving  of 

$1  per  annum  for  ever  as  to  ensure  it  for  7  years  only.     At  the  much  higher  rates  which 

people  often  wish  to  be  assured  of  before  spending  money  in  new  enterprises  it  is  worth 

practically  nothing  to  save  money  more  than  6  or  8  years  ahead. 


CHAP.   IV.— PROBABLE  VOLUME   OF   TRAFFIC.  85 

80,  All  this  is  undeniably  correct  in  theory,  except,  indeed, 
that  it  understates  the  case  ;  for  we  might  enter  into  further 
mathematical  subtleties,  and  prove  that  if  the  ratio  of  growth  of 
traffic  is  greater  than  the  rate  of  interest  on  capital,  the  present 
justifiable  expenditure  to  provide  for  such  increase  of  traffic  is 
infinite.  But  this,  while  an  excellent  exercise  for  the  student,  we 
shall  not  attempt  to  do  ;  confining  ourselves  instead  to  the  more 
profitable  work  of  pointing  out  the  reasons  why,  with  any 
ordinary  corporation,  all  such  speculations  are  wholly  delusive, 
so  that  even  the  indications  of  Table  18  are  of  value  only  as  fixing 
a  maximum  which  should  never  be  exceeded. 

81.  The  first  and  most  vital  reason  is  that,  while  it  may  be 
taken  as  a  practical  certainty  that  the  traffic  of  any  ordinary 
railway  not  only  will  grow,  but  that  it  will  grow  at  an  average 
rate  of  something  like  5  to  8  per  cent  per  annum  east  of  the 
AUeghenies,  and  7  to  10  or  15  or  even  20  per  cent  per  year  west 
of  there,  yet  that  the  rate  of  this  growth  of  traffic  is  excessively 
variable  and  uncertain — liable  to  cease  altogether  at  any  time  for 
many  years,  and  at  periods  when  it  is  particularly  inconvenient 
to  put  interest  on  discounted  expectancies. 

For  this  cause  alone  it  is  in  general  inexpedient  to  look 
forward  more  than  at  most  five  years  for  traffic  to  justify  an 
increase  of  immediate  expenditure  ;  and  when,  as  is  of  course 
more  likely  to  be  the  case,  a  new  project  is  floating  upon  the  top 
of  a  "  boom"  or  upward  wave  in  the  tide  of  business,  it  is  unsafe 
to  look  ahead  more  than  two  or  three  years.  It  is  at  such  times 
especially  to  be  remembered  that  the  wave  may  begin  to  flow 
backward  at  any  time,  and  that  even  if  it  do  not,  the  line  is  built 
with  borrowed  capital,  and  that  it  is  difficult  for  the  average 
financier  to  borrow  large  sums  on  future  expectancies  ;  nor  can 
he  in  any  case  borrow  $2000  per  mile  as  cheaply  as  $1000  per 
mile.  Borrowed,  however,  the  money  must  be  if  the  first  supply 
gives  out,  or  the  whole  investment  of  the  original  company  will 
probably  be  lost ;  and  the  instances  are  rare  in  which  any  large 
proportion  of  the  entire  capital  has  been  positively  secured 
before  the  surveys  are  substantially  complete  and  construction 
in  progress. 


86  CHAP.   IV.— PROBABLE  VOLUME   OF   TRAFFIC. 

82.  A  sequence  of  events  which  has  been  again  and  again 
repeated  is  that  the  company  shall  enter  upon  the  work  with 
vague  visions  of  boundless  prosperity,  and  look  with  certainty 
to  securing  "  all  the  money  they  need  ;"  shall  encourage  their 
engineer  in  a  costly  style  of  construction  which,  with  the  natural 
preference  of  an  engineer  for  massive,  durable,  and  stately  works, 
he  is  all  too  ready  to  adopt ;  and  finally,  often  within  a  ridicu- 
lously short  time  of  the  period  of  their  brightest  hopes,  be  left 
stranded  by  the  ebb-tide  of  speculation,  a  complete  and  helpless 
financial  wreck. 

83.  Finally,  there  is  another  and  still  stronger  reason  why  the 
growth  of  traffic  should  not  be  counted  on  for  many  years  ahead 
in  designing  the  works.  It  is  usually  a  simple  matter  to  so- 
design  large  parts  of  the  line,  including  most  of  the  more  expen- 
sive works,  that  their  construction  may  be  postponed  until  a 
more  convenient  season — a  possibility  so  important  that  it  is- 
separately  discussed  hereafter  (Chap.  XXIII.).  By  so  doing  we 
at  least  make  sure  of  keeping  the  capital  account  at  a  minimum 
and  of  (usually)  retaining  the  line  in  the  hands  of  the  original 
company;  while,  when  all  causes  are  considered,  the  loss  from 
postponing  the  execution  of  all  more  costly  work  which  can  be 
postponed  will  not  be  very  great,  even  if  one's  brightest  dreams 
are  realized — which  will  rarely  be  the  case. 

84.  We  may  conclude,  therefore,  that  although  a  railway 
corporation  which  has  in  truth  as  well  as  in  imagination  un- 
limited means  ;  which  is  able  to  look  ahead  with  certainty  for  a 
long  period  of  years  ;  which  is  able  without  doubt  to  tide  over 
long  periods  of  depression  without  danger  to  its  stability,  and 
which  has  no  anxiety  to  realize  present  profit,  or  even  avoid 
present  losses,  on  investments  which  will  be  ultimately  profit- 
able ; — although  such  a  corporation  may  legitimately  make  a 
large  increase  in  its  investments  for  the  sake  of  a  traffic  which  is 
still  in  the  distant  future,  yet  that  no  ordinary  corporation  can 
afford  to  look  ahead  more  than  two  to  five  years  for  the  traffic 
to  pay  interests  on  increased  investments,  and  that  even  in  that 
case  they  take  much  risk  in  doing  so.     Traffic  should  therefore,, 


CHAP.   IV.— PROBABLE  VOLUME   OF   TRAFFIC.  87 

in  ail  cases,  be  ratlier  under-  tlian  over-estimated,  to  the  end  that 
in  no  case  extravagant  expenditures  shall  be  made  for  a  costly- 
perfection  of  alignment  which  the  traffic  will  not  justify  :  bearing 
in  mind  that  an  under-estimate  of  admissible  expenditure  is 
simply  a  failure  to  invest  a  small  (or  it  may  be,  large)  additional 
sum  of  money  which  would  have  earned  good  interest,  but  which 
may  be  invested  later  at  nearly  if  not  quite  as  good  advantage  ; 
whereas  an  over-liberal  investment  of  additional  sums  on  which 
interest  cannot  be  earned  greatly  endangers,  in  the  trying  years 
which  usually  come  soon  after  the  line  is  opened,  the  permanency 
of  the  whole  investment. 

In  the  one  case,  our  economy  only  endangers  a  minor  loss,  if 
the  enterprise  as  a  whole  turns  out  well  ;  and  if  it  does  not,  may 
save  it  from  ruin.  In  the  other  case,  our  extravagance  only 
gives  us  a  fair  investment  for  a  little  more  money  if  all  goes 
well,  and  if  it  does  not,  may  be  the  ounce  of  additional  load 
which  breaks  the  back  of  the  enterprise.  Our  only  grave  dan- 
ger, therefore,  is  of  error  in  one  direction  only  ;  which  makes  it 
the  easier  to  make  an  estimate  of  traffic  sufficiently  exact  for  all 
important  purposes — that  is  to  say,  one  which  will  be  certainly 
not  too  large. 

85.  Tables  21  to  27  give  various  statistics  of  the  growth  of 
American  railway  traffic,  such  as  are  likely  to  be  useful  for 
checking  in  a  rude  way  the  estimated  growth  of  traffic  on  any 
line.  The  most  accurate  and  satisfactory  method  for  estimating 
both  traffic  and  expenses  in  any  given  case,  however,  is  com- 
parison with  the  experience  of  neighboring  roads  of  the  same 
general  character,  because  it  is  much  easier  to  count  on  a  line 
doing  so  much  better  or  worse  than  another  line,  than  to  esti- 
mate the  absolute  traffic  independently. 

Tables  23  to  27  inclusive,  for  the  groups  of  States,  cover  a  period  extending 
from  one  period  of  business  activity  to  another,  with  a  severe  depression  be- 
tween. Table  28,  for  the  whole  United  States,  covers  two  preceding  and  four 
following  years  likewise,  and  by  comparison  with  this  table  the  general  course 
of  traffic  and  earnings  for  the  same  additional  years  can  be  determined  with 
approximate  accuracy. 

All  these  tables  were  computed  from  the  statistics  of  Poor's  Manual. 


88 


CHAP.   IV.— PROBABLE   VOLUME   OF   TRAFFIC. 


i. 

o 

u 

X    0 

o  8 

Per 
cent 
Oper- 
ating- 
Exp. 

0     o 

0 

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13  .2  S 

C   •  G  ni  e  «3 


CHAP.    IV.— PROBABLE  VOLUME   OF   TRAFFIC. 


89 


>    « 


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90 


CHAP.   IV.— PROBABLE  VOLUME   OF   TRAFFIC. 


The  groups  of  States  are  those  of  Poor's  Manual,  which  see  for  the  years  1882  and 
1886  for  details.  The  population  used  for  the  first  part  of  the  Table  (1881)  was  that  of 
the  Census  of  1880,  which  was  about  three  per  cent  too  small. 

By  a  different  estimate,  the  number  of  inhabitants,  of  acres  in  grain  and  cotton,  of 
bushels  of  grain  and  bales  of  cotton  produced,  per  mile  of  railway,  have  been  as  follows 
for  the  last  seven  years,  in  all  cases  taking  the  mileage  and  population  at  the  close  of  the 
year  and  the  crops,  etc.,  of  the  previous  summer  : 


Popu- 
lation. 

Acres. 

Bushels  of 
Grain. 

Bales  of 
Cotton. 

1879 

1880    

581 
545 
509 
473 
466 
458 
461 

1,565 
1,466 
i>359 
i,*36 
1,204 
1,216 
1,216 

31,600 
28,932 
19,804 
23,405 
21,563 
23,690 
23,241 

67-73 
70-53 
52.65 
60.18 
47.00 

45-44 
50.41 

1881 

1882      

1883 

1884          ..... 

1885  

Table  22. 

Statistics  of   Revenue  Per  Head  of   Population  and  Per  Mile 

FOR  Each  State  Separately — 1881. 
[These  statistics  are  based  upon  the  same  figures  as  those  given  for  groups  of  States  only 
in  the  first  part  of  Table  21.     The  division  of  the  miles  of  road  operated  between  the  dif- 
ferent States  is  not  exact,  so  that  the  figures  can  be  regarded  as  approximations  only.] 


Per  Mile  Railway. 

Per  Cent. 

Sidings. 

Per  Cent. 
Operating 
Expenses. 

Gross  Revenue. 

Square 
Miles. 

Popula- 
tion. 

Per  Mile 
Railway. 

Per  Head 
Populat'n.. 

32.0 
10.3 
12.2 

3-47 
8.55 
5-II 

593 
387 
397 
793 
1,810 
670 

19.0 
17.6 

15.4 
63.0 

46.5 
35-0 

69.0 
64.0 
80.5 
71-3 
61.4 
64.0 

$4,130 
5.200 
4.690 

10 . 200 
9.200 
9-650 

$6.54 

New  Hampshire 

10.90 
12.40 

Massachusetts 

16.50 

Rhode  Island 

5-90 

Connecticut 

16.00 

New  England 

II. 0 

650 

37.4 

70.0 

8.420 

13- 10 

New  York 

7.67 
5-00 
6.81 

9-75 
9.60 
100.5 

848 
679 
633 
677 
485 
271 

75-3 
79-6 
64.6 

52.2 
19-3 

61.0 

63.9 

61.5 

70 

60.7 

83.4 

13.000 
6.850 

15.800 
2.880 
5-490 
3.670 

15.90 

New  Tersev 

28.10 

Pennsylvania 

23.70 

4.08 

Maryland  and  D.  C 

12.30 
13.60 

Middle  States 

8.60 

775 

67-3 

62.9 

14.000 

18.50 

CHAP.   IV.— PROBABLE  VOLUME   OF   TRAFFIC. 


9r 


Table  22. — Continued. 


Per  Mile 

Railway. 

Per  Cent. 
Sidings. 

Per  Cent. 
Operating 
Expenses. 

Gross  Revenue. 

Square 
Miles. 

Popula- 
tion. 

Per  Mile 
Railway. 

Per  Head 

Populat'n. 

Virginia 

15-3 
31-4 
25.2 
22.1 

70.7 
22.0 
100.3 
26.0 
24.0 
13-4 

602 

228 
738 
586 
344 
551 
2,470 

594 
811 
569 

I3-0 
6.4 
7-1 

7-7 
5.0 
8.6 

5-4 
II. I 
22.0 
13. 1 

65.6 
66.5 
68.0 
60.7 
62.8 
69.9 

65.9 
71.0 

67.7 

55.8 

5-590 
2.590 
3-250 
3-740 
3.210 
4.150 
3-320 
8.080 
4-500 
5-590 

7.00 

N.  Carolina 

2.  70 

S.  Carolina 

4.04 

Georgia 

6.14 

Florida 

1. 61 

Alabama 

6-43 

Mississippi 

1.03 

Louisiana 

10.40 

Tennessee 

Kentucky 

4.36 
5.90 

Southern  States 

25-7 

681 

10.9 

65.0 

4-550 

5.20 

Ohio 

5.08 
13-9 
5.65 
5.20 
10.2 
21.0 

14-3 
24.2 

202 
400 

331 

288 

249 
199 

478 
718 

29.6 
29.6 
27.0 
27.0 
10.6 

7.0 
II. 4 

9.9 

62.8 
68.2 
76.5 
54-7 
59-7 
61.4 
54-0 
64.0 

8.790 
5-850 
5-750 
7-560 
3 -930 
4-370 
7.000 
3 -570 

20.50 

Michigan 

12.40 

Indiana 

17.30 

Illinois 

29.05 
14.70 

Wisconsin 

Minnesota 

15.90 
13.60 

Missouri 

Iowa 

3.92 

N.  W.  Central  States. 

9.90 

351 

21.3 

60.9 

6.520 

17.60 

Nebraska 

226 
303 
254 
283 
95 
1,200 

309 

17.0 

53-7 

1. 160 

^Vvominsf  .    ..    ...      .. 

Dakota... 

7-5 
5-9 
5-9 
3-9 

62.8 
61. 1 

58.5 
68.0 

5-170 
6.530 
3-960 
4.480 

Colorado 

46.90 

Arkansas 

Texas 

FarW.  andS.  W.... 

61.9 

310 

7-1 

60.2 

6.420 

16.10 

230 
104 
148 
140 
301 
230 

Arizona     • 

Utah    

13-7 

49-3 
53-8 
49-5 
56.4 

Nevada 

California 

8.620 

Oregon 

........ 

Pacific  States........ 

181. 0 

261 

9.6 

- 

49-9 

(7.500) 

23-15 

United  States 

29.0 

481 

25.1 

61.9 

7.690 

14.50 

92 


CHAP.   IV.— PROBABLE  VOLUME   OF   TRAFFIC. 


Table  23. 

Main  Results  of  Operation  of  the   Railways  of  the   New  England 

States,  i  873-1881. 


Year. 

Popula- 
tion. 

1,000,000. 

Miles 
Railway 
Operated. 

Revenue. 

I  =  $1,000,000. 

Divi- 
dends. 

Revenue  per  head. 

Rev. 
per 

Mile. 

Pass. 

Fght. 

Total 

Net. 

Pass. 

Fght. 

Total 

1=  1,000 

1873 

74 

3-644 
3.696 

5,303 
5,617 

22.36 
22.11 

29.31 

27-95 

51-68 
50.06 

15.06 
16.71 

9.00 
8.51 

6.15 
6.00 

8.03 
7-55 

14.18 
13-55 

9-73 
8.91 

1875 

3-748 

5,732 

21.78 

26.55 

48.33 

15-32 

8.79    ;  5-80 

7.10 

12.  QO 

8.41 

1876 

77 

78 

79 

3.801 
3-853 
3-905 
3.958 

5,783 
6,036 
5,760 
6,156 

20.52 
20.07 
17.97 
17-52 

25.24 
24.52 
23-29 
23.81 

45-76 
44-59 
41.26 

41-33 

15-38 
13-74 
13.69 
15-59 

7.61 
6.98 
7-57 
7-24 

5-44 

5-21 

4.60 
4-45 

6:67 
6.36 
6.00 
6.02 

12.11 

"•57 
10.60 
10.47 

7.90 
7.38 
7.18 
6.71 

1880 

4.010 

6,071 

19.32 

29.44 

48.76 

17.19 

8.00    1  4.82 

7-37 

12.19 

8.00 

1881 

4.062 

6,261 

20.17 

32-71 

52.88 

15.92 

II. 14 

4.98 

8.05 

13-03 

8-43 

Table  24. 

Main  Results  of  Operation  of  the  Railways  of  the  Middle  States, 
WITH  Maryland  and  West  Virginia,  1873-1881. 


Year. 

Popula- 
tion. 

1,000,000. 

Miles 
Railway 
Operated. 

Revenue. 

I  =  $1,000,000. 

Divi- 
dends. 

Revenue  per  head. 

Rev. 

mie. 

Pass. 

Fght. 

Total 

Net. 

Pass. 

Fght. 

Total 

1=1,000 

1873 

74 

10.915 
II. 123 

12,441 
12,874 

42.36 
41.70 

151-7 
144.8 

194. 1 
186.5 

69-3 
90.2 

36.5 
37-6 

3-88 
3-26 

13.90 
13.00 

17.78 
16.26 

15.6 
14-5 

1875 

11-331 

13,173 

40.77 

134.9 

175-7 

656 

39-4 

3.60 

11.84 

15-44 

13.3 

1876 

79 

11.540 
11.749 
11.95S 
12.167 

13,647 
13,607 
14,600 
14,941 

47-48 
39.26 
35-95 
43.20 

130.1 
116.7 
119.5 
127. 1 

177.6 
155-9 
155-5 
170-3 

69.4 
61.0 
61.6 
70.4 

33-7 
24-9 
21. 1 

23-9 

3-58 
4.10 
3-34 
3.00 
3-55 

12.91 

11.30 
9.90 
10.00 
10.45 

16.49 
15.40 
13.24 
13.00 
14.00 

14-5 

13-3 
II. 4 
10.6 
"-3 

1880 

12.376 

14,882 

44-97 

154.0 

199.0 

83.9 

28.5 

3-63 

12.40 

16.03   1     13.3 

1881 

12.585 

16,213 

49.92 

178-5 

228.4 

84.9 

33-3 

3-97 

14.20 

18.17 

14.1 

CHAP.   IV.— PROBABLE  VOLUME   OF   TRAFFIC. 


93 


Table  25. 

Main  Results  of  Operation  of  the  Railways  of  the  Southern  States, 
(South  of  Potomac  and  Ohio),  1873-1881. 


Year. 

Popula- 
tion. 

1,000,000. 

Miles 
Railway 
Operated. 

Revenue. 

I  =  $1,000,000, 

Divi- 
dends. 

Revenue  per  head. 

Rev. 

^li1e. 

Pass. 

Fght. 

Total 

Net. 

Pass. 

Fght. 

Total 

1=  1,000 

X873 

74 

11.022 
II. 196 

13,908 
13.505 

15-30 
H-13 

38-39 
38.13 

53-70 
52.26 

18.13 
17.27 

0.90 
1.07 

1.38 
1.26 

3-49 
3-41 

4.87 
4.67 

3.86 
3-86 

1875   

11.370 

13^522 

13.86 

36.53 

50.40 

16.74 

1.50 

1.22 

3.22 

4.44 

3-73 

1876 

77 

78 

79 

11-544 
II. 718 
11.892 
12.066 

13,948 
11,272 
12,498 
13,389 

11.88 
9-95 
11.22 
11.32 

38.87 
29.86 
31-58 
32.60 

50-74 
39-81 
42.80 
43-92 

17.12 
12.66 
14-38 
14.67 

1.86 
2-74 
2.81 
2.13 

0.84 
0-99 
0.94 

3-37 
2-54 
2.66 
2.70 

4-40 
3-38 
3-65 
3-64 

3.64 
3-53 
3-43 
3-28 

1880 

12.241 

13,548 

10-45 

37-87 

48.32 

18.12 

3-53 

0.86 

3.10 

3.96 

3-56 

1881 

12.415 

14,002 

17. II 

46.63 

63-74 

22.24 

3-59 

1.38 

3.76 

5.14 

4.72 

Table  26. 

Main  Results  of  Operation  of  the  Railways  of  the  Western  and 
Southwestern  States  (all  North  of  Ohio  and  West  of  the  Missis- 
sippi and  East  of  the  Rocky  Mountains),  1873-1881. 


Year. 

Popula- 
tion. 

1,000,000. 

Miles 
Railway- 
Operated. 

Revenue. 

I  =  $1,000,000. 

Divi- 
dends. 

Revenue  per 

head. 

Rev. 

Mile. 

Pass. 

Fght. 

Total 

Net. 

Pass. 

Fght. 

Total 

1=  1,000 

1873 

74 

16.025 

16.589 

32,973 
35,639 

51.62 

56.78 

160. 1 
158. 1 

211. 7 

214.9 

75-5 

19.06 
16.61 

3.23 
3.4= 

10.00 

9-53 

13.23 

1^-95 

6.42 
6.02 

1875 

17.154 

36,058 

54-99 

151. 2 

206.2 

75-6 

19.23 

3-21 

8.80 

12.01 

5-73 

1876 

77 

78 

79 

17.718 
18.282 
18.847 
19. 411 

36.753 
39,136 
41,605 
44,104 

43.36!i42.9 
44.44148.8 
49.001160.9 
54-45  177-9 

189.2 
193.2 
209.9 
232.4 

63-9 
66.1 
78.0 
99.0 

17-39 
14.56 

19-34 
23-56 

2.45 
2.43 
2.60 
2.80 

8.07 
8.13 
8.53 
9.16 

10.52 
10.56 
II. 13 
11.96 

5-95 
4-95 
5.05 
5.27 

1880 

19.976 

45,9" 

64.10 

226.  s 

290.6 

125-2 

33-12 

3.21 

11.30 

14-51 

6-34 

1881 

20.540 

53,224 

71.40 

273.0 

344-4 

134.8 

40-85 

3-48 

13-30 

16.78 

6-49 

94 


CHAP.   IV.— PROBABLE  VOLUME   OF  TRAFFIC. 


Table  27. 

Main  Results  of  Operation  of  the   Railways   of  the  Pacific  States, 

1873-1881. 


Year. 

Popula- 
tion. 
I  = 

1,000,000. 

Miles 
Railway- 
Operated. 

Revenue. 

I  =  $1,000,000. 

Divi- 
dends. 

Revenue  per  head. 

Rev. 

iSue. 

Pass. 

Fght. 

Total 

Net. 

Pass. 

Fght. 

Total 

1=  1,000 

1873 

74 

1. 124 
1.185 

1. 612 

1,639 

(5-9) 
6.27 

(10.3) 
10.48 

(16.2) 

16.77 

(9-3) 
9-85 

(2.6) 
3-25 

5. 26 

5-99 

9.17 
8.83 

14-43 
14.12 

10.2 
10.2 

1875 

1.246     j         1,790 

6.70 

15-74 

22.44 

12.23 

5-43 

5-39 

12.60 

17.99 

12.5 

1876 

77 

78...... 

79 

1-307 
1.368 
1.429 
1.490 

1,867 
3,109 
3,617 
3,663 

7.64 
7-89 
8.53 
8.86 

16.37    24.01 
16.56    24.65 
17.3s    26.88 
18.08    26.44 

"-75 
11.32 
12.97 
9-97 

4-53 
4-58 
(6.0) 
1.63 

5-85 
5-76 
5-97 
5-93 

12.50 
12.10 
12.07 
12.17 

18.35 
17.86 
18.04 
18.10 

12.9 
7-9 
7-4 
7.24 

1880 

1.551 

3,813 

8.82 

19.92    28.74 

10.79 

3-99 

5-68 

12.77 

18.45 

7-53 

1881 

1. 612 

5,418 

10. II 

26.43 

36.54 

18.64 

7-79 

6.28 

16.40 

22.68 

6.75 

Table  28. 

Main  Results  of  Operation  of  the   Railways  of  the  Entire  United 

States,  1871-1885. 


Year. 

Popula- 
tion. 

1,000,000. 

Miles 
Railway- 
Operated. 

Revenue. 

I  =  $1,000,000. 

Divi- 
dends. 

Revenue  per  head. 

Rev. 

MUe. 

Pass. 

Fght. 

Total 

Net. 

Pass. 

Fght. 

Total 

1=  1,000 

1871 

72 

73 

74 

39-585 
40.640 
41.722 
42.834 

44,614 
57,323 
66,237 
69,273 

108.9 
132-3 
137-4 
141. 0 

294.4 
340.9 
389.0 
379-5 

403 
465 
526 
520 

3 
2 

4 
5 

141-7 
165.8 
183.8 
189.6 

56.5 
64-4 
67.1 
67.0 

2.76 
3-24 
3-30 
3-30 

7-44 
8.40 
9-30 
8.85 

10.20 
11.64 
12.60 
12.15 

9.04 
8.10 
7.93 
7.53 

1875 

43-976 

71,759 

139-1 

364.0 

503 

I 

185.5 

74-3 

3.16 

8.27 

11-43 

7.02 

1876 

77 

78 

79 

45-147 
46.350 

47.585 
48.853 

73,508 
74,112 
78,960 
82,223 

136. 1 
125.2 
124.6 
142.3 

361. 1 
347-7 

365-5 
386.7 

497 
472 
490 
529 

3 
9 

I 
0 

186.5 
171. 1 
187.6 
219.9 

68.0 
58.6 
53-6 
61.7 

3.01 
2.71 
2.61 
2.92 

8.00 
7.50 
7.62 
7.92 

II. 01 
10.21 
10.23 
10.84 

12.25 

6.77 
6-39 
6.21 
6.42 

1880 

50.155 

84,225 

147.7 

467-7 

615 

4 

255-2 

77.1 

2-93 

9-32 

7-3T 

t88i 

82 

83 

84 

51.491 

52.863 

54.271 
55.717 

94,486 
95,752 
106,938 
113,173 

173.4 
188. 1 
206.8 
206.8 

552.0 
485-8 

544-5 
502.9 

725 
728 
807 
763 

3 
0 

I 
3 

276.7 
264.8 
291.6 
266.5 

93.3 
97-2 
101.6 
93-2 

3-37 
3-56 
3-80 
3-71 

10:72 
9.20 

10.02 
9.06 

14.09 
13.80 
14.82 
13-70 

7-67 
7.60 
7-54 
6.76 

^885 

57.202 

123,110 

200.9 

519-7 

765 

3 

266.5 

77-7 

3-50 

9.09 

13-38 

6.22 

CHAP.   IV.— PROBABLE  VOLUME   OF   TRAFFIC.  95 

86.  Experience  has  shown  that  the  probable  number  of 
TRAINS  PER  DAY  is  at  once  the  most  convenient  and  the  most 
exact  basis  for  arriving  at  estimates  of  probable  future  traffic, 
and  especially  expenses.  It  is  the  most  convenient,  because  it 
can  be  more  easily  and  more  correctly  anticipated  than  any  other 
item  of  future  business, — as  tonnage,  for  example, — and  also  be- 
cause we  use  the  same  unit  for  all  our  traffic,  both  freight  and 
passenger  ;  and  it  is  the  most  exact,  because  it  is  by  very  much 
the  most  uniform,  measure  of  operating  expenses,  the  cost  of  a 
train-mile  being  very  nearly  the  same  whether  the  trains  are  run 
full  or  empty,  or  long  or  short,  and  not  being  materially  differ- 
ent for  freight  or  passenger  service,  although  usually  less,  by 
one  third  to  one  fourth,  for  the  latter,  as  we  shall  see  hereafter. 

Assuming,  therefore,  this  basis  for  estimates,  it  may  be  al- 
ways anticipated  that  there  will  be  one  passenger  train  per  day 
each  way,  and  that,  unless  the  traffic  be  exceedingly  limited,  this 
train  will  be  exclusively  for  passengers.  Mixed  trains,  so  called, 
are  in  but  little  and  decreasing  favor  with  railway  managers,  al- 
though it  is  not  always  possible  to  avoid  them.  When  used  at 
all,  they  are  usually  nothing  more  than  freight  trains  under  an- 
other name — accommodations  for  a  few  passengers  being  added 
chiefly  as  a  convenience  to  special  classes  of  travel,  in  the  hope 
that  such  additional  convenience  may  have,  as  it  usually  does,  a 
favorable  influence  on  the  volume  of  travel.  With  freight  traffic 
of  course  no  such  motives  intervene  to  modif}?-  the  number  of 
trains,  so  that  mixed  trains  are  always  freight  trains  carrying  a 
few  passengers,  and  never,  in  regular  service,  passenger  trains 
carrying  freight. 

87.  Therefore,  under  the  most  unfavorable  circumstances 
there  are  pretty  sure  to  be  two  regular  trains  per  day,  one  pas- 
senger and  one  freight  or  "  mixed"  train,  over  lines  of  any  length. 
Less  than  this  is  certainly  never  contemplated  on  lines  built  as 
private  business  enterprises,  unless  on  very  short  branches  built 
as  feeders. 

88.  The  point  at  which  it  becomes  reasonable  to  anticipate 
running  two  regular  passenger  trains  daily  is  more  difficult  to  de- 
termine. 


96  CHAP.    IV.— PROBABLE  VOLUME   OF   TRAFFIC. 

In  the  Northeastern  third  of  the  United  States,  as  may  be 
seen  by  examining  any  railway  guide  only  a  very  small  propor- 
tion of  the  minor  branch  lines  run  only  one  passenger  train  a 
day,  and  but  a  very  few  of  the  lines  run  as  few  as  two  passenger 
trains  a  day.  In  the  North  Central  United  States,  including 
both  slopes  of  Mississippi  Valley,  two  passenger  trains  per  day 
may  be  said  to  be  the  rule,  exceeded  only  in  the  more  populous 
regions  and  on  the  important  trunk  lines  ;  but  only  a  small  pro- 
portion of  the  lines  run  as  few  as  one  train  a  day.  In  the 
Southern  and  extreme  Western  States  the  mileage  may  be  said 
to  be  about  equally  divided  between  one  train  oer  day  and  two, 
only  a  few  leading  lines  or  sections  of  lines  running  more  than 
two  trains  per  day.  In  England  and  on  the  Continent  the  aver- 
age number  of  passenger  trains  per  day  is  much  greater  than  in 
the  United  States,  except  in  the  extreme  Northeast :  but  this 
distinction  is  constantly  growing  less  with  the  rapid  increase  of 
population  and  wealth  in  the  United  States.  Tables  29  to  80 
give  many  statistics  of  the  average  number  of  trains  per  day  on 
single  roads,  and  in  groups  of  States. 

89.  There  are  immense  local  fluctuations  in  every  State  and 
Territory,  but  as  a  rule,  when  the  conditions  are  at  all  favorable 
for  the  development  of  passenger  travel,  a  minimum  of  two 
trains  per  day  may  be  looked  for  with  some  confidence.  This  is 
especially  probable  because,  in  order  to  encourage  and  develop 
traffic,  it  becomes  expedient  to  put  on  two  trains  a  day  long  be- 
fore a  single  train  becomes  so  crowded  as  to  actually  compel  it. 
The  greater  facilities  so  offered  are  almost  certain  to  add  a  con- 
siderable percentage  to  the  aggregate  travel  and  revenue  ;  and 
as  the  actual  additional  cost  of  the  extra  train  is,  on  the  contrary, 
but  a  small  percentage  of  the  average  cost  per  train-mile,  such  a 
train  is  almost  always  put  on  long  before  the  mere  statistics  of 
tickets  sold  begin  to  indicate  that  it  is  a  necessity.  It  is  impos- 
sible, in  fact,  until  the  volume  of  travel  becomes  large  and  the 
number  of  passenger  trains  at  least  two  or  three  per  day,  to 
make  any  attempt  to  regulate  the  number  of  trains  so  as  to  have 
them  run  full,  without  serious  injury  to  net  revenue. 


CHAP.   IV.— PROBABLE  VOLUME   OF   TRAFFIC. 


97 


90.  Beyond  three  or  four  trains  per  day  there  is  much  less 
necessity,  as  a  rule,  to  add  trains  to  accommodate  and  develop 
travel  until  the  seating  capacity  itself  becomes  too  small ;  this 
being  one  of  the  many  cases  in  which  "  the  destruction  of  the 
poor  is  their  poverty."  Nevertheless  the  results  of  experience 
with  even  the  heaviest  traffic  is  that  it  does  not  pay  to  scrimp 
train  facilities.  Certain  trains  carry  enormous  loads  and  bring 
up  the  average  materially,  but  a  multitude  of  trains  carrying 
much  lighter  loads  are  run  with  the  heaviest  traffic,  at  frequent 
intervals,  bring  about  the  close  correspondence  in  average  train- 
load  on  roads  of  widely  different  character,  shown  in  Table  29. 


Table  29. 

Average  Freight  and  Passenger  Train-Load,  Haul,  Train  Service,  etc., 
FOR  THE  United  States  and  Groups  of  States,  1885. 


Freight  Traffic. 

Passenger  Traffic. 

Aver- 

Train- 
Load. 

Aver- 

ag^e 

hIuI. 

Miles. 

No. 
Trains 

day. 

Miles 

per 

Engine. 

I  =  1000 

Ton- 
Miles 
per  Car. 

I  =  1000 

Aver- 

^^^^ 
Train- 
Load. 

Aver- 
age 
Haul. 

No. 
Trains 

Day. 

A.  New  England 

B.  Middle 

102 
179 
139 

125 
118 
148 
"5 

60 

145 
108 
103 
132 

159 
162 

3-74 
7.42 
4.44 
2-43 
2.31 
2.17 
2.13 
1. 81 

19.8 
21.3 
26.3 
19.8 
21.0 
20.6 
17.9 
14.4 

42.4 
53-9 
72.8 
60.9 
61.3 
58.  J 
69.6 
51.8 

59 

443^ 

38^ 

32 

43 

36 

47^ 

69^ 

16 

18^ 

37% 

48 
49 
60 

31^ 

4-52 
4.64 
2-33 
1.52 
1.64 
1.36 
1. 21 
1-35 

C    No.  Central 

D.  So.  Atlantic 

E.  Gulf  and  Miss.  V.   ... 

F.  So.  Western 

G.  No.  Western 

H.  Pacific 

Total  U.  S.,  1885... 
"       1884... 
"       1883... 
"       1882... 

143 
134 
126 
129 

112 
112 
no 
109 

3-8i 
4.05 
4.48 
5.32 

21.6 
22.1 
22.8 
21.3 

57-4 
56.0 
56.6 
53-8 

43^ 
423^ 
46M 
45^ 

26 
26M 
27M 
26 

2.36 
2.51 
2.41 
2-37 

U.S.  Census,  1880.. 

129 

III 

3-91 

22.4 

41^ 

21 

2.16 

Excepting  the  figures  for  1880  from  the  U.  S.  Census,  the  above  is  computed  from  the 
statistics  of  Poor's  Manual.     In  this,  as  in  all  other  tables  in  this  volume,  the  railroad 
year  is  taken  at  365  days,  owing  to  the  regrettable  fact  that  the  distinction  between  Sun- 
day and  week  days  is  fast  disappearing.     The  ' '  number  of  trains"  always  means  each  way. 
7 


98 


CHAP.    IV.— PROBABLE  VOLUME   OF   TRAFFIC. 


Table  31. 

Statistics  of  Passenger  Traffic,  Lake  Shore  & 
Michigan  Southern   Railway,  1870-1885. 

2 

< 

pL, 

0 

IT) 

^       0       0         M 

vo      in    10     t^ 

6    6    6    6 

6 

6606 

0 

00     in     w      ^ 
r^   CO      r^   0 

d     0     d     d 

m 

0 

1     " 

m 

N       0        N       N 
N       <N        <N       ro 

^ 

^_    2  c^  5. 

M       M       6       6 

On 

d 

8   8   S^ 

H          H          0          0 

6 

^ 
^ 

00      t>.     t>.    0 

hi         M         H         CJ 

?- 

0       >n     H       fO 

00 

t^    ^O        0       w 

t^    00      t-.    in 

% 

t: 

a  ^v?  'g^ 

t?> 

^       ^       ^      ^ 

in 

^  s  s  s. 

in 

Ci 

i 

irt    m   00     t^ 

S    ^    3    ^ 

^ 

r^    00      00       fO 

^      in     in   vo 

.g^ 

ej      d      rn     in 
t^    t>   \o      in 

00 

d 

g.is8 

g 

S     5-    K    S 
cT    cT    fT    cT 

t^ 

cT    cT    cT    w 

S 

0      t^     ro     0 

H      n    0    <o 

On     C^      -<»•      'i- 
cT     ro     ro     M 

1 

< 

00 

t^    t^    t^    t^ 

in 

CO 

VO       t^    00       Ov 

t^    t^    t^    i> 

00 

d  ^  ^  ^ 

: 
f 

Table  30. 

Statistics  of  Freight  Traffic,    Lake   Shore  & 
Michigan  Southern  Railway,  1870-1885. 

2 

< 

cs: 

a 

MS 

2 

M       0         H         ■* 
VO      "O       >A    VO 

0660 

6 

^     m    in    in 

dodo 

d 

m  CO    00    vo 
m     in    vq      in 

d     d     d     d 

d 

°  °  "  - 

N 

N         M          M         W 

q     w     0     ON 

M          H         H          d 

" 

On     t»-    ^       in           M 

q     0     q     q        q 

1  "^ 

Pi -53 
0 

=°  ~  ^  ~ 

o\    ^^    m    0 
T»-  >o     in    vo 

~ 

-J-    in    •*    H 

vo     vo       t-.    'O 

J 

2 

2^1    g    2^ 

CO 

8    ?  S    ?? 

c< 

is?? 

8 

^ 

ro    •<«■   vo      0\ 
m     rrj     m    ;d 

s 

-: :-  s  .- 

J^ 

M     ov    m    tn 
N      c<      w      « 

2  A  c«  8 

bxi.S  w  0 

! 

58    1  \  1 

»o    tC  of  >o' 

4 

m    0     t~    o\ 

tC  tc;  tC  10 

5 

< 

1 

H     ci     CO    ■>*■ 

C^      bs     t^     t^ 

00 

U3        !>.     03        0 

t^     t>.     r^     t~. 

1 

d  d  ^  d 

f 

CHAP.   IV.— PROBABLE  VOLUME    OF   TRAFFIC. 


99 


Table  32. 
Traffic  Statistics,  Lake  Shore  and  Michigan  Southern  Railway 


Miles 
Road. 

Per  Mile  Operated. 

Dividends. 

Year. 

Earnings. 

Expenses 
and  Taxes. 

Net 
Earnings. 

Earned. 

Paid. 

1870   

1,013 

13,336 

8,261 

5,075 

9.60 

8.00 

71    

1,074 
1,136 
1,154 
1,178 

13.872 
16,682 
16,824 
14.592 

9,106 
11,177 
11,928 

9,491 

4,766 
5,505 
4,896 
5,101 

8.37 
8.55 
6.10 
6.04 

8.00 

72 

8.00 

73...-" 

74. 

4.00 
3-25 

1875 

1,178 

12,284 

8,963 

3.321 

2.20 

3.26 

3-57 
5.61 
7.24 

2.00 

76 

77....-.- 

78 

1,178 
1,178 
1,178 
1,178 

11,851 
11,484 

11,877 
12,975 

8,135 
7,622 
7.210 
7.591 

3.716 
3.862 
4.667 

5.384 

3-25 
2.00 
4.00 

7Q     

6.50 

1880 

1,178 

15,922 

8,846 

7,076 

11.28 

8.00 

81 

1,178 
1,274 
1,340 
1,340 

15,261 
14,306 
13,817 
11,075 

9.577 
8,679 
8,211 
6,815 

5,684 
5.627 
5,606 
4,260 

8.02 

8.37 
8. II 
4.02 

8.00 

82 

8.00 

8c?    

8.00 

84 

5.00 

1885 

1.340 

10,545 

6,929 

•     3,616 

1.98 

The  Lake  Shore  and  Michigan  Southern  Railway  being  one  of  the  few  im- 
portant lines  which  have  been  operated  under  substantially  similar  conditions 
and  with  substantially  the  same  mileage  and  motive-power  for  fifteen  years,  its 
statistics  have  an  especial  interest,  and  Tables  30,  31,  and  32  are  added  for 
that  reason. 


It  is  not  expedient,  nor  indeed  possible,  therefore,  to  base 
estimates  of  the  probable  number  of  passenger  trains  on  esti- 
mates or  statistics  of  the  probable  number  of  passengers  to  be 
carried,  further  than  to  assume  that  the  smaller  the  traffic  the 
smaller  will  be  the  average  number  of  passengers  per  train. 

91.  The  same  is  true,  in  less  degree,  even  of  estimates  of  the 
probable  number  of  freight  trains.  It  is  not  correct  to  assume  a 
certain  tonnage  to  be  moved,  divide  that  by  the  load  of  a  car  to 
get  the  number  of  loaded  cars,  divide  that  again  by  the  number 
of  cars  per  train,  and   so  get  the  number  of  trains.     There   is 


100 


CHAP.   IV,— PROBABLE  VOLUME  OF   TRAFFIC. 


always,  in  the  first  place,  a  certain  wastage  of  capacity  amount- 
ing to  anywhere  from  ten  to  thirty  per  cent,  according  to  cir- 
cumstances, which,  if  the  traffic  is  to  be  estimated  on  the  basis 
of  tonnage,  must  be  allowed  for.  This  wastage  also,  as  with 
passenger  business,  is  a  much  less  serious  matter  on  lines  of  large 
traffic,  especially  those  with  a  heavy  excess  of  tonnage  in  one  di- 
rection; for  in  this  case,  although  the  average  car-load  in  both 
directions  is  much  reduced,  yet  in  the  direction  of  heaviest  traf- 
fic the  obtaining  of  full  loads  is  facilitated.  A  very  heavy  dis- 
proportion of  traffic,  from  three  or  four  to  one,  exists  on  nearly 
all  east  and  west  lines  in  the  United  States  ;  and  most  of  them 
succeed  in  filling  up  their  average  car-load  and  train-load,  in  the 
direction  of  the  heaviest  traffic,  to  very  nearly  its  nominal  ca- 


Table  33. 
Growth  of  Average  Freight-Train  Load  of  Various  Roads, 

1873   TO    1885. 


New  York  Trunk  Lines. 

Minor  Trunk  Lines. 

Year. 

N.Y. 
Cent. 

N.  Y., 
L.  Erie 
&W. 

Penna. 

B.  & 

Alb. 

Del., 

Lack. 
&W. 

Can. 

So. 

Mich. 
Cent. 

Pitts., 

Ft.  W. 

&C. 

P.,C. 

& 

St.  L. 

129 
139 

Ill 

122 

75 
81 

88 
89 

89 
103 

79 

166 

134 

128 

82 

83 

135 

06 

98 

76  

180 
166 
186 
191 

138 
145 
146 
185 

132 
137 
154 
170 

87 
88 
92 
94 

83 
78 
93 
77 

155 
190 

147 
158 
167 
195 

97 
96 
116 
120 

116 

129 

78..  

140 

156 

80 

219 

211 

184 

97   

208 

201 

125 

166 

81 

218 
219 

2CX) 

196 

218 
228 

211 
213 

184 
189 

189 
205 

102 
104 

103 
106 

90 
86 

99 
99 

275 

186 

172 

132 

132 

131 
139 

155 

82  

165 

8^ 

184 
198 

160 

84. 

161 

85 

204 

227 

209 

109 

107 

202 

138 

182 

CHAP.   IV.— PROBABLE  VOLUME   OF   TRAFFIC. 


lOI 


pacity.  Nevertheless,  even  on  such  lines,  fluctuations  and  irreg- 
ularities of  traffic  are  always  so  great,  that  it  is  no  infrequent 
spectacle  to  see  trains  running  light  in  the  direction  of  heaviest 
traffic  ;  and  the  difficulty  of  fully  filling  up  trains,  of  course,  be- 
comes much  greater  as  the  tonnage  is  less,  or,  as  already  stated, 
when  it  is  nearly  equal  in  each  direction.  There  is  also  always 
one  train  per  day,  the  way-freight,  which  averages  little  more 
than  one  half  an  ordinary  train-load,  owing  to  the  irregular 
service. 


Table  33. — Continued. 

Pennsylvania  Railroad,  by  Half-decades. 
<For  the  figures  for  each  year,  and  for  direction  of  heaviest  traffic  only,  see  Index.) 


t853-5. 

1856-60. 

1861-4. 

1865-70. 

1871-4. 

1876-80. 

1881-5. 

75-4 

83.2 

94-3 

104.4 

116. 8 

155-5 

196.0 

These  figures  not  unfairly  represent  the  general  law  of  growth  in  train-load  in  the  past 
.30  years  under  favorable  conditions. 


Year, 


1873- 
74- 
75- 
76. 
77- 
78. 
79 
80. 
81. 
82. 
83- 
84. 
85- 


Chicago  Roads. 


111. 
Cent. 


83 
94 
90 
97 
97 
112 
115 
no 
103 
120 
100 
120 
116 


C, 
R.  I. 
«&P. 


119 

81 

124 

80 

142 

99 

139 

85 

95 
107 
104 
109 
106 
105 
105 


Ch.  & 

Alt. 


138 
161 
177 


190 
184 


CM. 

& 
St.  P. 


C.& 
N.W. 


107 
101 
99 
108 
no 
122 
122 
132 
132 
132 
121 
126 
132 


Minor  Western  Roads. 


0.& 

M. 


115 
121 

133 
129 
107 
126 
103 
152 


L.  & 

N. 


137 


cc 

C.  &I. 


90 

99 
112 
122 
191 
205 
218 
205 
212 


Wise. 
Cent. 


Below  the  cross-fines  in  the  second,  third,  and  fifth  columns  there  was  a  large  increase 
of  mileage  operated,  as  also  in  some  cases  not  marked.  Most  of  the  other  cases  in  which 
the  train-load  has  decreased  are  due  to  a  falling  off  in  total  ton-mileage. 


102  CHAP.    IV.— PROBABLE  VOLUME   OF   TRAFFIC. 


The  enormous  increase  in  average  freight-train  loads  which  has  taken  place 
in  recent  years,  without  any  considerable  changes  of  grades,  and  often  without 
much  change  in  the  motive-power  likewise,  is  shown  in  Table  33,  as  also  in 
Table  30  and  others.  \ 

92.  Nevertheless,  it  still  remains  true  that  in  the  main,  ex- 
cepting the  "  way-freight,"  the  freight  traffic  can  be  and  is  regu- 
lated in  close  accordance  with  the  volume  which  offers  from  day 
to  day.  So  many  freight  trains,  usually  from  two  to  six,  are  put 
upon  the  time-table.  If  more  are  needed,  ''extras" — a  train  run- 
ning behind  another  train  and  "on  its  time,"  but  with  a  certain 
number  of  minutes'  interval — are  added,  sometimes  to  the  num- 
ber of  a  dozen  or  twenty,  and  very  frequently  from  two  to  six; 
the  leading  train,  and  each  succeeding  "  extra"  except  the  last, 
carrying  a  red  "  flag"  as  a  signal  that  another  train  having  its 
time-table  "  rights"  is  following. 

On  the  other  hand,  if  less  trains  are  needed  than  appear  on 
the  schedule,  such  and  such  trains  are  abandoned  for  the  day — 
often  for  days  and  weeks  together,  even  when  other  trains  are 
running  extras.  A  near  approach  to  conditions  which  actually 
obtain  in  practice  will  be  given  by  assuming  that  the  number  of 
daily  freight  trains  will  always  be  one  more  than  is  nominally 
required  by  the  tonnage,  and  often  more,  the  office  of  the  extra 
trains  being  simply  to  serve  as  equalizers. 

93.  The  time-table  or  schedule,  in  fact,  is,  as  regards  freight  traffic,  nothing 
more  than  a  row  of  hooks  to  hang  the  trains  on  as  required.  If  one  or  a  dozen 
of  the  hooks  stand  empty,  no  great  harm  is  done.  As  trains  come  in  or  are 
made  up,  they  are  started  off  as  either  "regulars"  or  "extras"  indifferently — 
whichever  will  give  quickest  despatch  ;  some  little  effort  being  made  indeed  to 
send  out  at  least  one  train  on  each  schedule  train's  time,,  on  account  of  the 
practical  inconvenience  and  danger  of  frequent  abandonment  of  trains  ;  but  the 
chief  purpose  in  preparing  freight  schedules  is  not  to  give  a  separate  time  to 
each  train,  which  are  often  behind  time,  but  to  afford  an  established  method 
for  despatching  regular  trains  promptly  at  any  hour  desired.  More  or  less  uni- 
formity naturally  prevails  in  the  business  from  day  to  day,  but  there  is  also 
much  irregularity. 

On  the  crowded  Eastern  division  of  the  Erie,  running  often  a  hundred  trains 
per  day,  there  are  but  two  regular  scheduled  trains,  one  for  a.m.  and  one  for 
P.M.,  and  all  others  are  run  as  sections  of  this  train. 


CHAP.   IV.— PROBABLE  VOLUME   OF   TRAFFIC.  I03 

94,  It  should  be  mentioned  also  that,  in  attempting  to  draw  conclusions  as 
to  probable  traffic  from  statistics  as  to  "miles  run  by  freight  trains"  on 
neighboring  roads,  such  statistics  must  be  accepted  with  the  greatest  caution. 
An  unfortunate  custom  exists  of  comparing  locomotive  expenses  on  the  basis 
of  the  engine-mile  instead  of  the  car-mile,  and  as  a  consequence  a  habit 
has  arisen  among  master  mechanics  and  other  officers  of  exaggerating  the 
switching  mileage  (which  is  heavy  enough  at  best)  in  every  possible  manner,  by 
heavy  allowances  for  switching  at  stations,  and  for  running  to  and  from  the 
round-house.  Instances  might  be  given  in  which  the  excess  of  this  nominal 
mileage  over  that  actually  run  between  termini  amounted  to  nearly  one  fifth, 
independent  of  the  usual  and  regular  switching  allowance  of  so  many  miles  per 
hour  to  switching  engines  proper,  which  is  separately  given.  This  fact  is  im- 
portant to  remember  not  only  in  estimating  the  volume  of  traffic,  but  also  in 
estimating  locomotive  expenses  ;  for  most  roads  make  more  or  less  allowance 
for  mileage  outside  of  the  regular  revenue  distance,  and  it  is  always  more  or 
less  deceptive,  consequently,  to  use  such  data  uncorrected  for  estimates  of  cost 
per  revenue  train-mile.  Whenever  there  is  a  marked  discrepancy  in  the  cost 
per  train-mile  on  similar  roads  this  cause  may  with  some  confidence  be  regarded 
as  the  true  explanation.  Some  reasonable  approach  to  a  correct  estimate  of  the 
probable  traffic  can  thus  be  made,  by  a  little  effort,  from  published  statistics  of 
various  roads  and  towns,  unless  in  a  region  which  is  entirely  new  to  the  rail- 
ways, or  for  other  exceptional  causes.  The  following  statistics  will  also  be  of 
assistance: 

95.  The  average  payment  to  railroads  of  each  man,  woman, 
and  child  in  the  United  States  now  averages  about  $13.50,  of 
which  about  $3.50  is  for  passenger  transportation  and  f  10  for 
freight.  Table  34  and  several  others  (see  Index)  give  further 
statistics  for  various  groups  of  States,  but  the  fluctuations  from 
such  averages  are  of  necessity  great.  Points  which  are  centres 
of  manufacturing  and  transportation  interests  will  have  a  many 
times  greater  traffic  than  this  to  dispose  of  ;  while,  on  the  other 
hand,  there  are  few  local  stations  which  will  fall  very  far  below 
it,  the  great  excess  of  the  few  points  being  compensated  by  the 
great  multitude  of  small  deficiencies. 


104 


CHAP.   IV.— PROBABLE  VOLUME   OF   TRAFFIC. 


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CHAP.   IV.— PROBABLE  VOLUME   OF   TRAFFIC. 


105 


Table  34. — Continued. 
Foreign  Countries. 


1876  ... 
1880-1. . 
1880  .. 
1880  . . . 
1881..   . 

1876-80. 


Great  Britain  and  Ireland. . . 

France 

Austria 

Italy 

Mexico  (one  railway  only).. . 

So'n  U.  S.  (E.  of  Miss.  Riv.), 
N.  and  W.  U.  S 

Total  U.  S 


Miles. 

16,658 

15)227 

7,086 

5,418 
293 


66,714 


78,606 


Pass. 
5-19 


1.78 
0.55 
0.06 


(Total  of  all  earnings,  S9.20), 


0-93 
3-35 


2.84 


5.66). 
5.28). 
I-33)- 
0-53)- 


3.80). 
12.98). 


10.91). 


Fr'ght 
4.01 


From  the  above  statistics  we  may  conclude  that  the  average  revenue  to  railways  from 
each  inhabitant  of  the  different  sections — bearing  in  mind  that  much  of  the  trunk-line 
freight  traffic  credited  to  the  Middle  States  is  in  reality  a  part  of  New  England  and 
Western  payments — is  (average  of  1880-85)  about  as  follows  : 


New  England  States 

Middle  States 

Pass. 

$5.00 

3-50 
3.00 
5-50 

Freight. 

$8.00 

11.00 
11.50 
14.00 

Total. 

$13.00 

14.50 
14.50 
19.50 

Ranging  from 
$6.50  to  $16.50 

4.08  to    28.10 

Western  and  Southwestern  States 

Pacific  States 

Average  of  all  Northern  and  W'n  States. 

3-50 
1. 00 

11.00 
3-50 

14-50 
4-50 

Southern  States  (E.  of  Miss.  River) 

Average  of  the  entire  U.  S 

3.00 

9.00 

12.00 

The  fluctuations  from  year  to  year  hardly  exceed  10  to  15  per  cent  more  or  less  of 
these  averages.  There  is,  however,  a  gradual  yearly  growth  in  the  payments  per  inhabi- 
tant amounting  to  an  average  of  perhaps  one  per  cent  per  annum,  due  largely  to  causes 
considered  in  Chapter  XXI. 

The  fluctuations  in  the  average  payments  of  difl'erent  localities  are  no  doubt  ex- 
treme, as  may  be  seen  from  the  statistics  in  other  tables.  The  State  of  Florida  pays  but 
$1.60  per  annum  to  its  railways.  The  larger  Eastern  cities,  probably  $30  per  head  at 
least.  There  are  doubtless  considerable  sections  of  each  of  the  States  in  the  above  groups 
where  the  payments  may  be  as  low  as  half  or  as  high  as  double  the  average  for  the  whole 
group  of  States.  The  trunk-line  export  traflic  constitutes  only  an  insignificant  fraction 
of  the  total  revenue  of  United  States  railways,  large  as  it  is  absolutely. 


CHAPTER  V. 


OPERATING    EXPENSES. 


96.  We  may  gain  a  profitable  insight  into  the  general  nature 
of  the  causes  which  modify  operating  expenses,  and  especially 
of  the  effect  thereon  of  differences  of  alignment,  by  first  consid- 
ering them  in  a  very  general  way,  neglecting  all  detail. 

We  have  previously  (Chap.  II.)  compared  the  railway  to  a  great 
manufacturing  establishment — manufacturing  transportation. 
Its  operating  expenses,  to  carry  out  the  analogy,  should  be  only 
another  name  for  the  total  cost  of  producing  the  commodities 
which  it  sells  ;  but  as  a  matter  of  fact  this  is  not  the  case.  The 
interest  or  "  rental "  charge  on  its  real  estate,  and  on  most  of  its 
machinery  and  plant — the  heaviest  single  item  by  far  in  the  real 
"operating"  or  manufacturing  expenses — is  never  included  in 
what  are  called  the  operating  expenses,  but  constitutes  the  fixei> 
CHARGE  for  interest  on  bonds  (see  Figs,  i,  2,  3).  Counting  in 
the  "  fixed  charges"  as  part  of  the  "  operating"  or  manufacturing- 
expense,  the  latter  never  amount  to  much  less  than  80  per  cent, 
and  from  that  to  considerably  over  100  per  cent,  for  long  periods 
of  time.  The  average  for  the  whole  United  States  is  somewhat 
under  90  per  cent,  leaving  but  little  more  than  10  per  cent  profit 
on  the  goods  sold  to  be  distributed  to  the  managing  companies. 
Under  favorable  circumstances  this  profit  is  as  much  as  15  or 
20  per  cent ;  very  rarely  more.  Tables  35  and  ^6  give  a  clearer 
idea  of  the  law  in  this  matter. 

97.  As  these  fixed  charges  increase  in  somewhat  faster  ratio 
than  the  cost  of  construction,  and  are  the  same  per  year  whether 
the  business  be  large  or  small  or  none  at  all,  the  great  impor- 
tance of  (i)  diminishing  the  expenditure  for  construction  as  much 


CHAP,   v.— OPERATING  EXPENSES. 


107 


Table  35. 
Stock  and  Bonds  Per  Mile  of  Road  by  Sections  of  the  United  States. 


Groups  of  States, 

Miles. 

Stock  and  Bonds  Per  Mile. 

I  =  $1,000. 

Revenue 

per  Mile. 
I  =  $1,000. 

Stock. 

Bonds. 

Other  D't. 

Total. 

New  England 

5,910 
14,942 
12,978 
46,102 

4.461 

31.6 
47.5 
15.8 
24.8 
33-2 

21.5 
49-3 
19.2 
22.7 
35.8 

2.75 
2.87 
1.37 
1.48 

2.58 

55-85 
99-67 
36.37 
48.98 

71.58 

8   00 

Middle 

13-30 
3-56 
6.34 

7.53 

Southern 

Western 

Pacific 

United  States 

Canada 

84,393 

28.4 

27-3 

1.86 

57.76 

7-31 

, 

1885. 

New  England 

6,412 

18,595 
20,584 

74,854 
7,284 

31.8 

57.3 
20.2 
25.2 
34.0 

21.9 
53-6 
24.6 
25.6 
28.5 

2.46 
4.87 
1.20 
1.49 
2.20 

56.16 

115-77 
46.00 
52.29 
64.70 

8.87 

11-53 
3.66 

5-25 
4-55 

Middle   

Southern 

Western 

Pacific   

United  States 

1884. 

127,729 

39-9 
30.1 
30.8 
30.7 

29  5 
29-3 

28.7 
28.3 

2.03 
2.0 
1.9 
1-9 

61.43 
61.4 
61.4 
60.9 

6.22 
6.76 

7-54 
7.60 

i88q 

"            1882  

The  nominal  cost  of  road  and  equipment  for  the  whole  United  States  was  for  these 
years : 

1882.  1883.  1884.  [885. 

$52,790  $55,500  $55,300  $55,100 

The  Canadian  railways  average  but  $11,000  of  bonds  per  mile,  and  $58,230  of  stock 
and  bonds  together.  Excluding  the  Grand  Trunk,  which,  with  26  per  cent  of  the  mileage, 
has  45  per  cent  of  the  capital,  there  are  only  $28,000  per  mile  of  both  stock  and  bonds. 
More  than  one  fourth  of  the  total  capital  (145  millions  out  of  558,  for  9,575  miles,  in  1884) 
was  contributed  from  governmental  sources.  Earnings  are  correspondingly  small,  being 
for  1884 : 

Canada  Southern,  )  ^^^^^  j^^jj^g  \  $10,600  per  mile. 

Grand  Trunk,         '    '  (      6,290  "       " 

36  remaining  lines,  6,625    "  2,010  "      " 


9»575  miles,       3,491  per  mile. 


io8 


CHAP,  v.— OPERATING  EXPENSES. 


Table  36. 
Distribution  of  Gross  Revenue,  in  Per  Cent  of  Total  Receipts. 

1880. 


Per  Cent  of  Receipts  Devoted  to— 

Groups  of  States. 

Op'g  Exp. 

Net  Rev. 

Interest. 

Dividends. 

New  Ensrland 

68.1 
62.4 
63-5 
53-9 
50.2 

31-9 
37.6 
36.5 
46.1 
49.8 

11.25 
19-33 
16.84 
16.98 
23-05 

16.83 

Middle   

14.24 

7-43 

Western   

11.72 

Pacific 

14.50 

Total  U.  S 

58.3 

41.7 

17.58 

12.55 

1885. 


New  England 

69.8 
64.7 
67.3 
65.0 

55-7 

30.2 
35-3 
32-7 
35.0 
44.3 

13-53 
27-56 
27.14 
22.24 
45-00 

16.10 

Middle 

13.92 
3.40 

Southern     

Western 

Pacific 

9.06 
4-57 

Total  U.  S 

65.1 

34-9 

24-52 

10.05 

United  States  for  each  Year  from  1879  to  1885. 


1879- 
1880. 
1881. 
1882. 
1883 
1884. 
1885. 


21.18 
17.58 
18.32 
20.02 
21.00 
22.90 
24.52 


11.72 
12.55 
13-30 
13.23 
12.38 
12.09 
10.05 


as  true  economy  permits,  and  (2)  increasing  the  traffic  (sales)  so 
that  this  burden  may  constitute  a  less  percentage  of  the  entire 
business,  is  evident.  Omitting  them,  the  operating  expenses 
PROPER  (corresponding  to  the  expenses  of  simply  running  and 
maintaining  a  factory  which  has  once  been  thoroughly  equipped, 
and  of  selling  the  manufactured  products)  amount  usually  to 


CHAP,    v.— OPERATING  EXPENSES.  109 

about  two  thirds,  or  67  per  cent,  of  the  receipts,  varying  however 
enormously  (from  but  little  over  50  to  more  than  90  per  cent) 
with  different  roads.  Table  37  and  others  give  an  idea  of  the 
general  tendency  for  a  long  period  of  years. 

As  the  ratio  of  expenses  to  receipts  may  be  made  less  either 
by  the  receipts  being  larger  or  the  expenses  being  smaller,  the 
fact  that  the  ratio  is  low  or  higli  is  no  real  test  of  economy  in 
operation,  nor  of  the  value  of  the  property.  Wherever,  from 
absence  of  competition,  the  rates  are  very  high, — as  formerly 
on  the  Pacific  railways,  Panama  Railroad,  and  many  lines  in 
Europe, — this  ratio  will  be  small,  even  in  the  face  of  heavy  ex- 
penses. Wherever  all  or  nearly  all  railways  have  been  very 
costly,  as  largely  throughout  Europe,  it  will  also  be  small,  since 
the  fixed  charges  will  constitute  a  larger  proportion  of  the  tax 
on  earnings,  and  rates  will  naturally  adjust  themselves  to  pay  (i) 
all  operating  expenses,  (2)  all  rental  or  fixed  charges,  and  (3)  a 
fair  profit  to  the  managing  company. 

Wherever  several  lines  are  so  situated  that  their  business  is. 
largely  competitive,  and  must  be  handled  at  the  same  gross 
price,  but  one  or  more  of  them  has  better  grades,  or  a  shorter 
line,  or  more  traffic,  or  other  special  advantages,  one  line  will 
permanently  show  a  lower  percentage  of  expense  than  the  others, 
which  will  have  no  meaning  as  an  indication  of  real  excellence 
of  management.  This  latter  law  is  strikingly  illustrated  by  the 
trunk-line  percentages  in  Table  37,  the  cause  for  the  differences 
in  which  is  explained  in  a  following  note  and  in  Chap.  XXI. 

98.  The  operating  expenses  proper  are  very  irregularly 
affected  by  the  amount  of  business  or  by  the  character  of  the 
alignment.  A  very  large  proportion  of  them  are,  like  the  rental 
or  fixed  charges,  independent  of  both  :  such  as  the  salary  of  the 
president  and  other  officers  ;  maintenance  of  works  and  plant 
against  the  deterioration  which  comes  with  time,  irrespective  of 
work  done  ;  salaries  of  local  freight  and  passenger  agents,  a 
large  proportion  of  whom  must  be  employed  anyway,  whether 
considerable  sales  are  made  or  not.  This  immense  class  of  the 
expenses  amounts,  as  we  shall  see,  to  nearly  one  half  of  the 


no 


CHAP,    v.— OPERATING  EXPENSES. 


Table  37. 
Percentage  of  Operating  Expenses  to  Revenue. 


Trunk  Lines. 

Sections  of  U.  S. 

N.Y.C. 

Erie. 

Penn. 

B.&O. 

N.  E. 

Mid. 

w.  & 
s.w. 

So. 

Pac. 

Av. 
U.S. 

1849-50. 

1851-55- 
1856-60. 

1861-65. 
1866-70. 

1871-75- 
1876-80. 

56. O2 

57.1 
68.0 
69.7 
63.1 
61.3 

51.64 

66.4 

64.6 

76.2 

71-3 
70.0 

45-0 
62.5 

58.8 
60.1 
71.0 

59-7 

55-7 

! 

58.82 
53-9 

Nos 

68.63 
659 

tatisti 

59-63 
59-7 

cs  ava 

(64-7)3 
(61.2) 

liable. 

66.63 
65.8 

43.83 
56.5 

64.2 
60.9 

I88I.... 

1882.... 
1883.... 
1884.... 
1885.... 

65.1 
67.9 
66.1 
67.6 
72.8 

64.0 

65-5 
67-7 
75-6 
75.8 

56.0 
58.0 
57-2 
58.2 
62.2 

56.4 
56.7 
53-1 
54-5 
59-2 

68.6 
70.7 

74-5 
71.8 
69.8 

63.0 
64.8 
64.0 
65.5 
64.7 

58.2 

51-2 

63.2 
64.2 
65.0 

67.4 
66.7 
66.5 
65.5 
67.3 

55-5 
63.6 
63.0 
60.2 

55.7 

61. 1 

63.6 
63.8 
65.2 
65.1 

I88I-5.. 

67.9 

69.7 

58.3 

56.0 

71. 1 

64.4 

60.4 

66.7 

59.6 

63.8 

United  Kingdom 1876  54-6 

Prussia 1879  54.3 

Italy 18S0  68.0 

Spain 1880  61.5 

India 1880  51.0 

Subscript  figures^  i,  a,  etc.,  indicate  the  number  of  years  for  which  the  average  is 
given  when  less  than  5.  The  group  of  States  are  those  of  Poor's  Manual  for  the  years 
before  1886. 

From  the  above  table  we  may  conclude  that  no  marked  tendency  exists  to  increase  or 
diminish  the  ratio  of  receipts  to  operating  expenses,  both  of  which — as  may  be  seen  from 
other  tables — have  a  tendency  to  fall  rapidly  and  about  equally. 

The  fluctuatio7is  of  individual  lines  in  respect  to  this  ratio  are  often  extreme,  as  may 
be  seen  even  with  the  trunk  lines,  and  rarely  affords  any  trustworthy  indication  of  efficiency 
of  management,  the  cause  almost  always  lying  deeper,  and  being  incapable  of  essential 
modification  by  any  skill  of  management  without  change  of  external  conditions.  Thus  the 
Pennsylvania  Railroad,  having  the  shortest  haul  (and  consequently  the  highest  receipts 
per  mile)  on  traffic  between  almost  all  points  in  the  West  and  the  Atlantic  coast,  will  forever 
maintain,  under  equal  skill  in  management,  a  ratio  of  receipts  to  expenses  from  10  to  15 
per  cent  higher  than  the  Erie.  The  New  York  Central  would  compare  still  more  un- 
favorably in  this  respect  except  that  the  enormous  volume  of  its  local  traffic  favorably 
modifies  its  average,  which  will  on  this  account,  under  existing  conditions,  be  always  more 
favorable  than  the  Erie.  The  low  ratio  of  the  Baltimore  &  Ohio,  as  respects  the  Penn- 
sylvania, is  due  almost  exclusively  to  the  greater  relative  volume  of  its  coal  traffic,  which 
is  always  carried  in  full  trains  at  low  cost.  The  same  effect  is  still  more  strikingly  visible 
in  table  giving  the  history  of  the  Philadelphia  &  Reading  Railroad.  See  Index,  and 
Chapter  XXI,,  pars.  973-4. 


CHAP,   v.— OPERATING  EXPENSES.  Ill 

operating  expenses  proper — the  other  half  only  varying  more  or 
less  closely  with  the  details  of  the  line  and  grades,  and  very 
much  less  than  half  with  slight  changes  in  volume  of  traffic. 

99.  Therefore,  it  may  be  said  in  a  general  way  that  ten  per 
cent  added  to  revenue  is  as  good  as  fifteen  per  cent  taken  off 
operating  expenses  ;  and  this  again  means  thirty  per  cent  taken 
off  that  portion  of  the  operating  expenses  which  varies  with 
line  and  grades.  To  gain  or  lose  ten  per  cent  in  revenue  by 
slight  differences  in  the  route  selected  is  very  easy.  To  reduce 
the  whole  operating  expenses  fifteen  per  cent  by  differences  in 
alignment  which  do  not  increase  the  cost  of  construction,  is  not 
so  easy.  Let  us  illustrate,  by  examples  free  from  detail,  the  very 
important  moral  conveyed  in  these  facts.  We  will  assume  the 
case  of  a  fairly  prosperous  line  of  the  second  grade,  whose  in- 
come and  outgo  we  shall  find  may  be  distributed  in  something 
like  the  following  manner  : 

Per  Cent.       Per  Mile. 

Gross  revenue, loo.o  $7,ooo 

Operating  expenses,  unaffected  by  either  alignment  or 

volume  of  traffic  (50  p.  c.  of  operating  expenses),     .     33.3  $2,333 

Ditto,  increasing  directly  with  considerable  changes  in 

alignment  or  volume  of  traffic,  but  not  with  trifling 

changes  (40  p.  c), 26.7  1,867 

Ditto,  increasing  directly  with  the  less  i7nporta7it  changes 

in  alignment  or  traffic  (10  p.  c), 6.']  467 

Total  of  nominal  operating  expenses, 66.7  $4,667 

Add  to  the  latter  the  rental  or  interest  charge  (6  p.  c.  on 
$30,000  per  mile,  assumed  cash  cost  of  road  and 
plant), 25.7  1,800 

Total  of  true  operating  expenses,  or  cash  cost  of 

producing  the  transportation  sold, 93.4  $6,467 

Surplus   available   for   dividends    being    the    business 

profit  resulting  from  operation, 'j.6  $533 

Let  us  now  see  the  effect  of  increasing  or  decreasing  the 
gross  revenue  ten  per  cent,  as  it  is  frequently  possible  to  do  (one 


112  CHAP,   v.— OPERATING  EXPENSES. 

might  perhaps  more  fairly  say,  rarely  difficult  to  do)  by  probable 
differences  of  alignment  alone.    We  have,  if  it  has  been  increased: 

Per  Mile.       Per  Cent 
Increase. 

Gross  revenue  (increased  lo  per  cent), $7.7oo  lo.o 

Operating  expenses  (lo  p.  c.  only  increased  lo  p.  c), 

or  $47  per  mile  increase,       4,713  i-o 

Fixed  charges  (assumed  unchanged), 1,800  0.0 

Total  charges  against  revenue, 6,513  0.7 

Surplus  available, 1,187  119.0 

The  surplus  available  for  dividends  is  more  than  doubled. 
On  the  other  hand,  if  there  has  been  ten  per  cent  loss  of 
traffic,  we  have — 

Per  Mile,      Per  Cent. 
Decrease. 

Gross  revenue, $6,300  10,0 

Operating  expenses  (10  p.  c.  of  10  p.  c.  only  decreased 

10  p.  c), 4,620  i.o 

Fixed  charges, 1,800  0.0 

Total  charges  against  revenue, 6,420  — 

The  expenses  are  a  little  over  the  receipts,  and  the  road  is 
on  the  way  to  a  receivership,  if  it  has  been  opened,  as  it  is  very 
apt  to  be,  in  one  of  the  years  in  which  an  ebb  in  the  business  tide 
is  beginning,  and  there  is  no  apparent  growth  (often  a  decrease) 
in  traffic  for  several  years. 

100.  Again:  Let  us  suppose  that,  by  an  improvement  of  or  in- 
jury to  the  line  and  grades,  we  increase  or  decrease  the  average 
train-load  30  per  cent — often  not  difficult  to  effect.  Our  account, 
if  we  have  improved  the  grades,  will  then  stand  as  follows: 

Per  Mile.      Per  Cent. 

Gross  revenue, $7,000  0.0 

Operating  expenses  (30  p.  c.  of  50  p.  c.  saved,  or  $700),     3,967  15.0 

Fixed  charges  (as  above), 1,800  00.0 

5>767 
Surplus  available  for  dividends, 1,233  131.0 


CHAP.    V— OPERATING  EXPENSES.  II3 

Or,  we  have  benefited  the  line  greatly  indeed,  and  yet  but 
little  more  than  if  we  had  added  10  per  cent  to  revenue.  On 
the  other  hand,  reversing  this  process,  we  find,  as  before,  that 
the  road  is  on  the  way  to  a  receivership. 

101.  Let  us  suppose,  by  an  unnecessarily  extravagant  scale  of 
expenditure,  for  purposes  which  do  not  really  add  much  in  dol- 
lars and  cents  to  economy  of  operation,  we  have  increased  the 
capital  account  or  rental  charge  2i'^  per  cent,  in  a  way  which 
does  not  decrease  operating  expenses  more  than  2  per  cent, 
nor  add  anything  to  revenue — a  not  uncommon  case,  since  the 
use  of  6°  instead  of  10°  maximum  curves  will  alone  suffice  to  do 
it,  in  some  cases.     We  have  then 

Per  Mile. 

Increased  the  rental  charge  33  p.  c,  or $622 

Decreased  operating  expenses  5  p.  c,  or       ....        93 

Net  increase, $529 

Or  within  $4  of  wiping  out  the  surplus  over  expenses  and 
fixed  charges.  If  we  have,  in  addition,  adopted  a  line  which, 
instead  of  being  better,  is  really  more  expensive  to  operate 
than  another  line  which  would  have  cost  no  more — or  if,  pos- 
sibly, we  have  adopted  a  line  which,  in  addition  to  being  more 
expensive,  involves  a  certain  sacrifice  of  revenue,  a  receiver- 
ship is  practically  assuerd.  Both  of  these  are  very  probable 
contingencies,  but  if  we  have  escaped  them,  we  have  barely 
saved  ourselves.     The  profit  from  the  enterprise  is  destroyed. 


102.  A  great  change  has  taken  place  within  the  past  ten 
or  fifteen  years,  and  indeed  is  still  in  progress,  in  the  operat- 
ing expenses  of  railways,  as  a  result  of  the  introduction  of  cer- 
tain modern  improvements,  and  notably  the  steel  rail.  At  so 
recent  a  period  as  the  publication  of  the  first  edition  of  this 
treatise  (1877)  these  improvements  had  hardly  begun  to  tell  at 
all  upon  the  statistics  which  were  available  for  its  preparation  ; 
but  they  have  already  (1885)  modified  them  profoundly,  and 
w^here  the  process  will  end  it  is  impossible  to  foresee  with 
8 


114  CHAP,    v.— OPERATING  EXPENSES. 

exactness — further  than  that  the  change  will  be  very  much  more 
radical  than  even  yet  appears  upon  the  surface. 

103.  Besides  the  steel  rail,  there  has  been  a  great  increase  in 
the  power  of  locomotives.  The  old  eight-wheel  "American" 
locomotive,  then  almost  universal  for  freight  as  for  passenger 
service,  is  now  almost  completely  out  of  use  for  heavy  freight 
service.  Mogul  or  Consolidation  locomotives  are  rapidly  super- 
seding it,  and  will  in  the  near  future  almost  wholly  supersede  it. 
On  all  but  roads  of  very  light  traffic  the  Consolidation  locomo- 
tive appears  to  be  the  engine  of  the  future  ;  and  a  still  heavier 
type,  the  "  Mastodon"  locomotive,  has  been  introduced,  with  ex- 
cellent prospects  of  wider  use. 

104.  The  capacity  of  ordinary  freight  cars  has  also  been 
increased  from  ten  or  twelve  tons  to  fifteen  and  twent}^  tons, 
with  but  a  comparatively  slight  increase  in  the  weight.  In 
fact  the  20-ton  car  has  already  become  the  standard  both  for 
coal  and  all  other  traffic,  and  many  25-ton  and  not  a  few  30-ton 
cars  have  been  built.  The  movement  in  their  favor  has  gone 
so  far  that  a  committee  of  the  Master  Car-Builders'  Association 
has  reported  standard  dimensions  for  such  a  car,  but  it  is  as  yet 
regarded  as  exceptional,  but  many  25-ton  cars  are  already  in  use, 
and  it  may  confidently  be  expected  that  the  average  car-load  will 
increase  for  many  years.  It  has  increased  fully  50  per  cent  in 
the  past  ten  3^ears. 

105.  Still  other — comparatively  unimportant — changes  which 
are  gradually  reducing  the  cost  of  operating  are,  first,  the 
creosoting  or  otherwise  preserving  of  cross-ties  (a  practice  in 
small  but  increasing  use);  and,  secondly,  the  substitution  of  first- 
class  ballast  for  what  has  heretofore  done  duty  for  that  purpose. 

The  almost  incredibly  rapid  growth  of  traffic  (see  Tables  21 
to  34,  and  others)  has  been  perhaps  the  most  potent  factor  of 
all,  and  these  causes,  and  the  gradual  fall  in  the  cost  of  producing 
every  form  of  manufactured  commodity  consumed  by  railways, 
render  it  impossible  to  predict  with  any  certainty  either  the 
future  cost  of  a  train-mile,  or  the  ratio  which  the  various  ex- 
penses will  bear  to  each  other.    The  changes  of  the  next  ten  years 

Note  to  following  table.    The  groups  of  Slates  marked  *  includes  a  very  small  high-rate  mile- 
age.    Rates  of  8,  g,  lo,  13,  15,  and  44  cents. 


CHAP,    v.— OPERATING  EXPENSES. 


115 


Table  38. 

Receipts,  Expenses,  and  Profits  per  Ton-Mile. 


Trun 

K  Lines. 

Minor  Trunk  Lines. 

Year. 

Penn'a. 

N.  Y.  C. 

Erie. 

P.,Ft.  W. 
&C. 

B.  &  Alb. 

L.  S.  &  M.  S. 

Rec.  Exp. 

Pr. 

Rec. 

Exp.'  Pr. 

Rec. 

Exp. 

Pr. 

Rec. 

Exp. 

Pr. 

Rec. 

Exp.    Pr. 

Rec. 

Exp. 

Pr. 

1852 

53 

54 

55 

4 
3 
3 
2 

64  1    .. 
•78       .. 
27    2.28 
84  !i.68 

•99 
1. 16 

2.95 
3-27 

1. 31  I 
-34  I 

;64 

93 

1^95 
2.50 
2.58 
2.42 

i::i 

1. 41 
1^15 

.92 
1.22 

1. 17 
1.27 

L 

. 

i 

•'•'    i    •• 

Average.. 

3 

05  I1.98 

1.07 

3. II  1.32  I 

79!  2. 36 

1.22 

1. 14 

1856 

57 

58 

g:::::: 

2 

2 
2 

I 

70  ji.69 
•38  {1.52 

19    1.35 
.02    1. 18 

95   |i.i7 

1.04 

.86 
.84 
.84 
.78 

3.05  1.54  I 
3. 191. 701 

2. 63*1. 37  I 
2.16  1.28 

2.06  1. 341 

51 
49 
26 
88 
72 

2.48 
2.46 
2.32 
1.62 
1.81 

1. 17 

% 

^•34 

I. GO 

1-31 
1.56 

■:S 

.81 

2.27 
I.  go 
1.65 
1.67 

I 
I 

57 

18 

70 

58 
47 
49 

•• 

Averag^e.. 

2 

25   ii.38 

.87 

2.62,1.45  I 

17 

2.14 

I.OI 

1.13 

1.871 
1.71! 
i^9o! 
2.01 1 1 
2.38I1 
2.44  I 

31 
98 
98 
20 
50 

79 

73 
92 

88 
65 

..    1    .. 

•• 

1861 

62 

63 

I 
2 
2 
2 
2 

93   !    -91 
05    1.09 
20    1.16 
46   ,1.87 

66    2.28 

1.02 

.96 
1.04 

1.98 
2.23 
2.44 
2.76 
3-45 

1-34; 

1-361 
1. 511 

1.96! 

2.54' 

64 
87 
93 
80 

1.77 
1.89 
2.09 
2.34 
2.76 

•93 

•95 

.96 

1.46 

1.98 

.84 
•94 
1. 13 
.88 
•78 

•  • 

Average.. 

26    1.46  1.80 

2-57 

I  •74: 

63 

2.17 

1.26 

.91  2.09:1 

29 

80 

1866.   .... 

67 

68 

69 

70 

28    1.82     .46 
09   ii-54:    -S.S 
91   I1.25     .66 
72   11.20,    .52 
55     1. 00'    .55 

3^09 
2-75 
2.74 
2.39 
1.88 

2.16 

1-95 
1.80 
1.40 
^•15 

93 
81 
94 
99 
73 

2^43 
2.04 
1. 81 
1-54 
I  •  33 

1.66 
1.47 
1^34 
1. 17 
•97 

■11 
•57 
•47 
•37 
•36 

2.02  I 

1.70  I 
1.62,1 
1.45 

50 
44 
15 
II 

86 

52 
51 

55 
51 

59 

2.81 

2^43 

2.19 

.. 

1.50 

•93 

•57 

Average.. 

91 

1-36     .55 

2-57 
1.63 
i^59 
1^57 
1.46 
1.27 

1.69! 

88 
62 
46 
55 
48 
37 

1^83 
1.44 
1^53 
1.46 

I-3I 
1. 21 

1.32 

I.OI 

.96 
.96 

•51 

•43 
•55 
•50 
.40 
•25 

1^75  I 

21 

54 
65 
59 
45 
52 
42 

2.48 
2.09 
2.02 
1.96 
X.82 
1^53 

1^59 
1-39 
1. 10 

•37 
•43 
•43 

^■39 
1-37 
1-34 
1. 18 

I.OI 

.... 

1871 

72 

73 

74 

75 

39 

416 

416 

255 

058 

.87 
.886 
.857 
.719 
.616 

■52 
530 
•559 
•536 
.442 

I.OI 

I-I3 

1.02 

.98 

.90 

1.43 
1.40 
1.40 
1.26 
I. II 

78 
81 
95 
74 
69 

.91     .48 

■92;    .45 
•951    ^39 
■77    .^- 

■74     ^27 

Average.. 

307 

.790 

•517 

1.70 

I.OI 

49 

i_^ 
1. 10 
■95 
•97 
.78 
•83 

.96,    .43 
.8q    .21 
•75     ■■20 
.6j\    .30 
.56,    .22 
•53     •SO 

1.32 
•93 

I.OI 

.88 
.76 
.91 

79 
63 
67 
50 
44 
51 

i3 
30 

32 
40 

1.88 

1.28 
1. 21 

I-I3 
1. 10 
1. 21 

1.48 
1.03 
1.03 

:?i 

1.02 

.40 

•25 
.18 
.14 
•32' 
.19 

1.26 
.82 
.86 

% 

•75 

.86|    .40 

1876 

77 

78 

79 

80 

918 
796 
880 

.582: 
5-52 
.483 
.427 
.470 

.310 
.428 

•435 
■369 
.406 

1.05 
1. 01 

.88 

•71 
.70 
.60 
•55 

•54 

34 
31 
33 
25 
34 

•56 

■% 
.40 

•43 

.26 
.29 
.26 
•24 
•32 

Average.. 

873 

•503' 

•390 
.362 
•344 
•342 

•93 

.62 

11 
22 
14 
23 
21 
14 

-93 
.81 
•75 
•99 

.68!    .25 

•90 

•75 
•75 

•67 
•58 

_55 
43 
47 
55 
49 
44 

35 

32 
28 
24 
18 
14 

1. 19 
1.04 
1.07 
1. 19 
1.09 
■94 

•97 
.96 
.98 
1.09 
1.07 
.81 

.22 
.08 
.09 
1. 10 
.02 
•13 

.76 
.62 
•63 

% 

•55 

•49 
.42 
.41 
•45 
•43 
.40 

.27 

1881 

82 

799 
817 
819 

•437; 
•473 

•477, 
•441 
•3911 

•78 
•74 

.83 

.68 

■t 

.68 
.62 
•54 

•53 
•53 
•53 

.28 
.22 
•25 
.20 
.18 

.20 
.22 
.28 
,22 
■15 

Average,. 

760] .444 

.316    .79    .60 

19 

•75 

-52 

.23 

•71 

48 

23 

1.06 

.98 

.28 

.64 

.42 

.22 

For  the  whole  United  States  the  earnings  per  ton  per  mile  were  : 

1880  1881  1882  1883  1884  1885 

1.29  1.236  1236  1. 124  1.057 

The  receipts  per  ton  per  mile  in  the  various  sections  of  the  United  States, 
the  Census  of  1880,  were  : 


according  to 


Group.  ■ 

I. 

New 
Eng. 

II. 

N.  Y., 
D.C.,Ind. 

III. 
Va.,   Ky., 

Miss. 

IV. 

111.,  Mo., 

Minn. 

v.* 

La.,  Ark., 
Ind.  T. 

VI. 
Far  W  . 
and  So. 

[-■ 

Receipts 

1.83 
55.7 
90.6 

1.02 
•  106. I 

163.6 

2.15 
103.7 

55.5 

1.36 
153.3 

t22.8 

12.57* 

34.6 

61.3 

2  57 
166.9 
95-5 

1.29 
III. 
129. 

Average  haul— miles 
Tons  per  train 

ii6 


CHAP,    v.— OPERATING  EXPENSES. 


Table  39. 

Average  Cost  Per  Train-Mile  of  the  Four  Trunk  Lines  and  English 

Railways. 


Year. 

N.  Y.  Cent. 

Erie. 

Penna. 

B.  &0. 

Cents  per 
Train. 

Revenue. 

Mile. 

Revenue. 

Mile. 

Cents  per  Engine. 

l87'^ 

126.2 
127.3 

116. 6 
122.0 

95.5 
89.6 

71. 1 

67.7 

74 

1871; 

132.5 

II9-3 

80.1 

63„9 

76 

114. 6 
104.0 
lOI.O 

95-5 

114. 2 
102. 1 

99-5 
95.6 

76.2 
74-3 
73.6 
72.0 

60.9 
57.3 
54-5 
52.2 

77 

78 

7q 

1880 

107.3 

101.8 

83.8 

67.1 

81 

112. 5 

118. 3 
123.2 
108.5 

105.2 

108.0 

100.5 

95-7 

81. 1 

88.2 
85.7 
84.4 

71.6 

82 

71.5 

8-:? 

69.4 
66.3 

84 

i88«? 

92.6 

91.2 

78.1 

69.0 

See  also  Lake  Shore  &  Michigan  Southern  statistics,  Tables  30,  31,  and  others  fol- 
lowing. 

The  above  suffices  to  show  that,  while  there  has  been,  on  the  whole,  a  decline  in 
expenses  per  train-mile,  yet  the  main  part  of  the  enormous  economy  per  ton-mile  shown 
in  Table  38  has  come  about  by  the  increase  in  average  train-load  shown  in  Table  33,  and 
not  in  saving  of  cost  per  train-mile,  which  does  not  appear  likely  to  decrease  much 
further. 

The  average  earnings  per  train-mile  of  British  railways  have  fallen  every  year  but  one 
since  1874,  having  been  $1.36  in  1874,  $1.26  in  1879,  and  $1.19  in  1884.     But  the  decrease 
in  working  expenses  has  been  almost  as  regular,  and  until  1881  just  as  great,  so  that  the 
net  earnings  per  train  were  very  uniform,  varying  only  between  60.24  and  61.36  cents  per 
train-mile  from  1874  to  1880.     Since  1877  the  earnings  and  expenses  have  been,  in  cents 
per  train-mile : 

E877o  1879.  1880.  1881.  1882.  1883.  1884. 

Receipts.... c. ...... ....ISO,  50         126.24         123.42         123.48         123.80         121.76         119. 12 

Cost... 69.38  66,00  64.74  64.56  64.94  64.34  63.18 

Profit 61.12  60.24  60-68  58.92  58.86  57.42  55-94 

The  results  are  very  much  more  uniform  than  would  be  shown  in  this  country,  even  in 
those  parts  of  it  where  rates  are  steadiest.    The  larger  part  of  the  reduction  in  expenses  of 


CHAP,    v.— OPERATING  EXPENSES. 


117 


the  British  railways  has  been  in  the  cost  of  maintenance  of  road.  This  has  fallen  from 
15.70  cents  per  train-mile  in  1874  to  12.76  in  1879  ^iid  11.64  cents  in  1884.  Per  mile  0} 
road  expenses  ranged,  for  the  five  years  from  1874  to  1878  inclusive,  from  $1,865  to 
$2,G2o  for  maintenance  of  road,  and  averaged  $1,965.  Then  they  fell  off  suddenly  to 
$1,690,  and  have  never  been  so  low  since,  ranging  thence  to  $1,800  in  1883  and  $1,750  in 
1884,  and  averaging  $1,751  from  1879  to  1884. 

The  total  expenses  per  mile  of  road  have  ranged  from  $9,665  in  1875  and  $9,625  in 
1883  to  $8,775  in  1879,  and  the  gross  earnings  averaged  $17,690  for  the  five  years  from 
1874  to  1878,  reaching  the  maximum,  $18,255,  in  1885. 

will  probably  be  greater  than  those  of  the  last  ten,  and  all  that 
we  can  be  sure  of  is  that  the  cost  per  ton-mile  (not  probably  per 
train-mile)  will  continue  to  fall  rapidly,  although  it  hardly  seems 
possible  that  it  can  fall  quite  so  rapidly  as  in  the  last  ten  years. 
Table  2>^  and  others  will  show  the  recent  changes  in  the  cost 
per  ton-mile,  and  Table  39  the  changes  in  the  cost  per  train-mile. 

106.  Nevertheless,  it  fortunately  happens  that  those  items  of 
expenditure  with  which  we  are  more  immediately  concerned — 
those  which  are  affected  by  the  location  of  the  line — may  be 
anticipated  with  reasonable  certainty  from  known  facts  and 
tendencies,  although  it  is  not  expedient  to  rely  too  much  on 
existing  statistics  of  the  immediate  past  of  railways  in  respect 
to  some  items,  as  notably  steel  rails;  since  it  would  tend  to  the 
dangerous  error  of  overestimating  the  probable  expenses. 

107.  The  operating  expenses  of  railways  divide,  naturally, 
for  the  purpose  which  we  have  immediately  in  view,  and  in  the 
main  for  all  purposes,  into  the  three  great  classes  below  : 

1.  Maintenance  and  Renewal  of  Way  and  Works,  in- 
cluding all  permanent  structures  and  buildings,  except  engine 
and  car-shops. 

This  has  until  recently  averaged  very  uniformly  25  per  cent 
of  the  total  expenses  on  all  American  railways.  It  is  now 
decreasing  both  relatively  and  absolutely,  but  far  less  rapidly 
than  might  be  expected,  because  of  both  temporary  and  per- 
manent causes  below  mentioned. 

2.  Train  Expenses,  including  all  expenses  of  every  nature 
and  kind  connected  with  the  running,  handling,  maintenance 
and  renewal  of  motive-power  and  rolling-stock,  but  not  includ- 


Il8  CHAP,    v.— OPERATING  EXPENSES— RAILS, 

ing  any  station  or  terminal  expenses,  except  switching.  These 
expenses  have  heretofore  averaged  very  close  to  42  per  cent 
of  the  total  operating  expenses,  and  cost  from  30  to  50  cents 
per  train-mile.  They  have  decreased  considerably  per  train- 
mile  for  the  same  class  of  engines,  but  the  introduction  of 
heavier  engines  will  have  a  tendency  to  keep  them  more  nearly 
constant.  Relatively  to  the  other  operating  expenses  they  are; 
growing  continually  more  important. 

3.  Station,  Terminal,  and  General  Expenses  and  Taxes. 
With  these  we  are  very  little  concerned.  Most  of  them  vary 
more  or  less  (for  the  most  part,  less)  witlrthe  tonnage  or 
volume  of  business  ;  but  all  of  them  are  independent  of,  or  in- 
appreciably affected  by,  any  of  the  details  of  lines  and  grades,, 
and  therefore,  for  our  present  purpose,  may  be  included  to- 
gether and  neglected,  except  as  to  their  aggregate.  Taxes  at 
first  sight  appear  to  be  affected  by  the  alignment,  in  so  far  as 
they  might  increase  with  the  length  of  the  road  ;  but  taxes  are 
based  upon  value  and  not  on  cost,  and  hence,  although 
nominally  based  upon  distance,  are  in  reality  much  more  truly 
based  upon  low  grades,  large  traffic,  and  good  rates.  They  are,, 
moreover,  too  small  and  variable  an  item  to  justify  their  consid- 
eration as  one  of  the  expenses  affected  by  any  of  the  details  of 
alignment.  Station  expenses  also,  and  all  the  other  expenses 
mentioned,  are  the  same  for  the  same  business,  whatever  changes 
in  the  alignment  may  be  made,  except  as  such  change  brings, 
additional  way  business  ;  but  even  then  the  change  will  rarely 
be  sufficient  to  appreciably  modify  the  station  expenses.  For 
its  indirect  value  in  such  cases  and  others,  and  as  a  matter  of 
general  information,  Tables  75  to  80  give  what  the  cost  of  the 
various  items  of  station  and  general  expenses  amount  to  on. 
various  roads  and  in  various  sections. 

maintenance  of  way. 
109.  The  steel  rail  has  revolutionized  maintenance  of  way.     Previous 
to  its  advent  the  great  trunk  lines  were  engaged  in  an  unceasing  strug- 
gle, which  was  rapidly  becoming  hopeless,  to  maintain  their  lines  in  a. 
decently  safe  and  passable  condition.     Much  of  this  difficulty  was  due  to 


CHAP,    v.— OPERATING  EXPENSES— RAILS.  1 19 

the  most  culpable  carelessness  as  to  the  quality  of  rails  purchased  ;  but 
the  difficulty  existed,  and  was  only  partially  remediable  at  best.  The 
cost  of  rail  wear  alone  per  train-mile  was  from  7  to  9  cents,  and  their  life 
on  important  lines  was  measured  by  months  rather  than  years. 

Under  these  circumstances  the  track  was  constantly  disturbed,  the 
ties  cut  full  of  spike-holes,  the  joints  imperfect  and  irregularly  spaced, 
owing  to  the  constant  cutting  of  rails,  the  line  and  surface  difficult  to 
maintain  correctly,  and  anything  like  a  permanent  rock  ballast  well-nigh 
out  of  the  question,  although  it  was  occasionally  used.  As  a  further  and 
very  natural  consequence  all  maintenance  expenses  for  the  above  items 
varied  to  a  very  remarkable  degree,  in  almost  exact  ratio  with  the  ton- 
nage and  rail  wear — as  indeed  they  still  do,  but  to  a  less  noticeable  ex- 
tent. Some  evidence  of  the  former  conditions  is  still  preserved  in  Table 
40,  but  further  space  need  not  be  devoted  to  the  discussion  of  conditions 
which  no  longer  exist  to  any  extent. 

110.  The  superiority  of  the  steel  rail  lies  not  so  much  in  its  greater 
strength  and  toughness  (although  it  is  stronger  by  20  to  30  per  cent)  as 
in  its  greater  homogeneousness  and  absolute  freedom  from  grain.  In 
other  words,  when  of  good  quality  it  is  tough  enough  to  last  until  it  is 
worn  out,  whereas  the  iron  rail  splits  into  pieces  long  before  it  had  lost 
any  serious  amount  by  wear.  The  wearing  properties  proper  of  iron  and 
steel  rails — their  resistance  to  abrasion — are  not  materially  different. 

111.  The  average  life  of  GOOD  steel  rails  properly  manufactured  and 
inspected  so  as  to  eliminate  all  imperfections  arising  from  a  lack  of  ordi- 
nary care  and  skill,  and  weighing  60  to  80  lbs.  per  yard,  according  to 
the  weight  of  engine,  has  now  been  determined  with  a  considerable 
approach  to  certainty  to  be  about  150,000,000  to  200,000,000  tons,  or 
(what  is  probably  a  more  correct  way  of  putting  it)  from  300,000  to 
500,000  trains.  From  10  to  15  lbs.  or  three  eighths  to  five  eighths  of  an 
inch  in  height  of  the  head  of  such  a  rail  is  available  for  wear,  and  abrasion 
takes  place  at  the  rate  of  about  i  lb.  per  10,000,000  tons,  or  one  sixteenth 
inch  per  14,000,000  to  1 5,000,000  tons.  This  durability  may  be  regarded 
as  nearly  a  minimum  for  strictly  first-class  rails,  as  many  recorded  obser- 
vations indicate  a  much  higher  durability. 

112i  Unfortunately,  it  may  be  said  to  be  the  rule  rather  than  the  ex- 
ception, that  American  railways  nov/  bu}^  their  steel  rails,  as  they  for- 
merly bought  their  iron  rails,  without  any  effective  inspection  as  to  quality  ; 
the  so-called  inspections,  when  there  is  any  even  in  form,  being  confined  to 
the  exterior  qualities  of  the  rail.  Unfortunately,  also,  a  few  years  since  the 
result  of  an  investigation  on  the  Pennsylvania  Railroad  into  the  wearing 


I20 


CHAP.    V.~OPERATING  EXPENSES— RAILS. 


Q 

< 

< 
Z 

w 
a; 

Q 

si 

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CO    <; 

«        (V) 


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CHAP,    v.— OPERATING  EXPENSES— RAILS.  121 

qualities  of  steel  rails,  which  showed,  or  seemed  to  show,  that  very  hard 

rails  did  not  wear  so  well  as  softer  and  tougher  rails,  was  taken  to  indi- 
cate that  softness  in  itself  was  a  desirable  quality  in  a  rail ;  and  the  pains- 
taking character  of  the  investigation  and  high  reputation  of  the  road 
having  given  these  conclusions  wide  dissemination,  manufacturers  for 
many  years  took  them  as  a  guide,  and  between  1880  and  1885  produced 
rails  which  have  deformed  readily  under  the  impacts  of  service,  espec- 
ially at  the  joints,  and  have  also  worn  away  very  rapidly,  so  that  their  life 
has  often  been  only  a  year  or  two  under  very  moderate  trunk-line  traffic. 
In  instances  it  has  been  only  a  few  months. 

113.  The  particular  cause  for  this  deterioration  of  quality,  whether  it 
is  chemical  or  mechanical,  or  both,  is  as  yet  obscure.  It  is  probable  that 
as  there  has  been  no  adequate  inspection  to  enforce  sound  practice  the 
chemical  composition  has  suffered  by  the  use  of  cheaper  ores,  cheaper 
men  to  supervise  manufacture,  and  less  care  in  all  the  processes.  But  a 
chief  cause  is  probably  mechanical — that  the  "  bloom,"  or  first  rough  cast- 
ing of  the  steel  from  the  converter,  out  of  which  the  finished  rails  are  fash- 
ioned, is,  in  the  first  place,  heated  undul}^  hot  for  passing  through  the 
rolls,  and,  in  the  second  place,  is  passed  through  them  a  less  number  of 
times,  or  too  rapidly,  or  both.  In  order  to  roll  a  rail  very  rapidly  and 
with  few  passes  it  must  necessarily  be  very  hot,  both  to  begin  with  and 
when  it  finally  leaves  the  rolls.  Its  molecular  structure  might  be  expected 
to  be  disadvantageously  affected  by  this  lack  of  surface  compression,  inde- 
pendently of  the  fact  that,  being  left  to  cool  slowly  after  it  leaves  the 
rolls,  it  is  thoroughly  annealed  by  the  same  process  as  makes  the  finest 
tool  steel  soft  enough  to  readily  suffer  deformation  from  dies.  The 
rapid  motion  of  the  rolls,  moreover,  may  not  give  the  molecules  suffi- 
cient time  to  flow  upon  each  other  properly,  and  a  spongy,  unhomogene- 
ous  metal  is  the  result. 

114.  Whether  or  not  this  is  the  true  explanation,  it  cannot  be  ques- 
tioned that  there  is  some  equally  simple  and  easily  remedied  expla- 
nation, because  certain  makers  do  produce  rails  of  excellent  quality 
which  are  sold  at  the  same  price  as  the  inferior  ones.  The  remedy, 
therefore,  lies  simply  in  more  thorough  tests,  especially  for  ability  to 
resist  deformation ;  and  it  would  be  erroneous  to  conclude  from  this  ad- 
mitted but,  it  may  reasonably  be  hoped,  temporary  evil  that  the  estimate 
of  cost  of  rail  service  should  be  permanently  increased.  The  reasonable 
cost  per  train-mile  of  rail  wear  may,  on  the  basis  of  the  facts  above 
given  as  to  the  life  of  rails,  be  estimated  at  from  0.3  to  0.5  cents,  as  fol- 
lows : 


122  CHAP,    v.— OPERATING  EXPENSES— RAILS. 


Cost  of  one  mile  of  steel  rails,  95  long  tons,  at  $30,      .     .  $2,850 
Less  scrap  value  of  unworn  steel,  say  nearly  half,     .     .     .     1,350 

Leaving  as  net  cost  of  wearable  portion,  per  mile,  .     .     .  $1,500 

Divided  by  total  life  of  300,000  to  500,000  trains,  this  gives  0.3  to  0.5 
cents  per  train-mile  ;  but,  in  view  of  the  present  difficulty  of  getting  good 
rails,  and  tendency  to  increase  the  weight  of  trains,  we  may  assume  the 
even  figure  of  i.o  cents  per  train-mile  as  a  maximum  which  there  is  no 
need  of  ever  exceeding. 

No  allowance  for  interest  or  discount  to  represent  the  present  value  of  the 
scrap  is  made  in  this  estimate,  nor  should  there  be,  although  at  first  sight  an 
argument  to  the  contrary  seems  plausible.  The  whole  original  cost  of  the  steel 
is  a  permanent  part  of  the  cost  of  the  property  on  which  interest  must  be  paid, 
like  the  cost  of  the  ties  and  structures.  The  renewals  for  each  j^ear  simply 
represent,  in  the  long-run,  the  rail  wear  for  that  year,  and  no  question  of  inter- 
est is  involved  in  the  cost  of  simply  using  the  steel  to  run  trains  over. 

115.  The  locomotive  alone  causes  by  far  the  greater  portion  of  this 
wear — how  much  is  not  positively  known.  Freycinet.  a  French  engineer,. 
writer,  and  politician  of  much  prominence,  recently  Minister  of  Public 
Works,  estimates  that  the  locomotive  does  three  fourths  of  the  damage 
and  the  train  itself  only  one  fourth.  Launhardt,  a  German  writer  on  the 
subject,  after  noting  the  fact  that  the  locomotive  and  tender  together 
constitute  only  one  fifth  of  the  total  weight  of  train  on  the  Prussian  State 
railways  (it  would  be  considerably  less  in  this  country),  considers  that  half 
the  wear  is  due  to  the  locomotive  and  tender  and  half  to  the  train.  This 
in  all  probability  is  a  very  moderate  estimate.  Experience  on  the  gravity 
railways  in  Eastern  Pennsylvania,  worked  solely  by  inclined  planes  and 
carrying  a  heavy  coal  traffic  with  the  ordinary  vehicles,  and  with  all  other 
usual  conditions  except  that  no  locomotives  run  over  the  rails,  shows 
that  the  rail  wear  even  of  iron  rails  is  very  slight  indeed  under  heavy  ton- 
nage, but  with  light  loads  per  wheel ;  but  exact  figures  of  the  wear  cannot 
be  presented.  Mr.  O.  Chanute  investigated  this  question  somewhat  by 
placing  impression  paper  between  the  rails  and  wheels  and  determining 
the  areas  of  the  surfaces  in  contact.  He  points  out  that  the  pressure  of 
the  drivers  approximates  to  the  ultimate  crushing  resistance  of  the 
metal,  and  that  the  pressure  per  unit  of  area  is  very  much  less  with  ordi- 
nary car-wheels.  He  therefore  reaches  substantially  the  above  conclu- 
sions—that from  one  half  to  three  fourths  of  the  total  wear  of  the  rails- 
originates  from  the  engine  alone. 


CHAP,    v.— OPERATING  EXPENSES— TRACK  LABOR.       1 25 

116.  We  may  assume,  therefore,  the  cost  of  maintaining  fairly  good 
steel  rail  at  0.5  to  i.o  cent  per  train-mile;  the  cost  of  additional  engine- 
mileage,  the  car-tonnage  remaining  constant,  being  only  half  as  great. 
These  values,  although  in  round  figures,  probably  approximate  very 
closely  to  the  facts,  and  the  very  best  quality  of  rail  might  reduce  them 
one  half;  but  the  poorer  qualities  which  have  been  so  generally  sold 
of  late  years  greatly  increase  it,  when  so  poor  that  the  rail  speedily 
mashes  out  of  shape,  and  from  this  cause  and  renewals  of  the  still  re- 
maining iron  rails  combined,  2  cents  is  nearer  the  present  average  (see 
Tables  75-80).  Much  of  the  rapid  wear  of  rails  results  from  the  imper- 
fections of  the  fish-plate  type  of  joint  which  is  now  universal.  Its  de- 
fects of  principle  are  such  that  it  seems  quite  certain  to  be  supplanted 
within  a  decade  by  something  better — probably  by  something  closely  re- 
sembling in  principle  the  Fisher  "  bridge"  joint,  if  not  identical  with  it. 

TRACK   LABOR. 

117.  This  item  includes  all  the  considerable  elements  of  cost  in  main- 
tenance of  way  proper  outside  of  rails,  ties,  and  frogs  and  switches.  It 
has  been  unmistakably  falling  in  the  last  ten  years,  the  decrease  on  many 
roads  having  been  as  much  as  fifty  per  cent.  About  one  fourth  to  one 
third  of  this  decrease  is  accounted  for  by  the  decrease  in  the  rate  of 
wages  to  what  bids  fair  to  be  a  permanent  average  of  about  $1.25.  The 
remainder  is  almost  wholly  due  to  the  advent  of  the  steel  rail.  Except 
that  the  joints  are  still  so  weak  and  imperfect  a  detail,  it  would  unques- 
tionably fall  very  much  more. 

This  decrease  is  destined  to  continue,  but  less  rapidly,  for  some  time 
in  the  future  ;  and  in  making  estimates  of  operating  expenses  for  the  next 
few  years — if  not  for  a  long  period  ahead — the  apparent  indications  of 
the  statistics  of  other  roads  must  be  accepted  with  much  caution.  All 
the  roads  now  laid  with  steel — with  hardly  an  exception — are,  instead  of 
reducing  track  expenses  to  the  lowest  limit  possible,  maintaining  for  the 
time  being  something  like  the  old  rate  of  expenditure  and  perfecting  the 
condition  of  their  road  by  adding  better  ballast,  dressing  up  the  road-bed 
and  right  of  way,  improving  their  yards  and  switched,  etc.,  etc.  This 
wise  procedure  is  in  reality  an  addition  to  the  capital  account,  but  for 
obvious  reasons  of  expediency  it  is  still  called  and  charged  to  mainte- 
nance of  way. 

118.  It  is  also  very  evident  that  the  larger  the  business  of  a  road,  i.e., 
the  more  prosperous  it  is,  the  more  likely  will  it  be  to  continue  this 
process  extensively.  For  example,  the  Pennsylvania  Railroad,  although 
laid  with  steel  and  ballasted  v/ith  stone  throughout,  still  includes  a  very 
heavy  charge  per  mile  of  road  (although  not  per  train-mile)  in  its  annual 


124  CHAP,    v.— OPERATING  EXPENSES— CROSS-TIES. 

accounts  for  "  maintenance  of  way,"  the  reason  being  simply  that  it  is 
engaged  in  giving  the  last  degree  of  finish  to  its  road-bed,  track,  and 
right  of  way ;  and  the  same  is  true  in  a  less  degree  of  many  other  rail- 
ways. 

119.  It  is  even  possible  that  this  practice  will  be  continued  indefinitely 
as  a  matter  of  permanent  policy;  and  when  it  comes  to  dressing  up  the 
edges  of  rock  ballast  with  a  string,  sodding  and  planting  slopes,  etc.,  etc., 
there  is  hardly  any  end  to  the  labor  which  may  be  kept  busily  employed 
in  "maintenance  of  way,"  nor  can  it  be  doubted  that  such  expenditure 
would  be  returned  in  part,  perhaps  many-fold,  by  its  value  to  the  line ; 
for  its  value  lies  not  alone  in  the  direct  economy  of  such  fine  condition, 
but  in  its  value  as  an  advertisement,  by  making  travel  over  the  line  more 
attractive,  and  likewise  in  its  effect  to  instil  habits  of  caution,  neatness, 
and  watchfulness  into  the  entire  force  of  employes.  Nevertheless,  such 
facts  should  not  lead  us  to  confound  advertising  and  landscape  gardening 
with  "  maintenance  of  way,"  nor  blind  us  to  the  fact  concealed  from  sight 
in  the  current  statistics — and  likely  to  be  for  some  years  yet — that  the 
cost  of  maintaining  steel-rail  track  is  no  longer  greatly  affected  by  the  ton- 
nage. It  will  for  some  time  appear  to  be  the  case — as  it  came  very  near 
to  being  actually  the  case  during  the  iron-rail  period — that  the  total  cost 
of  maintaining  track  varies  very  nearly  with  the  tonnage,  and  that  it  has 
not  been  so  very  largely  diminished  by  the  steel  rail  as  was  expected. 
Perhaps  there  is  more  that  is  permanent  in  this  appearance  than  is  ex- 
pected, as  certainly  there  is  unless  the  current  carelessness  in  buying  bad 
rails  at  good  prices  is  reformed;  but  the  following  estimates  (par.  124) 
seem  reasonable  and  sufficient. 

120,  Cross-ties  alone  cost  from  $150  to  $225  per  mile  of  main  track, 
about  I330  per  year  (one  eighth  of  the  total  number)  being  required  per 
mile  of  main  track,  at  an  average  cost  of,  say,  50  cents  per  tie  (it  is  often 
only  30  or  40  cents  in  favored  localities),  with  about  two  thirds  as  many, 
or  $220  per  year,  per  mile  of  side  track.  Side-track  ties  will  hardly  aver- 
age in  cost,  however,  more  than  half  as  much  per  mile  per  year  as  main- 
track  ties,  being  largely  "culls,"  or  of  otherwise  inferior  quality. 

In  England  and  Europe  generally  the  number  used  per  mile  is  less — ordi- 
narily 1760  per  mile,  or  three  feet  apart,  the  dimensions  being  in  England  some- 
what greater,  usually  9  feet  by  10  X  5  inches  instead  of  8  to  8^  feet  by  6  X  8  inches, 
and  the  wood  inferior  fir  instead  of  oak  ;  and  yet  the  average  life  of  English 
sleepers  is  longer  by  about  50  per  cent  than  in  America,  the  difference  being 
due  in  part  to  better  ballast  and  road-bed,  in  part — perhaps  mainly — to  greater 
care  to  have  the  ties  well  seasoned  before  putting  them  in  the  track  (in  respect 
to  which  American  roads  are  very  careless),  and  in  part  to  the  use  of  cast-iron 


CHAP,    v.— OPERATING  EXPENSES— CROSS-TIES.         1 25 

chairs  on  English  tracks  to  carry  the  rail  and  protect  the  sleepers  from  "cutting." 
The  differences  of  practice  in  England  and  America  result,  for  the  most  part, 
from  differences  of  conditions,  and  not  from  mistakes  of  judgment  on  either 
side.  Where  wood  of  any  kind  is  dear,  hard  wood  out  of  the  question,  and 
labor  and  rails  cheap,  the  English  and  Continental  plan  of  widely  spaced  ties, 
with  the  rail  carried  in  chairs,  is  at  least  defensible,  although  it  may  be  ques- 
tioned if  there  is  any  real  economy  in  spacing  ties  so  widely.  Where  good 
hard-wood  ties  are  cheap  it  would  be  folly  to  space  ties  farther  than  two  feet 
apart,  or  to  use  a  rail  requiring  chairs.  One  effect  of  the  English  plan  is  that, 
for  equal  stability  and  strength,  very  much  heavier  rails  must  be  used  than 
with  the  ties  nearer  together,  which  is  the  chief  explanation  of  the  fact  that  they 
are  heavier. 

121,  The  expense  of  cross-ties  will  probably  be  considerably  reduced 
within  the  next  ten  years  by  the  more  general  introduction  of  burnettizing- 
or  other  equivalent  processes,  and  it  will  then  be  almost  wholly  true,  as 
it  is  now  in  part,  that  the  life  of  ties  is  independent  of  the  tonnage.  The 
only  way  in  which  tonnage  seriously  affects  the  life  of  a  tie,  under  a  steel 
rail,  is  by  helping  on  that  process  of  local  rotting  which  is  popularly  and 
erroneously  known  as  "cutting"  into  ties.  The  difference  m  this  respect 
between  m.ain-track  ties  (especially  if  of  soft  wood)  and  side-track  ties,  is 
very  considerable ;  but,  given  three  or  four  trains  a  day  over  the  track, 
the  effect  of  even  twenty  or  thirty  more  trains  a  day  is  much  less  impor- 
tant, and  the  "cutting"  does  not  take  place  noticeably  faster.  This  re- 
sults from  the  fact  that  the  only  real  assistance  which  the  train  gives  to 
the  "  cutting"  is  to  wear  away  the  rotted  surface,  so  as  to  leave  a  fresh 
surface  exposed  to  decay.  It  is  physically  impossible  for  the  rail  to  cut 
into  a  sound  tie  under  existing  loads,  except  as  assisted  by  the  greater 
rapidity  of  rotting  under  the  rail  than  alongside  of  it.  That  this  is  true 
is  conclusively  proved  by  the  fact  that  creosoted  or  similarly  preserved 
ties  do  not  cut  to  any  im.portant  extent,  even  when  the  wood  is  soft. 

The  importance  of  this  distinction  as  to  the  cause  of  "  catting"  is 
obvious ;  since  it  follows  from  it  that  the  wear  will  not  be  very  greatly 
increased  by  an  increase  in  number  of  trains,  beyond  four  or  five  per  day, 
whereas  otherwise  the  wear  of  ties  would  be  directly  as  the  train-mileage. 

122.  Putting  ties  into  the  track  costs  about  one  third  as  much  as  the 
tie  itself,  including  all  labor  incident  thereto,  or  about  15  cents  per  tie, 
or  $50  to  $75  per  year.  Including  with  this  the  maintenance  of  ballast 
and  ditches  and  ordinary  track-walking,  but  not  including  policing  the 
right  of  way  and  road-bed,  special  watchmen,  removing  snow  and  ice, 
care  of  structures,  or  extraordinary  repairs — the  TOTAL  COST  OF  track 
LABOR,  as  thus  defined,  properly  and  necessarily  chargeable  to  the  main- 


126       CHAP,    v.— OPERATING  EXPENSES— MAINT.   WAY. 

tenance  of  steel-rail  track,  once  reasonably  well  ballasted  and  in  good 
general  condition,  is  not  far  from  $300  per  mile  of  single-track  main  line 
per  year,  or  say  five  men  for  every  six  miles.  This  amount  is  only  to  a 
very  limited  extent  affected  by  the  volume  of  traffic  if  the  standard  of 
maintenance  is  not  increased.  It  does  not  now  appear  probable  that  it 
can  ever  be  materially  reduced  to  advantage,  since  it  is  necessary  to  have 
that  number  of  men  available  for  emergencies  for  prudential  reasons; 
and  work  can  and  will  be  easily  found  for  that  number,  after  the  track  has 
been  brought  in  the  course  of  years  to  a  condition  of  far  greater  excel- 
lence than  the  present  average,  by  continuing  the  present  rate  of  expen- 
diture, and  not  a  few  lines  of  the  first  rank  will,  by  aiming  at  absolute 
perfection,  permanently  incur  a  still  larger  expense. 

123.  About  $50  per  mile  of  the  above  total  will  ordinarily  go  for  track- 
walking,  which  is  about  all  the  expense  for  track  watchmen  that  will 
usually  be  incurred  on  roads  running  only  three  or  four  trains  per  day 
each  way.  For  a  traffic  beyond  that,  the  usual  expense  per  annum  is 
about  $5  per  mile  for  each  daily  train  round  trip  (or  say  three  fourths  of 
a  cent  per  train-mile),  up  to  a  total  of  about  $150  to  $200  per  mile,  beyond 
which  this  account  very  rarely  runs.  Snow  and  ice  is  another  source  of 
irregular  expense  for  "  maintenance  of  way."  It  amounts  to  about  $50 
per  mile  of  main  line,  single  track,  per  year,  and  about  $100  per  mile  of 
double-track  road  in  ordinarily  unfavorable  regions — running  much  high- 
er, of  course,  on  short  sections.  Long  shallow  cuttings  are  the  greatest 
sources  of  annoyances  and  expense  in  respect  to  snow  and  ice — a  consid- 
eration often  forgotten  in  fixing  gradients. 

124.  The  total  cost  of  maintenance  of  way  for  single-track  railways  of 
moderate  traffic  may  be  safely  estimated  as  follows,  for  those  items 
■only,  which  are  practically  independent  of  volume  of  traffic  : 

Cross-ties, $150  to  $225-) 

Do.  for  sides,    . 10  to  40 

Labor  on  track, 150  to  200 

Track-walkmg, 50  to  100 

Snow  and  ice,  . o  to  50  J^ 

Ballast, 50  to  100 

Fences  and  miscellaneous,    .     .  25  to  50 

$435  to  $765 
To  which   must  be   added   for 
cattle-guards,    open   culverts, 
and  crossings,  about  25  to       50 

Total, $460  to  $815 

Steel  rails,  sav 20  to     100 


Per  mile  of  main  track, 
not  including  mileage  of 
sidings.  Common  track 
labor  $1.25  per  day. 


CHAP,   v.— OPERATING  EXPENSES— MAINT.    WAY.      12/ 

To  this  estimate  must  be  added  certain  allowances  for  maintenance  of 
structures,  for  the  maintenance  of  large  yards  and  terminal  facilities,  and 
for  extraordinary  damages  and  repairs,  and  also  for  the  wear  of  steel,  and 
other  expenses,  according  to  traffic.  The  amount  of  necessary  expendi- 
ture which  can  with  any  propriety  be  assumed  to  vary  directly  with  the 
tonnage  will  be — 

Steel  rails,  i  ct.  per  train-mile,  or  $20  per  1,000,000  gross  tons 
(including  all  expenses  for  relay- 
ing, spike,  etc.,  connected  there- 
with). 

Track    labor,    etc.,   \\  cts.  p.  t.  m.,  25    "  "  "        " 

Track  watchmen,       f     "       "  15    " 

Total,     .     .      3     "       "         $60    " 

This  amount  will  vary  almost  exactly  with  the  number  of  trains,  inde- 
pendent of  their  weight  and  length.  As  will  be  seen  from  Table  41, 
the  present  rate  of  expenditure  for  rail  renewals,  in  all  parts  of  the 
United  States,  is  much  higher  than  the  above,  or  about  $200  per  mile, 
but  this  can  hardly  continue  to  be  permanently  the  case. 

125.  Yet  it  must  be  admitted  that  there  are  some  strange  anomalies  in 
the  records  of  maintenance  of  way  expenses  which  seem  to  indicate  that 
such  expenditures  will  continue  to  bear  a  nearly  constant  ratio  to  the  train 
expenses  proper,  as  they  have  in  the  past.  For  example,  if  Table  41  be 
examined,  it  will  be  seen  that  in  every  item  of  maintenance  of  way — even 
those  which  seem 'most  nearly  independent  of  the  number  of  trains,  like 
ties,  bridges  and  buildings,  repairs  of  road-bed  and  track — it  is  the  cost 
per  mile  of  road  which  varies,  and  that  the  cost  per  train-mile  or  the 
percentage  of  the  total  remains  far  more  nearly  constant.  In  fact,  the 
cost  of  rails,  which  one  might  expect  to  be  almost  precisely  so  much^<?r 
trai?i-mile,  comes  much  the  nearest  of  all  to  being  uniform  per  mile  of 
road.  Beginning  with  the  section  of  heaviest  traffic, — the  Middle  States 
group,  which  includes  Ohio,  Indiana,  and  Michigan,— the  cost  of  rail  re- 
newals, in  cents  per  train-mile,  is 

3.50,    4.08,    5.03,  6.08,  6.72,  3.66,  averaging  4.43  ; 

while  that  of  road  and  track  labor  is 

9.2,    II. o,    ii.o,    8.7,  16.5,    8.3,    averaging  10.2. 

Individual  roads  may  be  compared  almost  at  random  with  similar  in- 
dications.    The  following  two  roads,  not  selected  in  any  way  except  as 


128        CHAP,    v.— OPERATING  EXPENSES— MAINT.   WAY. 


representing  extremes   of  traffic,  may  serve   as  illustrations,  the  years 
given  being  fairly  representative  : 

Penn.       Char., 

R.  R.     Col.  &  Aug.  Av.  U.  S. 

1883.        1882.  1880. 

Trains  per  day  each  way  (main  line) 64.5                3.4  6.1 

Repairs  road-bed  and  track  (cts.  per  train- 
mile) 9.81  cts.     12.36  cts.  10.2  cts. 

Total  cost  of  train-mile 86.0     "      87.5      "  91.0    " 


Table  41. 
Maintenance  of  Way  Details. 

Deduced  from  U.  S.  Census  of  1880.    See  also  preceding  table. 


Groups  of  States. 


New  England 

Middle 

Southern 

Northwestern. 
Southwestern. 
Far  Western . . 


Average  U.  S 6.07 


Cost  Repairs  Road-bed  and 

Trains 

Total  Cost 

Track. 

each  Way 

Per 

Per  Day. 

Train -Mile. 

P.  C. 

Cents  Per 

Per  ^Tile 

Expenses. 

Train-Mile. 

of  Road. 

7.4 

$1.05 

10.51 

II. 0  Cts. 

$574 

9-3 

0.902 

10.13 

9.2    " 

621 

4.3 

0.715 

12.12 

8.7    " 

273 

4.5 

0.88 

12.45 

II. 0    " 

361 

3.0* 

0.608 

13-59 

8.3    " 

480 

3.22 

I. 21 

13-63 

16.5    " 

382 

6.07 

$0.91 

11.23 

10.2  Cts. 

$450 

*  Estimated.     The  report  of  one  road  in  this  small  group  contains  an  obvious  and  large 
error  which  vitiates  the  total. 


Items. 


Repairs  road-bed  and 
track,  p.  c 

Per  mile 

Tie  renewals,  p-  c. .  . 

Per  mile 

Bridges.  buildings, 
and  fences,  p.  c. 

Per  mile 

Rail  renewals,  p.  c.  . . 

Per  mile 

Total,  p.  c   

Per  mile 

Cost  per  train-mile. . . 


New 
Eng. 


10.51 

$574 
2.64 
$144 

6.64 

$36.3 
4.20 
$220 

19.79 
|i,o8i 
$1.05 


Middle. 


10.13 
S621 
2.78 
$168 


4.44 
$268 

3-47 
$236 

17-35 
$1,051 
$0,906 


South. 


12.12 

$273 
4-30 

$97 

5.80 

$131 
6.16 
$210 

22.42 
$501 

$0,715 


N.  W. 


12.45 
$361 
3-07 


6.0S 
$176 
5-03 
$166 
21.60 
$625 


s.  w. 


13-59 
$480 
4.21 
$148 

3-45 
$121 
3.66 
$213 
21.25 

$749 
$0,608 


Far 
West. 


13-63 

■  $382 
3-48 


4-95 

$139 
6.8t 
$158 

22.06 
$6ig 

$1.21 


Total 
U.  S. 


11.23 
$450 
3-04 
$121 

5.14 
$207 
4.40 
$196 

19.41 
$778 

$0.91 


CH.    V.—OPER'G  EXP.—MAINT,    WAY  AND  ROLLG-STOCK.     1 29 

Table  42. 

Trunk-Line    Maintenance  Expenses   in  Cents   per  Train-Mile  by 
Decades  for  34  Years. 


N.Y.C.&  H.R. 

i860 

1870 

1880 

1884 

Erie. 

i860 

1870 

.1880 

1884 

Penna.* 

i860 

1870 

t88o 

1884 

Bait.  &  Ohio.f 

i860 

1870 

1880 

Phil.  &  Read. 

i860 

1870 

1880 

1883 


Miles 
Run, 
Thou- 
sands. 


4,493 
11,430 
16,654 
16,453 

3,475 

9,326 

11,452 

11,305 

3,633 
10,185 
17,241 
21,491 

3,831 

7.941 

12,768 

1,853 
5,100 

7,799 
12,347 


Expenses  Per  Train-Mile. 
Maintenance  of — 


Way. 


CtS. 
19.8 
39-8 
18.9 
24.8 


21.4 
30.1 
14-5 

15.8 

15-9 
26.3 

18.3 

II. 2 
22.6 
26.3 
19. 1 


En- 
gines. 


CtS. 
9.0 
9.8 

5.8 
5.3 

9.0 

14. 1 

5-1 

4.4 

7-7 
9.1 
7.2 
7.0 

6.8 
6.9 
9.4 

8.6 
8.6 
7.8 
7-9 


Cars. 


CtS. 

8.9 
15-4 

14..  4 
10.3 

II. 7 

12,0 

8.0 

8.9 

8.2 
II. 7 
10.5 
II. 4 

8.7 

5-5 

20.6 

8.9 

13.5 
12. 1 
14. 1 


Total 
Rolling 
Stock 


CtS. 

17.9 
25.2 
20.2 
15.6 

20.7 
26.1 
I3-I 
13-3 

15.9 
20.8 
17.7 
18.4 

15-5 
12.4 
30.0 

17-5 
22.1 
19.9 
22.0 


Total 
Ex- 
penses 

Per 
Train- 
Mile. 


CtS. 

95-2 
122.2 

107-5 
108.6 

94.6 
129.5 

108.5 
106.8 


99-3 
no. 6 

81.8 
81.8 

51.8 
68.8 
82.0 

78.6 
108.2 

II7-5 
117. 2 


Percentages. 


Track. 


20.8 
32.6 
17.6 
22.8 

25-5 
30.5 
ig.o 
17.0 

21.5 
27.2 
17.7 
19-3 

30.7 
38.3 
22.3 

16.5 
19-3 
22.4 
16.3 


En- 
gines. 


Cars. 


9.4 
12.6 

13.4 
9-5 

12.4 
9.2 

7-4 
8.3 

8.3 
10.6 
12.9 
13-9 

16.7 

8.0 

25-1 

II-3 
II. 9 
10.3 
12.0 


*  Pennsylvania  Division  only. 


t  Main  stem  and  branches. 


In  Table  42  is  given  a  record  of  expenses  for  maintenance  of  way  on 
five  trunk  lines  for  the  past  34  years.  In  this  table,  it  will  be  noted,  an 
enormous  expansion  of  train-mileage  has  occurred,  ranging  from  four-  to 
seven-fold,  while  yet  the  cost  of  maintaining  track  has,  on  the  whole, 
decreased  less  rapidly  than  other  maintenance  expenses.  There  has 
been,  on  each  of  these  lines,  a  considerable  expansion  of  track-mileage 
as  well  as  train-mileage,  but  this  increase  has  been  of  branches  only,  not 
of  main  line.  Therefore,  while  due  allowance  for  the  effect  of  this  greater 
9 


130     CH.    V.—OPERG  EXP.—MAINT.    WAY  AND  ROLrC-STOCK. 

trackage  would  reduce,  it  will  not  seriously  modify,  the  striking  contrast 
in  number  of  train-miles  per  year  shown  in  the  table,  in  spite  of  which 
maintenance  of  way  has  decreased,  by  comparison  with  other  items,  so 
little. 

In  the  following  table  (43)  the  experience  of  the  Pennsylvania  Railroad 
only  is  carried  back  ten  years  further — to  the  very  beginning  of  its  oper- 
ation, and  every  year's  experience  is  included,  the  years  being  averaged 
together  by  half-decades  to  eliminate  accidental  variations  and  shorten 
the  table.  In  this  table,  but  not  in  the  preceding,  fuel,  stores,  and  en- 
gine-wages are  included  with  repairs  of  engines  and  cars  in  the  single 
item  "  motive-power  and  cars :" 

Table  43. 

Operating  Statistics  of  the  Pennsylvania  Railroad  (Main  Line  and 
Branches)  averaged  by  Half-Decades  from  the  Beginning  of  its 
Operation, 


Per  Cent 

OF  Total 

Per  Cent  of 

Years 
Averaged. 

Average  Miles 

Train  Load 

Expenditure. 

Maintenance 

Run. 
I  =  icxx>. 

E.  only. 
Tons. 

Motive-power 

Maintenance 

of  Way  to 
Motive-power 

and  Cars. 

of  V^ay. 

and  Cars. 

1851-55- •• 

1,416 

IOI.6 

42.3 

13-4 

31-7 

1856-60. . . 

2,934 

II0.6 

42 

9 

23-7 

55-4 

1861-65... 

5,530 

146.24 

48 

r 

22.8 

47-5 

1866-70. . . 

8.766 

15^.88 
1^.76 

41 

4 

27.2 

65.6 

1871-75... 

14,368 

38 

2 

23-4 

61.3 

1876-80... 

16,182 

251-32 

39 

4 

18.4 

44-3 

1881-84... 

20,808 

298.45 

41 

7 

20.0 

48.0 

The  remarkable  shoAving;  in  respect  to  the  growth  of  average  train-load  from  100  tons 
in  1851-5  to  300  tons  in  1881-4  is  worthy  of  special  note  in  this  table.  For  average  load  in 
both  directions  see  Table  33. 


The  drop  in  the  last  two  half-decades  is  the  effect  of  the  introduction 
of  steel  rails  ;  but  both  in  the  iron-rail  and  steel-rail  eras  it  will  be  seen 
that  the  tendency  of  cost  of  maintenance  of  vj2ly  per  train-utzle  is  to  in- 
crease faster  than  the  train  expenses  proper.  The  following  table  (44) 
brings  this  tendency  out  still  more  clearly  : 


CH.    V.—OFER'G  EXP.—MAINT.    WAY  AND  ROLrC-STOCK.     I31 

Table  44. 
Comparative  Cost  of  Maintenance  of  Way  to  Repairs  of  Engines  and 
Cars  on  Each  of  the   Five  Lines  in  Table  42,  Cost  of  Repairs  of 
Engines  and  Cars  being  $1.00. 


N.  Y.  Cent. 

Erie. 

Penna. 

B.  &0. 

P.  i&R. 

Average. 

i860 

1870 

1880 

1884 

I. II 

1.58 

0.945 

1.59 

1. 16 
I-5I 

1.58 

1.37 

1.33 
1.45 
0.82 
0.86 

1.025 

2.12 

0.615 

0.64 
1.02 
1.32 

0.87 

I -053 
1-536 
1.056 
1. 172 

Average. 

1.306 

1.405 

1. 115 

1-915 

0.962 

1. 199 

The  contrast  in  the  proportionate  cost  of  maintenance  on  the  various  roads  is  in  part 
genuine,  but  in  part  no  doubt  results  from  considerable  difference  in  what  items  are  in- 
cluded in  "maintenance  of  way"  or  of  cars  or  engines.  Less  pains  were  taken  in  this 
respect  than  to  have  the  comparison  of  one  year  with  another  correct  for  each  road  sepa- 
rately. 

The  last  column  of  this  table  is  the  most  instructive.  With  the  ex- 
ception of  1870,  which  was  an  abnormal  year,  it  will  be  seen  that  the 
tendency  of  maintenance  of  way  to  increase  in  relative  importance,  in 
spite  of  an  immense  growth  of  traffic,  seems  marked  and  clear. 

Table  45. 

Growth  of  English  Train-Mileage  and  Coal  Consumption  of  Engines 

Per  Mile. 


Train-miles  (i  =  1000)... .  ]  ^gp 
Increase  per  cent 

Engine-miles \  Jg^ 

Increase  per  cent 

Coal  burned,  lbs., per  train-  (  1873 

mile \  1883 

Increase  per  cent 

Coal  burned,  lbs.,  per  en- j  1873 

gine-mile 1  1883 

Increase  per  cent 


Great 
Eastern. 


8,932 

13,679 

52.0 

10,819 
17,077 

57-8 

41.65 
45-96 
10.35 

34-39 
36.81 

7-05 


Great 
Western. 


19,717 
3i»i28 

58.0 

22,778 

36,465 

60.3 

41-73 
37-69 
-9.8 

36.12 
32.17 
-  10.8 


London,  B. 
&  So.  Coast. 


5,300 
7,986 
50.8 

6,208 
9,630 

55-2 

43-33 
37.07 
16.9 

36.99 
30.74 
20.3 


Midland. 


19. 811 

33  087 
67.1 


57.18 
49.00 
14.3 


The  mileage  represented  above  is  5,221  miles,  or  only  a  trifle  less  than  one  third  of 


132 


CHAP,    v.  — OPERATING  EXPENSES— FUEL. 


that  in  Great  Britain,  and  is  fairly  representative  of  the  whole.     The  change  in  engine- 
and  train-load  is  given  only  for  the  Great  Eastern,  as  follows  : 


First-Class  Goods-Engine,  Great  Eastern 
Railway. 


Diameter  of  driving-wheels 

Cylinders 

Total  working  weight,  lbs 

Working  pressure 

Coal  Train  : 

Consumption  per  mile 

Speed,  miles  per  hour 

Average  load 

Consumption  per  mile  with  average  load,  400  tons. 


1873 


5  ft.  3  in. 

16^  X  24 

70,700 

140  lbs. 

43.7s  lbs. 

17.4 
398  tons. 
43.97  lbs. 


1883 


4  ft.  10  in. 

T-lM  X  24 

84,000 

140  lbs. 

46.68  lbs. 

20 
438J4  tons. 
42.58  lbs. 


Per  cent 
increase. 


8.6* 
12.4 

21.6 


6.78 
15.0 
10.2 
D.  3.17 


*  Increase  per  cent  in  power,  due  to  decrease  of  drivers.  The  total  increase  in  power  of  the 
engine,  due  both  to  decrease  of  drivers  and  increase  of  cylinders,  then  becomes  io8.6i  X  12.4  = 
122.3,  or  22.3  per  cent  increase;  almost  exactly  equivalent  to  the  increase  of  weight. 

The  high  average  speed  of  English  trains  and  the  small  power  of  a  '*  first-class  goods- 
engine"  compared  with  usual  American  practice  on  lines  of  heavy  traffic,  are  noticeable. 
The  tendency  of  switching-mileage  to  increase  comparatively  is  shown  in  this  table  to 
prevail  quite  as  strongly  in  England  as  here. 

The  above  figures  are  deduced  from  The  Engineer  of  Jan.  23,  1885,  which  paper,  how- 
ever, makes  some  very  erroneous  deductions  as  to  what  they  really  show,  pointed  out  in 
the  Railroad  Gazette  of  Sept.  11,  1885,  by  the  writer. 


Train  Expenses. 
Fuel. 

126.  The  cost  of  fuel  per  gross  ton  on  American  railways  ranges  from 
a  minimum  of  $1.20  to  $1.50  on  roads  obtaining  coal  at  mines  on  their 
own  road,  to  a  maximum  of  $4.00  to  $5.00  at  the  least  favored  points 
east  of  the  Missouri  River,  and  in  some  cases  to  $6.00  or  more  at  points- 
west  of  there. 

The  consumption  of  fuel  is  as  an  average  about  45  to  50  lbs.  per  mile 
run  for  heavy  passenger  trains,  running  down  sometimes  as  low  as  25  or 
30  lbs.  per  mile  for  light  passenger  trains.  A  passenger  engine  running 
light,  without  any  train,  burns  nearly  as  much  as  this,  or  from  20  to  30 
lbs.  per  mile.  A  heavily  loaded  freight  engine  of  the  "American"  eight- 
wheel  type  will  burn  almost  75  lbs.  per  mile,  a  heavy  "  Mogul "  about 
90  lbs.  per  mile,  and  a  "  Consolidation"  engine  from  100* to  120  lbs.  The 
weights  and  power  of  these  and  pther  engines  will  be  found  in  Chapter 


CHAP,    v.— OPERATING  EXPENSES— FUEL. 


133 


XL;  and  from  data  given  there,  in  connection  with  the  above,  it  appears 
that  the  average  consumption  of  fuel  increases  considerably  less  rapidly 
than  the  power  of  the  engine,  as  might  be  expected. 


Table  46. 
Motive-Power  Expenses  Per  Train-Mile  on  Various  English  Railways. 


Motive-power  Expenses  in  Detail. 

Great 
Western 
Railway, 

1869-76. 

Great 

Southern  and 

Western, 

1875. 

Midland 

Great 
Western, 

1875. 

Engine  repairs — labor 

cts. 
3.76 
2.46 

cts. 
2.82 
3.80 

cts. 
3-42 

2.78 

"             "      — materials 

Total  en  cine  repairs 

6.22 
4.66 

4.34 
0.42 
0.48 
0.12 
0.10 
0.40 

16.74 

6.64 
4-32 
6.61 
0.50 
0.66 

0.32 
0.66 

19.76 

6  18 

3.84 
6.50 
0.32 
0  82 

Fuel     

Water 

Oil  and  stores 

Repairs  shops,  etc 

Gas 

Office  and  general 

Total  motive-power 

0.20 
17.90 

The  above  is  from  a  paper  in  the  Transactions  of  the  Institution  of  Civil  Engineers, 
the  reference  to  which  the  writer  has  lost. 

127.  Several  newly  invented  types  of  compound  locomotive  engine,  having 
separate  high-pressure  and  low-pressure  cylinders,  are  being  extensively  intro- 
duced in  Europe  with,  it  is  said,  very  satisfactory  results.  If  we  may  judge 
from  what  has  already  taken  place  in  marine  engines,  it  is  probable  that  they 
will  eventually  come  into  general  use,  and  they  promise  a  considerable  reduc- 
tion of  fuel  consumption,  but  there  are  several  practical  disadvantages  with  the 
type  which  have  not  yet  been  fully  overcome — notably  a  difBculty  in  starting. 
The  burden  of  evidence  seems  to  be  that  the  coal  consumption  is  reduced  at 
the  rate  of  about  20  to  25  per  cent. 

The  consumption  of  fuel  on  English  railways  in  general,  however,  is  lower 
than  prevails  in  the  United  States,  although  very  much  less  so  than  commonly 
supposed.  It  was  reported  by  the  late  Howard  Fry,  in  a  paper  before  the 
Master  Mechanics'  Association,  at  from  26  to  35  lbs.  per  mile  run,  for  passenger 
service,  and  from'35  to  45  lbs.  per  mile  run,  for  freight  service  ;  but  the  follow- 
ing statistics,  which  have   been   compiled  by  the  writer  from  later  and  more 


134 


CHAP,    v.— OPERATING  EXPENSES— FUEL. 


definite  statistics  (Tables  45,  47,*  48,  49),  show  that  the  actual  difference  be- 
tween English  and  American  practice  is  less  extreme. 

It  is  unnecessary  to  enter  in  detail  into  the  causes  of  the  difference  in, 
English  and  American  fuel  consumption.  The  fact  exists,  and  in  part  is  easily 
explainable,  by  a  difference  in  the  average  train-load;  in  part  also,  doubtless,  to 
better  road-bed  and  alignments,  use  of  copper  fire-boxes,  and,  more  especially^ 
greater  skill  and  care  in  firing.  The  longer  average  trips  of  American  engines, 
other  things  being  equal,  should  reduce  the  average  fuel  consumption.  The 
most  important  single  cause  is  probably  that  fuel  economy  is  subordinated  in 
America  to  hauling  heavier  loads,  as  it  ought  to  be,  whereas  in  England  heavy 
freight  trains,  or  what  would  pass  for  such  in  America,  are  the  exception. 

Table  48. 
Passenger-Train  Coal  Consumption,  Pennsylvania  Railroad. 


Year. 

Cars  Per 
Train. 

Coal  Per  Mile. 

Per  Car. 

Total. 

1874 

1875 

1876 

1877 

1878    

1879 

1880 

1881 

1882 

1883........ 

1884 

5.5 

5-3 

5.6 

5.10 

5-13 

5-29 

5.27 

5.01 

5-14 

4-95 

5.02 

9.0 

8.5 
8.3 

8.72 

8.43 

8.40 

8.76 

10.78 

9.61 

10.84 

10.67 

49 

45 
46 

44 
43 
44 

46 

54 
49 
53 
53 

5 
I 

5 
5 
2 

4 
2 
0 
4 
7 
6 

The  last  column  is  not  given  in  the  reports,  but  is  obtained  by  multiplying  together 
the  two  preceding  columns. 

The  increase  of  i8J^  per  cent  in  the  coal  burned  per  car,  notable  in  this  table,  is  un- 
doubtedly the  price  paid  for  the  very  much  greater  average  weight  of  passenger  coaches, 
owing  to  the  increasing  proportion  of  parlor-  and  sleeping-car  mileage,  and  the  much 
greater  average  speed. 

The  Pennsylvania  has  been  selected  merely  because  its  statistics  are  most  conveniently 
accessible.  It  is  in  no  respect  pre-eminent  either  in  increase  of  train-load  or  in  low  fuel 
consumption.  The  movement  toward  increase  of  train-load  began  on  the  Lake  Shore 
&  Michigan  Southern,  for  example,  several  years  before  it  began  on  the  Pennsylvania.. 
The  Philadelphia  &  Reading  runs  about  58  lbs.  per  passenger  train-mile. 


*  Table  47  was  misplaced  in  making  up  this  Part,  and  is  given  at  the  end  of  the  volume. 


CHAP.    V— OPERA  TING  EXPENSES— FUEL. 


135 


Table  49. 
Average  Freight-Train  Coal  Consumption,  Pennsylvania  Railroad. 


Coal  Burned  Per  Mile. 

No.  Cars. 

Train-load 
Tons  Fr't 

Approx. 
Total  W't 

Year. 

Per  Car. 

of  Tram; 

Per  Ton 

Per  Car- 

Per  Train- 

Tons. 

Freight. 

Mile. 

Mile. 

1874- • 

21. 1 

(6.5) 

327 

(.646) 

4.2 

88.5 

1875.. 

21.5 

(6 

7) 

(-627) 

4 

2 

90.2 

1876.. 

22.2 

(6 

9) 

.... 

(.609) 

4 

2 

93-1 

1877.. 

22.92 

(7 

I) 

.... 

(•585) 

4 

15 

95-0 

1878.. 

25-.  06 

(7 

3) 

... 

(-497) 

3 

63 

91.0 

1879.. 

25.60 

7 

55 

436 

.490 

3 

70 

116. 7 

1880.. 

25-77 

8 

18 

.... 

-477 

3 

90 

112. 0 

1881.. 

24.40 

8 

68 

.... 

.492 

4 

27 

109.3 

1882.. 

24-55 

9 

01 

.... 

•494 

4 

45 

104.3 

1883.. 

23-97 

10 

28 

.... 

.454 

4 

.67 

100.5 

1884. . 

25.66 

10 

5B 

566 

-430 

4-55 

99.2 

The  tons  freight  per  car  was  obtained  by  dividing  the  coal  consumption  per  car  given 
by  that  per  ton  ;  the  approximate  total  weight  by  assuming  the  average  car  to  have 
weighed  18,000  lbs.  (9.0  tons)  in  1874,  19,000  lbs.  (9.5  tons)  in  1879,  and  23,000  lbs.  (11. 5 
tons)  in  1884 ;  the  coal  burned  per  train  by  multiplying  the  number  of  cars  by  the  coal 
per  car.     The  remaining  figures  are  direct  from  the  report. 

The  figures  in  parentheses  above  are  estimated,  not  being  given  in  nor  deducible  from 
the  reports  ;  but  they  are  not  far  from  the  truth,  a  gradual  increase  of  average  car-load 
having,  as  is  well  known,  been  going  on  even  in  the  years  1874-9,  "^vhich  has  gone  on 
much  more  rapidly  since.  One  of  the  chief  reasons  why  the  average  car-load  has  been  so 
small,  on  all  the  American  east  and  west  trunk  lines,  has  been  the  enormous  dispropor- 
tion (more  than  3  to  i)  in  east-bound  to  west-bound  traffic.  The  increasing  coal  ship- 
ments westward,  to  a  considerable  extent  in  cars  coming  east  with  grain,  has  in  recent 
years  helped  much  to  decrease  this  disproportion  on  some  roads  ;  so  that  the  increasing 
average  car-load  is  not  due  solely  to  increased  capacity  of  cars,  although  that  is  the  chief 
cause. 

The  proportion  of  switching  is  very  heavy  on  English  railways,  the  ratio  of 
engine-miles  to  train-miles  being  almost  uniformly  as  high  as  125  to  100,  and 
in  some  cases,  as  high  as  177  to  100. 

On  German  railways  the  average  consumption  is  about  50  lbs.  per  revenue 
mile,  costing  about  six  cents. 

128.  The  cost  of  fuel  per  mile  run  can  be  calculated  from  the  above 

data  for  any  particular  line.  In  absolute  cost,  it  is  by  far  the  most 
variable  element  in  the  running  expenses  of  railways,  but  its  percentage 
to  the  other  expenses  is  considerably  less  variable,  owing  to  the  fact  that 


136 


CHAP.    V— OPERATING  EXPENSES— FUEL. 


the  same  causes  which  make  fuel  more  expensive,  also  increase  the  other 
expenses  to  a  considerable  extent.  The  total  average  cost  per  mile  for 
all  trains,  according  to  railway  reports  at  the  present  time,  varies  from 
5  cents  as  a  minimum  (on  the  Pennsylvania  Railroad),  to  about  10  cents 
in  Massachusetts  and  12  cents  on  the  Pacific  railways.  There  are  a  few 
roads  in  the  Rocky  Mountain  region  on  which  the  reported  cost  runs 
still  iiigher  than  this — up  to  as  much  as  20  cents  ;  and,  on  the  other  hand, 
there  are  a  few  specially  favored  roads  on  which  the  cost  runs  still  lower — 
down  to  4  or  even  3  cents  :  but  these  latter  phenomena  are  mostly  due  to 
exaggerating  the  actual  train- mileage  with  fictitious  allowances. 


Table  50. 
Effect  of  Length  of  Train  on  Coal  Consumption. 

[Comparative  Coal  Consumption  with  Light  and  Heavy  Passenger  Trains— Michigan  Central 

Railroad.] 
Light  Trains. 


No.  of 

Av.  No. 

Coal  Consumption, 

Per  Mile. 

Per  Cent 

Corrected 

Round 

Cars 

Av.  Temp. 

Correction 

Lbs.  Coal 

Trips. 

Handled. 

Min. 

Max. 

Av. 

for  Temp. 

Per  Mile. 

3 

5 

58. 

67. 

62.3 

21.4° 

-4.3 

59.62 

3 

5i 

55-5 

65.5 

61. 

19.7° 

-5.15 

57.86 

2 

6 

62.1 

60.7 

61.4 

31.2 

+  0.6 

61.77 

I 

6i 

.... 

48. 

40.8° 

+  5.4 

50.60 

9 

5.56 

58.5 

64.4 

60.0 

25.2° 

-2.4 

58.56 

Hea 

VY  Trains. 

2 

7i 

746 

84.0 

79-3 

22.9° 

-3-55 

77.07 

I 

8 

.... 

78 

6 

33-1° 

+  1.55 

79.82 

7 

8i 

71.8 

87.0 

79 

4 

29-5° 

-0.25 

79.20 

2 

9 

81.6 

87.1 

85 

4 

36.3° 

+  3-15 

88.10 

3 

9i 

73.6 

79-3 

77 

3 

44.2° 

+  7.10 

82. 80 

I 

Hi 



75-0 

27.0° 

-  1.50 

73.88 

16 

8.78 

75-4 

84.4 

79-3 

32.4° 

+  1.20 

80.25 

Note. — The  averages  of  maximum  and  minimum  are  mere  arithmetical  averages  of 
the  figures  given.  In  the  last  column  the  total  coal  consumption  was  divided  by  the 
total  mileage  to  get  the  average. 

All  these  trains  made  frequent  stops  ;  30  in  115  miles,  or  about  one  every  four  miles. 
Speed  not  given  ;  probably  over  30  miles  per  hour  maximum  between  stations. 


CHAP,    v.— OPERATING  EXPENSES— FUEL.  13/ 

The  correction  for  temperature  is  by  a  rule  deduced  by  the  writer  from  records  cover- 
ing many  millions  of  train-miles,  that  the  effect  of  differences  of  temperature  alone, 
length  of  train  and  all  other  conditions  being  equal,  is  to  increase  or  dimi7iish  coal  con- 
sumptio7i  at  the  rate  ofO'S'Eper  cent  for  each  two  degrees  Fahrenheit  (and  a  small  frac- 
tion more)  difference  of  exter7ial  temperature :  a  rule  easily  remembered  and  one  which 
appears  to  apply  fairly  well  to  both  passenger  and  freight  service,  and  to  be  practically 
invariable  whenever  the  effect  of  all  other  causes  for  variation  can  be  eliminated. 

Since  the  effect  of  increasing  the  average  length  of  train  from  5.56  to  8.78  cars,  or  3.22 

cars,  is  shown  above  to  increase  coal  consumption  from  58.56  to  80.25  lbs.  per  mile  run, 

21.69  lbs. 

or  21.69  lbs.,  or  at  the  rate  of =  6.736  lbs.  per  mile  per  car,  we  have, 

3*22  cars 

Lbs.  coal 
per  mile. 

For  the  long  train,  burning, 80.25 

Consumption  due  to  cars,  8.78  X  6.736  = 59-14 

Leaving  as  due  to  the  engine  alone,  without  cars, 21. 11 

For  the  short  train,  burning, 58.56 

Coal  consumption  due  to  cars,  5.56  X  6.736, 37-45 

Leaving  as  due  to  engine  alone,  without  cars,  as  above,       .     .     21. 11 

This  result  agrees  closely  with  what  direct  experiment  has  shown  to  be  the  consump- 
tion of  heavy  passenger  engines  running  light.  Mr.  Reuben  Wells  some  years  ago  made 
a  test  of  a  light  passenger  engine,  14  x  22  cylinders,  running  108  miles  with  six  stops  at 
22  miles  per  hour,  and  losing  about  one  sixth  of  its  time  only  in  stops,  with  a  consump- 
tion of  only  i8J^  lbs.  per  mile,  and  this  test  was  in  warm  weather.  Allowing  for  the  dif- 
ferences of  weather,  size,  and  number  of  stops,  the  correspondence  is  close,  and  other 
tests,  which  need  not  be  referred  to  in  detail,  have  shown  from  20  to  30  lbs.  Mr.  Wil- 
liam Stroudley,  Mechanical  Superintendent  of  the  London,  Brighton  &  South  Coast  Rail- 
way, alleges  in  a  paper  before  the  Institution  of  Civil  Engineers  (1885),  that  a  heavy  pas- 
senger engine  was  run  light  between  London  and  Dover  with  a  consumption  of  07ily  7  lbs. 
per  mile.  As  the  distance  is  only  a  little  over  50  miles,  however,  and  the  quantity  stated 
would  amount  to  only  a  few  inches  over  the  bottom  of  the  fire-box  of  20  square  feet,  or 
barely  as  much  as  the  same  record  shows  was  habitually  used  to  get  up  steam,  there  is 
probably  some  error  in  this  estimate. 

The  best  existing  direct  evidence  on  the  effect  of  length  of  train  on  coal  con- 
sumption is  given  in  Table  50.  There  is  considerable  difficulty  in  obtaining 
records  of  this  kind,  in  which  a  series  of  trains  of  widely  varying  lengths  are 
run  with  all  other  conditions  approximately  identical.  The  correctness  of  the 
result  reached  in  Table  50  may  be  tested  by  grouping  the  various  single  records 
differently — a  test  which  should  never  be  omitted  in  computations  of  this  kind, 
since  it  will  often  be  found  that,  when  grouped  in  one  way,  the  records  will 
appear  to  lead  to  one  conclusion,  while  if  grouped  in  another  way  they  will 
indicate  something  quite  different. 

Tested  in  this  way,  the  correctness  of  the  preceding  conclusions  is  confirmed. 
If,  instead  of  averaging  the  single  tests  together  in  only  two  classes,  of  "light" 


138 


CHAP,   v.— OPERATING  EXPENSES— FUEL. 


and  "heavy"  trains,  we  divide  the  25  tests  as  tabulated  above  into  four  equal 
g^roups  of  six  tests  each,  as  nearly  as  may  be,  and  see  how  well  the  rule  deter- 
mined beneath  the  table  (lbs.  coal  per  mile  =  2i.i  -4-6.74  X  No.  of  cars)  checks 
with  the  actual  coal  consumption,  we  find  a  close  correspondence,  as  follows  : 


No.  of 

Cars  per  Train. 

Pounds  Coal  Per  Mile. 

Averaged. 

Range. 

Averages. 

Actual.* 

Computed.     ;      Difference. 

6 
6 

7 
6 

5  to      6 

6  to      8 
8     to     9 
8^  to  11* 

5-25 

6.92 

8.50 
9.67 

58-74 
68.02 
79.40 
83.08 

56-5 
67.7 
78.4 
86.3 

—  2.24 

—  0.32 

—  I.OO 

+  3.22 

*  Actual  consumption  after  correcting  for  difference  of  temperature. 

The  correspondence  of  the  results  under  this  entirely  different  grouping  is 
surprisingly  close,  indicating  that  the  whole  series  of  tests  do  clearly  conform 
to  one  general  law,  but  also  indicating  that  the  addition  to  the  fuel  consump- 
tion is  not  precisely  uniform  per  car,  but  decreases  as  the  train  is  longer,  as  is 
but  natural. 

Having  determined  a  law  for  experiments  on  a  small  scale,  we  may  check  it 
by  records  on  a  large  scale,  which  latter  do  not  otherwise  afford  the  means  of 
determining  the  law.  The  Pennsylvania  Railroad,  alone  among  American  rail- 
ways, publishes  a  table  showing  the  coal  consumption  per  car-mile  and  per 
train-mile,  and  the  number  of  cars  per  train  for  every  month  in  the  year.  As 
an  average  of  the  four  years  1881-84,  the  average  passenger  train  and  passenger 
car  coal  consumption  on  each  of  its  three  grand  divisions  was: 


Pennsylvania  RR.  Div 

U.  RR.  N.  J.  Div 

Phila.  &  Erie  Div . 


Cars  Per 
Train. 


5-03 
4.70 
4.20 


Pounds  of  Coal- 


Per  Car- 
Mile. 


10.47 
12.60 
12.10 


Per  Train- 
Mile. 


52.7 
59-2 
50.8 


Computing  what  ought  to  be  the  coal  consumption  per  mile  according  to  the 
rule  of  Table  50,  and  comparing  it  with  what  is,  we  have  the  following: 


Computed  Coal  Consi'mptjon. 
Pounds  per  Train-Mile. 

Actual. 
Pounds 

Tram- 
Mile. 

Error  in  Formula. 
4- or-. 

Due  to 
Engine. 

Due  to 
Cars. 

Total. 

;   Pounds. 

1    +2.3 
1     -6.4 
1    -  1-4 

Per  Cent. 

Penna.  RR.  Div 

U.  RR.  N.J.  Div 

Phila.  &  Erie  Div 

21. 1 
21. 1 
21. 1 

33-9 
31-7 
28.3 

55-0 
52.8 

49.4 

52.7 
59-2 
50.8 

+    4-4 

—  10.8 

-  2.8 

CHAP,    v.— OPERATING  EXPENSES— REP' RS  ENGINES.     1 39 

The  correspondence  here  is  close,  if  we  remember  that  the  Pennsylvania 
Division,  while  making  fewer  stops  than  the  Michigan  Central  train,  whose 
record  was  used  in  table,  has  a  large  proportion  of  heavy  sleeping-cars,  while 
the  New  Jersey  Division  not  only  has  a  large  proportion  of  parlor-  and  sleeping- 
cars  on  through  trains,  but  makes  an  enormous  number  of  stops  on  way  trains, 
both  into  New  Jersey  and  into  Philadelphia. 

129.  The  conclusion  is,  therefore,  not  unfair,  that  something  like  6\ 
to  6|  lbs.  of  coal  per  mile  is  added  to  the  consumption  for  each  passenger 
car  of  20  tons  or  more  moved  at  way-train  speed,  and  for  each  sieepmg- 
car  of  30  tons  or  more  moved  in  through  trains  making  few  stops,  and 
that  the  locomotive  alone  is  to  be  charged  with  rather  more  coal  than 
that  due  to  three  cars. 

This  leads  to  the  conclusion  that  dead  weight  to  the  amount  of  30  tons  added 
to  a  train  of,  say,  five  cars,  will  certainly  not  increase  coal  consumption  as  much 
as  to  add  another  car,  both  because  it  does  not  increase  air  resistance,  and  be- 
cause the  added  load  decreases  somewhat  the  rolling  resistance  per  ton.  If  we 
assume  it  to  add  5  lbs.  per  mile  to  the  coal  consumption,  we  are  certainly  not 
underestimating  it  proportionally.  Adding  6  tons  per  car,  therefore,  to  the 
average  weight  of  a  train  of  five  passenger  cars  means  no  more  than  an  in- 
crease from  55  to  60  lbs.  per  train-mile.  If  we  assume  this  5  lbs.  of  coal  to  be 
worth  one  cent  (at  the  rate  of  $4  per  ton  of  2000  lbs.  for  coal),  if  an  extra  pas- 
senger at  3  cents  per  mile  be  attracted  to  the  train  every  third  trip  he  will  pay 
for  the  loss  of  fuel  due  to  adding  6  tons  to  the  weight  of  every  passenger  car — 
which  goes  a  little  way  toward  explaining  the  tendency  to  increase  weight  for 
the  sake  of  luxury,  which  seems  so  reckless.  This  appears  to  neglect  the  effect 
of  the  extra  weight  on  grade  resistance,  and  so  in  a  sense  it  does,  as  well  as 
many  other  effects,  but  not  so  much  as  it  appears  to,  since  the  effect  of  gradients 
is  included  in  the  records  which  we  have  used. 

The  use  of  wood  for  fuel  is  rapidly  passing  out  of  date  in  all  parts  of  the 
United  States.  About  i-|  cords  of  good  hard  wood  (a  cord  being  4X4X8  feet, 
or  128  cubic  feet,  and  weighing  from  3200  to  3600  lbs.  when  well  seasoned)  is  usu- 
ally taken  as  equal  to  one  long  ton  of  coal.  Inferior  woods  will  average  from 
two  down  to  even  three  cords  of  wood  equal  to  one  ton  of  good  coal,  but  some 
of  the  poorer  Western  coals  will  evaporate  only  half  or  two  thirds  as  much  as 
good  bituminous  or  anthracite. 

REPAIRS  OF  ENGINES. 

130.  The  fall  in  the  cost  of  this  item,  of  late  years,  has  been  very  rapid,, 
but  it  is  probably  now  at  about  its  minimum,  unless  and  until  some  new 
process  of  manufacturing  steel  and  iron  shall  materially  reduce  the  cost 


140     CHAP.    V— OPERATING  EXPENSES— REFRS  ENGINES. 


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CHAP,    v.— OPERATING  EXPENSES— REP' RS  ENGINES.     I4I 


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142     CHAP,    v.— OPERATING  EXPENSES— REFRS  ENGINES. 

of  the  raw  material,  especially  in  shapes.  For  this  purpose  solid  steel 
castings  in  lieu  of  forgings  seem  to  be  already  on  the  verge  of  coming 
into  general  use. 

The  table  (51)  on  pp.  140  and  141  shows  the  cost  of  engine  repairs  per 
engine-mile  on  the  Penns3dvania  Railroad  for  a  long  series  of  years,  and 
sufficiently  illustrates  the  general  tendency  of  the  cost  of  this  item;  the 
table  showing  however,  it  must  be  remembered,  nothing  more  than  the 
cost  of  labor  and  materials  directly  applied  to  repairs  and  renewals  proper, 
without  including  any  allowances  or  charges  for  repairs,  and  renewals  of 
tools,  shops,  machinery,  and  other  items,  for  which  see  Table  57  and 
others.  The  figures  given  are  in  all  cases  for  what  is  now  known  as  the 
Pennsylvania  Railroad  Division,  excluding  the  later  acquisitions  of  the 
Philadelphia  &  Erie  Railroad,  and  United  Railroads  of  New  Jersey. 

131.  From  the  above  table  it  appears  that  the  cost  per  mile  on  the 
Pennsylvania  Railroad,  at  the  present  time,  is  from  5  to  6  cents  for  engine 
repairs  proper,  and  this  may  be  considered  the  minimum  under  the  most 
favorable  circumstances,  on  roads  having  a  heavy  traffic  and  convenient 
to  the  great  iron  and  coal  centres.  Many  roads — perhaps  most  roads — 
show  a  lower  average  than  this ;  but  such  a  result,  when  it  continues  for 
more  than  two  or  three  years,  is  very  apt  to  be  one  of  the  before-men- 
tioned miracles  of  bookkeeping,  based  upon  running  an  unusually  large 
mileage  in  the  general  office. 

132.  The  Massachusetts  roads  average  about  5^  cents — a  surprisingly 
low  average  for  that  region  of  the  country,  but  doubtless  very  nearly 
correct.  It  may  be  explained  largely  by  the  greater  proportion  of  pas- 
senger trains  (more  than  one  half  the  whole,  as  against  about  one  fourth 
in  the  remainder  of  the  country),  and  also  by  the  fact  that  a  very  exces- 
sive proportion  of  the  freight  traffic,  as  compared  with  the  rest  of  the 
country,  is  mere  way  business  with  light  loads.  A  densely  settled  region 
will  of  necessity  reduce  the  average  train-load  heavily  in  this  way. 

133.  Under  unfavorable  conditions,  the  estimate  of  engine  repairs  must 
be  considerably  increased  from  these  figures,  but  by  how  much,  as  a 
maximum,  is  extremely  difficult  to  determine.  The  Union  Pacific  Rail- 
road reports  repairs  of  engines  at  about  7  to  8  cents  per  train-mile,  which 
is  among  the  highest  reported  costs  at  the  present  time ;  and  yet,  except 
for  the  one  disadvantage  of  locality,  it  is  under  exceptionally  favorable 
conditions  for  a  low  cost  in  this  item,  its  engmes  not  being  heavy  and 
its  grades  very  light,  its  divisions  very  long,  and  its  traffic— quite  light  for 
a  trunk  line — almost  entirely  long  haul,  and  moved  at  a  slow  speed. 
From  5  to  8  cents  may  be  considered  as  about  the  present  average,  for 


CHAP,    v.— OPERATING  EXPENSES— REP' RS  ENGINES.     1 43 

all  classes  of  engines,  on  roads  with  sufficient  traffic  to  have  proper  facili- 
ties for  economy  in  shop  work.  Wages  do  not  vary  widely  in  any  part  of 
the  United  States,  and  no  causes  exist  for  very  wide  fluctuations  in  this 
item. 

Table  52. 
Cost  of  Locomotive  Repairs  in  Detail. 

Performance  and  Cost  of  Three  Passenger  Engines  for  Five  Years,  New  York  Central  & 
Hudson  River  Railroad  (Hudson  River  Div.). 


Engine  Only. 

Tender. 

Engine  and 
Tender. 

Per- 
cent- 

Mat. 

Lab. 

Total 

Mat. 

Lab. 

Total 

1  Mat. 

Lab. 

Total 

ages. 

Machinery  (and  %  machin- 
ist labor) 

Drivers  and  tires  (and  J4 

cts. 

.214 

.063 

.114 
.261 
.014 
.024 

cts. 

.465 

•  155 

.082 
.224 
.056 
.049 

cts. 

.679 

.2.S| 

•485' 

.070^ 

•073 

1. 721 

cts. 

.150 
.021 
.008 
.012 

cts. 

.018 

.020 
.017 
.015 
.010 

cts. 

.... 

.018 

.170 
.038 
.023 
.031 

cts. 

1     .214 

.063 

.264 
.282 
.022 
.036 

cts. 

•465 

•173 

.102 
.241 
.071 
.068 

cts. 
.679 

.236 

.366 
•523 
■093 
.104 

% 

33.9 

11,8 

Trucks     (and     blacksmith 
labor) 

18.3 
26.1 

Boilers  and  flues 

Wood-v?ork  and  fittings. . . 
Painting 

4-7 

5-2 

Totals,  cents,  per  mile  . . 

.690 

1-031 

.191 

.089 

.280 

.881 

1. 120 

2.001 

100. 0 

Percentages 

34-5 

51-5 

86.0 

9-5 

4-5 

14.0 

44.0 

56.0 

100. 0 

100. 0 

Average  mileage  per  engine  for  the  five  years  included, .        .        .  416,162 

"             "                "        year, 83,232 

"             "                "        month, 6,936 

"             "                "        day  in  service,  ....  278 

per  cent  of  time  idle  for  repairs  or  otherwise,    .        .        .  17.3^ 
"       for  all  engines  of  Pennsylvania  Railroad  from 

the  beginning  of  its  history  (see  Table  51),       ....  i7'9^ 


The  above  table  represents  the  very  lowest  cost  at  which  locomotives  can  be  operated 
in  actual  service  : 

First,  Because  the  engines  were  entirely  new  at  the  beginning  of  the  record,  and 
although  the  record  covers  something  over  half  the  average  mileage-life  of  a  locomotive 
(which  maybe  taken  as  600,000  to  800,000  miles),  yet  the  latter  half  of  its  mileage-life 
(including  cost  of  renewal)  would  average  three  to  four  times  as  high  as  the  first  half ; 

Secondly,  and  equally  important,  Because  of  the  very  heavy  mileage  duty,  which  is  at 
least  three  times  the  average  of  American  passenger  engines,  and  four  to  six  times  the 
average  of  European  engines.  This  heavily  reduces  the  expenses  arising  from  frequent 
cooling-off  of  the  engine.     Compare  the  following  Table  53. 


144     CHAP,    v.  — OPERATING   EXPENSES— REP' RS  ENGINES. 

Table  53. 

Engine  Repairs  Per  Mile  Run,  in  Detail,  1868-1873. 

Including  both  Repairs  and  Renewals.    Gt.  So.  &  W.  Ry.  of  Ireland  (1866-75). 


Engine  Only. 

Tender. 

Engine  and 
Tender. 

Per- 
cent- 

Mat. 

Lab. 

Total 

Mat. 

Lab. 

Total 

Mat. 

Lab. 

Total 

ages. 

cts. 

.694 

1.092 

1.090 
.272 
.118 

cts. 
1.008 

.418 

.588 
.152 
.130 

cts. 
1.702 

1. 510 

1.678 
.424 
.248 

cts. 

.436 

.070 

.026 

1     .040 

cts. 

.207 

.060 
.052 
.065 

cts. 

•643 

.130 
.078 
.105 

cts. 
.694 

1.528 

1. 160 
.298 
.158 

cts. 
1.008 

.625 

.648 
.204 
•  195 

cts. 
1.702 

2-153 

1.808 
.502 
.353 

26.1 

Drivers  and  tires  (and ) 

frames) >- 

Trucks ) 

Boilers  and  flues    

\  (11.3) 
\   29-9 
(  (18.6) 

28.1 

Wood-work  and  fittings . . 
Painting                         .  . 

8.0 

S-2 

Totals,  cents  per  mile 

3.266 

2.296 

5-562 

1     -572 

.384 

.956 

3-838 

3.388 

6.518 

100.0 

Percentages    

50.2 

35-1 

85.3 

8.8 

5-9 

14.7 

59.0 

41.0 

100. 0 

Tender  repairs  were  given  only  in  aggregate,  and  distributed  as  nearly  as  might  be  to 
the  several  items  in  same  ratio  as  above  table. 

This  same  table  is  given  in  the  following  Table  55,  rearranged  so  as  to  give  repairs 
and  renewals  separately. 


134.  Repairs  of  course  vary  materially  with  the  class  of  engine,  and  it 
would  be  quite  impossible  to  give  exact  statistical  evidence  on  this  point 
which  could  be  regarded  as  satisfactory.  It  may  be  estimated,  however, 
with  a  very  considerable  degree  of  certainty,  as  follows : 

About  one  eighth  of  the  cost  of  engine  repairs  is  for  repairs  of  tender, 
which  is  of  course  substantially  the  same  for  any  class  of  engine.  The 
remaining  cost  is  almost  equally  divided  between  material  and  labor,  as 
will  appear  from  Tables  52-53-55-56.  The  cost  of  the  labor  is  but  very 
slightly  affected  by  the  weight  of  the  engine  and  its  various  parts,  al- 
though it  is  so  affected  to  some  extent.  The  cost  of  material  will  be 
nearly  in  accordance  with  the  weight,  but  not  fully  so,  many  of  the  more 
expensive  parts  being  substantially  the  same  on  all  engines.  If.  therefore, 
we  say  that  half  the  total  cost  of  engine  repairs  (including  the  tender) 
varies  with  the  weight,  and  half  is  independent  thereof,  it  will  probably 
be  very  nearly  exact,  for  engines  engaged  in  the  same  service,  and 
equally  well  adapted  mechanically  for  that  service.  There  is  no  evi- 
dence whatever  that  the  heavier  class  of  engines  suffer  materially  in  wear 
and  tear  from  their  difference  in  proportion  and  design. 


CHAP,    v.— OPERATING  EXPENSES— PEP'RS  ENGINES.     1 45 


Table  54. 

Details  as  to  Cost  of  Locomotive  Repairs. 

Cost  Per  Train-Mile  of  Labor  and  Material. 


English  Railways, 
Average,  1868-75. 

Increase 
per  cent 
in  No.  of 
Engines. 

Labor. 

Mate- 
rial. 

Total. 

Per  cent 

of 

Labor. 

Av.  Total 
Cost  Re- 
pairs for 

21  preced- 
ing yrs., 
1849-69. 

London  &  Northwestern 

Midland                

% 
32.2 
73-6 

8.1 
42.2 
47.2 
15.0 

cts. 
3-04 
2.65 
3.12 

3.86 

3 -05 
3 -08 

cts. 
3.10 
3.10 

r$ 

3-34 
3.82 

cts. 
6.14 
5-75 
6.41 
6.44 
6-39 
6.90 

% 
49.6 
46.0 
48.7 
60.1 
47-6 
44.6 

6.90 
7.13 

5-87 

Great  Western 

Lancashire  &  Yorkshire 

Gt.  Southern  &  W.  of  Ireland. . 

^3. 

36.4 

3-13 

3.21 

6.34 

49-3 

French. 

1.70 
2.00 

2.32 
2.83 

4.02 
4.83 

42.4 
41.6 

Paris,  Lyons  &  Med.,  1865-74.. . 

Labor. 

1.70 
1.98 
0.97 

3-38 
4.47 
2.80 

50.0 
55-5 
65-4 

Prussian  Railways,  1874. 

R'd  H'se.l  General. 

0.58 
0.80 

I.  ID 
I. 16 
1.03 

State  Control  Railways 

Private  Railways 

American  Railways. 

Phila.  &  R'g  (1869-75),  repairs  only 

"            "    (1876-80),        "         "     

"            "    (1869-75),  renewals  only 

"            "    (1876-80),        "         (approx.). 

"            "    total  rep'rs  and  ren'ls '('69-75). 

('76-80). 

3-9° 
2.38 
0.81 
0.60 
4.71 
2.98 

2.94 
1-93 
1.22 
0.90 
4.16 
2.83 

6.84 

4-31 

2.03 

1-5 

8.87 

6.81 

(40.) 
(40.) 
(53-) 
(58.4) 

For  further  notes  as  to  ratio  of  cost  of  labor  to  material,  see  Index, 
None  of  these  figures  include  shop  and  general  charges^  maintenance  of  machinery, 
clerks,  draughtsmen,  policing  shops,  etc.,  which  run  about  50  per  cent  or  over  of  labor 
account  on  nearly  all  railways. 

These  statistics  are  supposed  to  be  all  per  train-mile.  The  ratio  of  engine-miles  to 
train-miles  on  English  railways  is  about  as  100  to  125 — sometimes  even  100  to  177.  The 
same  holds  substantially  true  of  American  railways,  reported  statistics  being  generally 
computed  per  engine-vaS!iQ.  A  deduction  of  15  to  20  percent  from  the  total  cost  of  engine 
repairs  per  train-mile  will  give  the  cost  excluding  switching-engines,  which  cost  much  less 
per  mile  for  repairs  than  others,  on  most  roads. 
ID 


146     CHAP,    v.— OPERATING  EXPENSES— REF RS  ENGINES. 

Table  55. 

Engine  Repairs  and  Renewals  in  Detail— Gt.  So.  &  W.  Railway  of 

Ireland  (1866-75). 

Cents  Per  Train-Mile. 


Items, 

Labor. 

Materials. 

Grand 
Total. 

Per- 

Re- 
newals. 

Re- 
pairs. 

Total. 

Re- 
newals. 

Re- 
pairs. 

Total. 

ages. 

Boiler 

cts. 
■134 
.112 
.118 
.258 
.052 
.030 

cts. 
(.302) 

(.04) 
(.30) 
(.75) 
(.10) 
(.10) 

cts. 
.436 
.152 
.418 

1.008 
.152 
.130 

cts. 
.656 

.092 
•574 
.190 
•154 
.058 

cts. 
.290 

.052 
.518 
.504 
.118 
.060 

cts. 
.946 

.144 

1.092 

.694 

.272 
.118 

1.382 

.296 

1. 510 

1.702 

.424 

.248 

Smoke-box,  etc 

Wheels,  frame,  etc 

Machinery 

4-5 
23.2 
26.1 

Mountings 

6.5 

3-8 

Total  Engine 

.704 

1.592 

2.296 

1.724 

1-542 

3.266 

5-562 
-956 

85-3 

Tenders 

.098 

.286 

.384 

.292 

.280 

.572 

14.7 

Total        

.802 

1.878 

2.680 

2.016 

1.822 

3-838 

6.518 

100. 0 

Percentages 

12.2 

28.8 

41.0 

31.0 

28.0 

59-0 

100. 0 

.... 

Credits  for  old  material  (amounting,  on  repairs,  to  .264  cent;  on  renewals,  to  .192 
cent — total,  .456  cent)  are  to  be  deducted  from  this  table  for  net  cost,  probably  about 
in  the  proportion  of  two  thirds  for  old  brass  in  boiler  and  one  third  for  other  parts. 

p7'oportion  of  renewals  to  repairs  about  normal,  for  general  practice. 

The  labor  on  repairs  is  an  approximate  distribution  where  given  in  brackets,  otherwise 
the  distribution  is  exact. 

Round-house  repairs  constitute  over  thirty  per  cent  of  the  labor  on  repairs  proper,  or 
.616  cent  per  mile. 


Under  these  assumptions  we  are  led  to  the  conclusion  that  engines  of 
the  Consolidation  type  will  cost  about  25  per  cent  more  per  mile  run  than 
the  eight-wheel  "  American"  engines,  or  say  6i  cents  under  the  most 
favorable  circumstances  for  repairs  and  renewals  proper.  Heavy  Mogul 
or  ten-wheel  engines,  similarly,  will  cost  about  one  tenth  to  one  eighth 
more.  This  estimate  is  entirely  consistent  with  the  as  yet  fragmentary 
and  imperfect  records  of  experience,  but  the  latter  do  not  exist  in  suffi- 
cient abundance  to  say  that  in  themselves  alone  they  prove  anything. 

See  foot  of  page  148. 
Note  to  Table  57. — The  American  statistics  (and  not  the  English)  show  the  cost 
per  revenue  train-mile  of  all  engines,  including  switching. 


CHAP,    v.— OPERATING  EXPENSES— MOTIVE-POWER.     I47 


Table  66. 
Engine  Repairs  and  Renewals,  Paris  &  Orleans  Railway  of  France 

(1865-75). 


Labor. 

Materials. 

Total. 

Grand 

Re- 
newals. 

Re- 
pairs. 

Re- 
newals. 

Re- 
pairs. 

Re- 
newals. 

Re- 
pairs. 

Total. 

Engines 

.130 
.040 

.842 
•370 

.342 
.106 

1.238 
•540 

•472 
.146 

2.080 
.910 

2.552 
1.056 

Tenders 

Total  repairs  proper 

.170 

I. 212 

.448 

1.778 

.618 

2.990 

3.608 

Tools  and  machinery 

Clerks  and  general 

.074 

.2a8 

.094 

.168 
.248 

.168 
.248 

i.y 

■^ 

Total  all  repair  expenses . . 

04 

2.320 

4.024 

4.024 

The  proportion  of  renewals  to  repairs  in  this  table,  and  in 
pairs  only,  is  stated  to  be  unduly  low,  as  appears  certain  from 


less  degree  the  cost  of  re- 
the  figures. 


Table  57, 
Total  Cost,  by  Items,  of  Motive-Power. 

Cents  Per  Train-Mile. 


American. 

Av.  of 

U.S. 

Census. 

1880. 

English. 

Penna. 
R.R. 

1879-83. 

L.S.& 

M.S.Ry 
1872-81. 

Mass. 
RRs. 

1878-81. 

Gt.  W.  Ry. 

1869-76. 

Gt.  So. 
&W. 
1875. 

Midi. 
Gt.W. 

1875. 

5 -450 

5-787 

7.0 

4.66 

4-32 

384 

^-'•■•■|^°oid;:.v.;;.v.v-- 

4-705 
.223 

5.910 
.612 
•435 

1-715 
-133 

[8.85 

10.94 

8.4 

4-34 

6.61 

6.50 

Repairs  proper 

5 -015 

5-02 

■5-6 

J  Lab.  3.76 

(  Mat.2.46 

0.22 

>-          0.40 

2.82 
3-80 
0.32 

0.66 

3-42 
2.78 

Locs.     1   "    tools  and  mach'y 

Clean'g-  and  polic'g 

-35 

0.20 

fOil 

•255 
-259 
.123 
.052 

•358 

^i.ii 

-i.o 

1 
J 

0.48 

0.66 

1  Tallow 

Stores. .  \  Waste 

1  Other  stores 

LLoc.  fixtures 

Water    j  Expenses 

.602 
.368 

.6 

h-H 

0.42 

0.50 

0.32 

(  Taxes 

.215 
.098 
•415 

G^«V. ..-(  Stationery 

21.928 

22.6 

16.74 

19.76 

17.90 

I4S     CHAP,    v.— OPERATING  EXPENSES— MOTIVE-POWER. 

Table  58. 
Cost  of  Motive-Power  and  Cars  on  Twenty  English  Railways. 


20  Largest 
Corporations. 

4  Largest 
Corporations. 

Mass. 
1878-81. 

11,005 

33,203 

335,158 

17,064 

6,118 
14,902 

171,431 
16,520 

XTn     nf  rflrria  crfc 

"Mn    nf  'waD'nn';                  .. 

Av.  mileage  per  year  per  engine 

12.46  CtS. 

6.17 " 

12.94  CtS. 

6.90  " 

''          pncrinp  rpoair^ 

18.63  CtS. 

19.84  CtS, 

2.58  CtS. 

3.88  " 

2.28  CtS. 

3.98 " 

25.09  CtS. 

26.  10  CtS. 

$1,086 

133 
23.41 

$1,148 

160 
20.80 

$1,108 

"           rarnap"p  >                  ■<......... 

370 
55.40 

cd-riidgc  ^                 -s 

'          waeon     1     ^          ( 

English  carriages  and  wagons  may  be  considered,  without  important  error,  to  have 
half  the  weight,  capacity,  and  cost  of  American  rolling-stock.     See  Index. 

In  answer  to  inquiry  as  to  experience  and  practice  with  Consolidation  en- 
gines on  the  Pennsylvania  Railroad,  the  writer  was  informed  as  follows  by 
Mr.  T.  N.  Ely,  Supt.  of  Motive-Power: 

"  I.  Consolidation  locomotives  are  not  much  harder  on  curves  than  other 
locomotives,  we  think. 

"2.  The  comparative  cost  of  repairs  per  hundred  miles  between  a  Class  I 
locomotive  (Consolidation  type)  and  a  Class  D  (ten-wheel)  locomotive  is  about 
as  follows: 

''Class  1 4.87 

"Class  D, 4.50 

Difference, «     0.37 

or  nearly  eight  per  cent  against  the  Class  I." 

This  percentage  of  difference,  although  founded  on  much  experience,  must, 
it  would  seem,  somewhat  underrate  the  normal  difference. 

Passenger  engines,  as  a  general  rule,  cost  about  twenty  per  cent  less 
for  repairs  than  freight  engines,  or  about  four  cents  per  mile  under  the 
most  favorable  conditions. 


CHAP,    v.— OPERATING  EXPENSES— MOTIVE-POWER.     I49 


Table  59-60. 
Minor  Details  as  to  Locomotive  Repairs. 


Detail  items.  Gt.   S. 
&  W.  Ry.,  Ireland. 

Cents  Per  Tra 

tN-MlLE. 

Detail  items.  Gt.   S. 
&  W.  Ry.,  Ireland. 
;     (Condensed  in  pre- 
1     ceding  table.) 

Cents  Per  Train-Mile. 

(Condensed  in  Ta-: 

ble  55.)                        Rep'rs. 

Ren'ls. 

Total. 

Rep'rs. 

Ren'ls. 

Total. 

Copper  plates 

•'        stays 

"        tubes 

Fire-bars  and   brick 

.052 
.020 
.062 

.128 
.028 

.162 
•034 
.200 

.214 
•054 
.262 

.416 

.118 

•  154 

.272 

Clothing.^   paintings 
etc 

.060 

.058 

.118 

arch 

Boiler  sundries 

Total  Engine 

1.542 

1.724 

3.266 

.290 

.656 

.946 

Total  Boiler 

Tender 

.280 

.292 

.052 

.092 

.144 

Sjnoke-box  and  j>lat- 
foTnt 

\ Engine  and  tender.. 

1.822 

1.870 

3-838 

Wheels 

.128 
.062 
.092 

.164 
.242 
.326 
.200 
.160 

Less  credits 

.264 

.192 

•456 

A  floe 

.114 
.198 
.138 
.068 

Tires  

Springs 

Labor  acct.,  as  distributed  in  detail  to  gen- 
eral items  in  Table  55: 

.518 

•574 

1.092 

Total  Running  Cr 

Labor,  r'd-h'serep'r. 
"       shop           " 
"       tender       " 

.616 
.976 
.286 

\  -704 
.098 

Cylinders  

.048 
.078 
.052 
.010 
•034 
.042 

•034 

:^ 

.070 

.058 

-.132 

1 
J 

.102 

•590 

2.296 

•384 

Big-end  brasses 

Pistons,  etc   

Glands  and  bushes. . 
Slide-valve  castings, 

Total  Labor 

1.878 

.802 

2.680 

Eccentric  liners 

White  metal 

Machinery  sundries. 

Proportion  of  round-house  repairs,  Phila. 
&  Erie  R.R.,  about  the  same,  viz.:  26  per  cent 

T:oX3.\  Machinery.. 

•  504 

.190 

.6,4 

See  also 

Table  13 

6. 

Table  61. 
Cost  of  Maintenance  of  Tires  in  Detail,  Gt.  S.  &  W.  Ry. 

Cents  Per  Train-Mile. 


Engines. 

Tenders. 

Date. 

Pass. 

Freight. 

All. 

Total. 

1860-64. . • 
1865-69.. . 
1870-74... 

•33 
•44 
.22 

.57 
.46 
.44 

.42 
•45 
.30 

.24 
.15 
•23 

.66 
.60 
.53 

Average . . 

•33 

•49 

•39 

.21 

.60 

Mileage  of  Tires,  4'  6"  6'  6" 

Iron,  52,300         114,500 

Steel,  105,700         196,600 


150     CHAP,    v.  — OPERATING  EXPENSES— MOTIVE-POWER. 


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CHAP,    v.— OPERATING  EXPENSES— MOTIVE-POWER.     151 


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152     CHAP,    v.— OPERATING  EXPENSES— MOTIVE-POWER. 

Table  64. 
Cost  of  a  Pennsylvania  Railroad  ' '  Class  I "  (Consolidation)  Engine, 


Material. 

Labor. 

Total. 
$9,.  980 

Boiler 

Machinery 

$1,877 

935 

1,456 

200 

652 

47 

Running  gear 

Fittings 

Painting 

Total  engine     

$5,167 
845 

Tender 

Tot.  engine  and  tender. 

$6,012 

$3,968 

Phila.  &  Reading,  1881,  average  of  18  engines.. 

$10,370 

See  also  Table  134. 


Table  65. 


Ratio   of  Cost  of  Materials  to  Total  Cost  for  both  New  Engines 

AND  Repairs. 


On  New  Engines  (or  Renewals). 


Chicago,  B.  &  Q.  RR.,  Class  A 

Pennsylvania          "          "      C....... 

"       I 

English  (R  Price  Williams) 

64.6^ 
66.7 
60.3 
78.1 

Gt  So  &  W^  of  Ireland         

72.9 
69.5 
71.8 

"             "             "      renewals 

Paris  &.  Orleans 

On  Repairs  Only  {ex  Renewals). 


New  York  Cent.  &  H.  R.  RR 

Philadelphia  &  Reading 

Av.  of  U.  S.,  repairs  only 

"  "       repairs  and  renewals.. 

Gt.  So.  &  W.  of  Ireland 

"  "    av.  repairs  and  renewals. 

Paris  &Orl.,  "        "        "  " 


44 -o^ 
43-3 
Abt.,  44 
"      50 
45-3 
55.8 
58.0 


CHAP,    v.— OPERATING  EXPENSES— MOTIVE-POWER.     153 

135.  The  apparent  cost  of  repairs  has  been  kept  down  on  all  our  rail- 
ways for  the  time  being  by  the  constant  additions  of  new  stock,  thus 
greatly  reducing  the  percentage  of  renewals  and  heavy  repairs.  Table  51 
will  show  to  what  a  very  important  effect  this  cause  must  have  contrib- 
uted to  reduce  the  apparent  average,  especially  during  the  rapid  growth 
of  traffic  of  the  last  ten  years. 

136.  The  distribution  of  the  cost  of  repairs  to  the  various  parts  of  the 
locomotive  concerns  us  quite  as  much  as  its  total  amount.  Information 
on  this  head  is  somewhat  difficult  to  procure,  as,  so  far  as  the  writer 
knows,  no  American  railways  publish  such  statistics  in  a  complete  form, 
and  few  take  much  trouble  to  collect  the  information.  Tables  53  to  dy, 
however,  give  the  cost  of  new  "  American"  engines  in  detail,  and  also 
very  full  statistics  of  the  cost  of  engine  repairs  and  renewals  on  English 
railways,  which  latter  are  undoubtedly  substantially  accurate,  and  (with 
proper  allowances)  of  general  application  to  all  railways. 

137.  From  these  data  we  may  conclude  that,  with  no  very  great  fluc- 
tuations, the  total  cost  chargeable  to  repairs  of  engines,  including  renew- 
als, may  be  distributed  about  as  follows  : 

The  boiler  and  its  attachments  require  about 20  per  cent 

The  running  gear  and  frame  (of  which  the  frame  consumes 

very  little,  say  2  per  cent), 20  per  cent 

The  machinery  proper, 30 

The  mountings,  fittings,  and  painting, 12       " 

The  smoke-box  and  attachments, c       " 

Total  of  engine,       87  per  cent 

The  running  gear  of  tender, p 

Tank  and  body  of  tender, 4 


Total, 100 


per  cent 


138.  Maintenance  of  shops,  tools  and  machinery,  and  other  miscella- 
neous motive-power  expenses  do  not  usually  appear,  as  before  stated,  in 
statements  of  the  cost  of  repairs  or  of  running  engines,  although  they  con- 
stitute a  legitimate  addition  thereto.  On  the  Pennsylvania  (Table  57) 
these  items,  including  stationery,  incidentals,  and  watchmen,  but  not  in- 
cluding the  item  of  "laborers," — the  latter  doubtless  largely  for  cleaning 
engines,— amount  to  twenty-five  per  cent  of  the  cost  of  engine  repairs,  or 
about  \\  cents  per  train-mile,  and  the  item  of  "  laborers"  to  as  much  more. 
This  is  higher  than  is  usual,  or  perhaps  it  would  be  more  proper  to  say 


154     CHAP,    v.— OPERATING  EXPENSES— MOTIVE-POWER. 

that  it  is  based  upon  a  closer  apportionment  than  is  usual,  many  lines; 
having  items  of  a  general  character  for  laborers,  clerks,  etc.,  to  which  all 
such  are  charged  for  the  whole  road,  without  separately  apportioning 
them  to  motive-power  and  other  departments. 

139.  Maintenance  of  tools,  shops,  machinery,  and  other  miscellaneous 
and  indirect  motive-power  expenses,  average  as  nearly  as  may  be  i  to  \\ 
cents  per  train-mile  on  the  larger  and  more  important  roads,  ranging 
considerably  higher  on  smaller  roads,  if  all  the  expenses  are  apportioned 
with  equal  care. 

This  is  an  expense  which  is  affected  but  slightly  by  very  considerable 
variations  in  engine-mileage,  and  hence  ought  to  be  kept  separate  from 
engine  repairs  proper,  but  rarely  is.  It  is  an  important  element  in  the 
total  cost  of  motive-power. 

140.  Oil,  waste,  and  small  engine  supplies  cost  on  an  average  about 
one  cent  per  mile,  but  often  run  as  low  as  half  a  cent,  or  even  less,  on  the 

Table  66. 


Percentages  of  the  Cost  of  Labor  and  of  Material,  and  of  the 
Various  Parts  of  New  Locomotives. 

(Shop  and  general  expenses  not  included,  amounting  to  about  50  per  cent  of  Labor 

Account.) 


Items. 
(For  amounts  see  Tables  6i, 

C,  B.  &  Q.  RR. 

(Class  H). 
St'd  Freight. 

Penna.  RR.,  "  C." 
St'd  Passenger. 

Penna.  RR.,  "  L'^ 
St'd  Freight. 

62,  etc.) 

Lab'r 

Mat'l 

Total 

Lab'r 

Mat'l 

Total 

Lab'r 

Mat'l 

Total 

Boiler  aDd  braces  

9.8 
10.6 

3-3 
2.1 

5-3 
0.9 

25-3 
7-1 

10.7 
2.1 

10. 1 
0-5 

35-2 
17.7 
14.0 

4.2 
15.2 

1.4 

7-4 
9.9 
2.1 
2.2 
5-5 
0.9 

20.6 
10.4 

13-9 
2.1 
7-4 
0.6 

28.0 
20.3 
16.0 

4-3 

12.9 

1-5 

(11. 0) 
(12.9) 
(4.0) 
(2.2) 
(5-o) 
(i.o) 

18.8 
9.4 

14.6 
2.0 
6.5 
0.5 

29.8 

18.6 

Frame  and  bed-casting 

Fittings  and  pump,  cab,  etc 

Painting                  

4.2 
1.5 

Total  eneine            

32.0 

55-8 

87.8 

28.0 

55-0 

83.0 

(35-2) 

51.8 

87.0 

3-5 

8.7 

12.2 

4.6 

12.4 

17.0 

(4.6)      8.4 

13.0 

Total  engine  and  tender 

35-5 

.64.5 

100. 0 

32.6 

67.4 

100. 0 

39.8       60.2    iIOO.O 

Reported  cost  labor  and  mat'ls. 

$5,803 

$7,954 

$9,980 

Cylinders  and  weight  (long  t'ns) 

17X24 

17X24—33.8  tons. 

20X24 — 40.9  tons. 

CHAP,    v.— OPERATING  EXPENSES— MOTIVE-POWER.     I55 


Table  67. 

Percentages  of  Cost  of  Various  Parts  for  Various   Foreign  Locomo- 
tives. 

(For  American,  see  preceding  table.    See  also  Table  131.) 


Items. 


Boiler,  smoke-box,  chim- 
ney, stays 

Ash-pan,  foot-plate,  cab, 
sand-box 

Wheels,  bearings,  frames, 
springs 

Machinery,  pumps,  re- 
verse-gear   

Cocks,  safety-valves 

Painting,  brass  sheathing. 


Total,   both  engine  and 
tender 


Reported  cost,  labor  and 
materials 


Cylinders     and    weight 
(long  tons) 


Approx.      increase     per 
cent  in  cost,  due  to.. 


Paris  &  Orleans 

(France). 

St'd  Freight. 


Lab'r  Mat'l  Total 


8.3 

2-3 

5-7 

10. 1 
0.9 


35-2 

2.9 

18.2 

10.6 
2.2 
2.6 


3      71.7     100. o 


43-5 

5-2 

23-9 

20.7 
3-1 
3-6 


$9,650 


(17X24)— 29.5  tons 


I  brass  in  b'r  16.0^ 
I  wr't-i.  wh's  11.6^ 


Items. 


Boiler 

Smoke-box,  etc  — 
Wheels,  frame,  etc . 


Machinery. 
Mountings. 
Painting. .. 


Total  engine  and  tender 


Gt.  So.  &  W. 

(Ireland). 
St'd  Freight. 


Lab'  r  Mat'l  Total 


5-6 

3-9 

3-3 

9-5 
II. 7 
I.I 


27.6 

4-3 

27-5 

8.7 
4.6 
2.2 


25.1       71.9     lOO.O 


33-2 

8.2. 

30. & 

1B.2 
6.3 
3-3 


$9,424 


17X24 — 30.0  tons. 


,10.0^ 
.12.8^ 


Gt 

So.  &  W. 

Great  Western  Railway  (England). 

Items. 

Heavy  Passenger. 

Heavy  Passenger. 

St'd  Freight. 

Lab'r 

Mat'l 

Total 

Lab'r 

Mat'l 

Total 

Lab'r 

Mat'l 

Total 

5-0 
4-5 
10.4 
5-1 

1.6 

2.1 

27.4 

2-5 

28.3 
33-0 
17.8 
8.9 

7-9 
4.1 

i^. 

(::: 

25.0 
19.4 
3-4 

II. 0 

28.8 

25.0 

8.3 

20.4 

4.1 

5-7 

4.9 

V9.6 

246 
16.0 

3-2 

12. J. 

28.7 

21.7 
8.1 

22.0 

f 

Total  engine                 

23-7 

58.8 

82.5 

24-3 

56.2 

80.5 

Tender           

5-8 

1 1. 7 

17-5 

6.5 

13.0 

19.5 

Total  engine  and  tender 

28.5 

72. 5 

100. 0 

29-5 

70-5 

100. 0 

30.8 

69.2 

100. 0 

Reported  cost,  labor  and  mat'ls 

$9,072 

$7,432 

$6,709 

Cylinders  and  weight  (longt'ns) 

(17X22)— 30.3  tons. 

17X24 — 31  tons. 

17X24—30.5  tons. 

Approx.    increase   per  cent    in 

(brass  in  b'r     %.o% 
\  wr't-i.  wh's  i^.q5? 

■;  o5^ 

\ 5.0^ 

10.0% 

10. 0^ 

' 

The  distribution  to  items  is  not  precisely  identical  in  these  tables,  as  will  be  apparent 
from  the  percentages.  Multiplying  any  percentage  by  the  total  cost  gives  the  absolute 
expenditure  for  the  item. 


15^     CHAP,    v.— OPERATING  EXPENSES— MOTIVE-POWER, 

larger  roads,  especially  where  there  is  an  independent  account  kept  with 
each  engine. 

141.  Water-supply  costs  about  half  a  cent  per  train-mile  as  an  average, 
sometimes  running  below  that  on  roads  of  very  heavy  traffic,  but  oftener 
running  nearer  to  one  cent  per  mile.  On  all  but  roads  of  very  consider- 
able traffic  one  cent  is  the  safer  estimate.  The  quantity  used  is  very  con- 
siderable. About  six  or  six  and  a  half  pounds  of  water,  as  an  average,  is 
evaporated  per  pound  of  coal,  and  a  freight  engine  burning  a  hundred 
pounds  of  coal  per  mile  will  use  some  eighty  gallons  of  water,  or  require 
the  refilling  of  a  2400-gallon  tank  within  thirty  miles  at  the  utmost,  as  an 
average.  Practically,  the  consumption  of  water,  as  of  coal,  is  irregular, 
and  a  full  tank  may  in  cases  be  used  up  within  fifteen  miles;  requiring, 
for  practical  convenience,  tanks  every  ten  miles,  which  is  the  average  on 

/    roads   of  thin  or  average   traffic.     On  lines  of  heavy  traffic,  tanks  are 
fA^\   \  placed  at  average  intervals  of  hardly  more  than  five  or  six  miles.     Table 
' ''      (  57  gives  considerable  data  as  to  these  minor  items. 

142.  Switching  engines  constitute  an  enormous  proportion  of  the  total 
number  in  service  on  most  roads,  the  average  of  the  whole  State  of  New 
York  being  twenty- eight  per  cent  of  the  whole  number  in  service,  or 
nearly  forty  switching  engines  for  every  hundred  in  through  service  earn- 
ing money.  Their  "mileage"  is  fixed  by  an  allowance  (usually  six  miles 
per  hour,  but  sometimes  eight),  so  as  to  bring  their  expenses  per  "  mile" 
in  some  reasonable  or  desired  ratio  to  that  of  through  engines.  The 
great  expense  of  this  service  does  not  tend  to  decrease,  but  rather  to  in- 
crease, with  growth  of  traffic,  and  is  with  reason  felt  to  be  largely  due  to 
removable,  and  hence  discreditable,  defects  of  administration.  The 
burden  is  somewhat  relieved  at  the  larger  terminals  by  fixed  terminal 
charges  allotted  out  of  the  through  rates  before  dividing  it  (at  New  York 
four  to  five  cents  per  hundred  pounds  out  of  through  rates  of  twenty  to 
thirty  cents,  or  even  less).  It  is  a  charge  but  little  affected  by  any  of  the 
details  of  alignment,  so  that  we  need  not  discuss  it  in  detail,  but  in  cer- 
tain computations  it  is  an  element  which  needs  to  be  remembered — nota- 
bly in  computations  of  the  value  of  reducing  grades  on  old  roads,  whereby 
this  portion  of  the  motive-power  expenses  is  not  seriously  reduced. 

The  diagram  given  in  Fig.  4  illustrates  very  fairly  the  past  tendency  of 
locomotive  expenses.  Alone  of  all  the  items,  wages,  it  will  be  seen,  have 
remained  practically  uniform.  There  was  a  slight  tendency  to  decrease  during 
the  hard  times  of  1877-79,  but  they  recovered  later,  and  remain  at  the  end  sub- 
stantially what  they  were  in  the  beginning. 

The  cost  of  fuel  declined  sharply  after  1872,  but  since  1876  has  been  nearly 


CHAP,    v.— OPERATING  EXPENSES— MOTIVE-POWER.      I  57 


Fig.  4.— Locomotive  Expenses,  C,  B.  &  Q.  R.  R. 


158     CHAP,    v.— OPERATING  EXPENSES— MOTIVE-POW£R. 

uniform.  Two  possible  causes  for  this  are  indicated  on  the  diagram,  both  of 
which  probably  had  their  effect.  One  was  the  increase  in  miles  operated,  which 
probably  gave  better  access  to  coal-mines,  but  another  and  probably  very 
important  contributing  cause  was  the  increase  in  miles  run  per  engine  per  year, 
which  likewise  began  simultaneously,  and  ceased  to  advance  sharply  after  the 
■cost  of  fuel  ceased  to  decrease. 

The  course  of  cost  of  repairs  is  very  instructive.  It  will  be  seen  that  the 
■decrease  has  been  enormous,  and  it  is,  doubtless,  in  great  part  due  to  natural 
and  permanent  causes,  such  as  the  decrease  in  cost  of  materials  and  better  shop 
facilities.  But  it  needs  but  a  brief  glance  at  the  line  showing  "Number  of 
engines  on  road,"  in  connection  with  the  cost  of  repairs,  to  detect  another 
explanation,  of  vast  importance  in  its  effect  on  operating  expenses,  which  is 
too  little  remembered  in  studying  maintenance  charges,  viz.,  the  enormous  and 
continuous  infusion  of  "  new  blood  "  into  the  locomotive  stock,  giving  at  all 
times  a  very  large  number  of  new  locomotives  in  the  stock  in  addition  to  the 
proportion  naturally  required  to  replace  old  engines  worn  out.  As  new  engines 
cost  comparatively  little  for  repairs,  it  is  inevitable  that  this  abnormal  propor- 
tion of  new  engines  should  greatly  affect  the  average  cost  of  repairs,  and  it  is 
very  clear  that  it  did  so.  The  very  small  expense  for  repairs  in  1875-9  ^^.s  not 
wholly  due  to  economies  enforced  by  hard  times,  although  no  doubt  largely  so, 
but  in  great  part  to  the  fact  that  there  was  a  greater  proportion  of  new  engines 
in  service  than  at  any  time  before  or  since.  Afterwards  the  inevitable  increase 
came  about,  in  spite  of  heavy  falls  in  the  cost  of  much  of  the  material  used,  due 
to  improved  processes  of  manufacture  and  cheaper  transportation,  and  should 
the  continual  additions  of  new  stock  cease,  it  is  very  certain  that  the  increase 
must  go  still  further.  It  is  to  be  remembered  also  that  these  nominal  "  repairs" 
■do  not  include  many  incidentals  for  maintenance  of  shops,  etc.,  which  are 
really  a  part  of  the  cost  of  repairs,  but  not  ordinarily  included  in  it.  A  chief 
reason  for  the  heavy  decline  since  1866  is  undoubtedly  the  continued  improve- 
ment in  the  character  of  the  road-bed  and  in  the  quality  of  the  workmanship  and 
material  used. 

The  increase  in  the  average  miles  run  per  engine  shows  an  unusually  favor- 
able record,  and  one  not  likely  to  be  much  further  improved  on,  since  an  average 
of  nearly  a  hundred  miles  per  day  for  every  day  in  the  year  and  for  all  engines 
nearly  reaches  the  possible  limit.  It  implies  that  single  engines  have  more 
than  doubled  this.  The  decrease  in  miles  run  and  simultaneous  increase  in  cost 
of  repairs  per  mile  run  in  1882  can  hardly  be  an  entirely  accidental  coinci- 
dence. 

Table  68  shows  the  average  miles  run  per  year  and  the  average  cost  per 
year  of  "locomotive  power"  (repairs,  stores,  wages,  and  fuel)  on  ten  repre- 
sentative English  and  American  lines.  The  latter  by  no  means  represent  the 
l)est  American  practice,  as  will  be  evident  from  Fig.  4,  but  are  those  lines  (for 


CHAP,    v.— OPERATING  EXPENSES— MOTIVE-POWER.     1 59 

the  most  part)  which  are  operated  under  the  most  fairly  comparable  conditions 
with  the  English  lines.  Could  the  ton-miles  and  passenger-miles  per  year  per 
engine  be  compared,  the  contrast  in  work  done  per  engine  would  be  astounding 
(over  three  to  one),  but  the  English  railway  statistics,  alone  of  those  of  civilized 
countries,  do  not  give  these  facts.  In  part  the  difference  in  work  done  is 
explicable  by  difference  of  conditions,  but  by  no  means  wholly  so. 

Table  69  gives  the  work  done  per  year  per  engine  and  the  number  of 
engines  in  all  countries,  from  which  it  appears  that,  far  as  American  practice 
is  ahead  of  English,  the  latter  surpasses  that  of  all  other  countries. 

Table  68. 

Annual  Average  Expenditure  Per  Locomotive  for  Locomotive  Power 
ON  Ten  Leading  Lines  in  the  United  Kingdom  and  in  the  United 
States,  with  the  Average  Annual  Number  of  Train-Miles  Run  Per 
Engine. 

[Abstracted  and  recomputed  from  "  Railway  Problems,"  by  J.  S.  Jeans,  Secretary  British  Iron 
and  Steel  Association.] 


English  Locomotives. 

American  Locomotives. 

Per  Locomotive. 

Road. 

Per  Locomotive. 

.Road. 

Average 
Annual 
Expendi- 
ture. 

Average 
Train- 
Miles. 

Average 
Annual 
Expendi- 
ture. 

Average 
Train- 
Miles. 

$3,320 
3,540 
3.040 
2,455 
3,000 
3,720 
2,980 
2,610 
4,370 
3,610 

21,518 
16,240 
19,600 
15,422 
19,313 
21,456 
18,101 
19,959 
22,323 
19,844 

Boston  &  Albany 

Boston  &  Lowell 

Boston  &  Maine.  ... 

Boston  &  Providence  . . . 

Old  Colony.   

N.  Y.,  New  Haven  &  H. 
N.  Y.,  Lake  Erie  &  W'n. 
N.  Y.  Cent.  &  Hudson  R. 
Pennsylvania— Pa.  Div.. 
Baltimore  &  Ohio 

Average 

$7,240 
8,600 
6,640 
6,840 
6,440 
8,610 
4,260 
7,720 
5,880 
2,700 

North-Eastern     

20,000 

Midland 

London  &  North-Western 
Great  Western 

18,000 

Caledonian 

North  British  ...   

London  &  South-Western 
iond..  Bright.  &  So.  C'st 

25,000 
26,000 
27,000 

Average 

$3,080 

17.539 

%r    COO                  "->   ^"2 

Average  earnings  per  year  per  locomotive, 


j  American, 
•  I  English,     . 


Average  rate  per  ton-mile, -j  American, 

Average  rate  per  passenger-mile, i  F^T^vf?' 


$14,860 
$10,940 


1.057  cts. 

2  to  2.4  cts. 

2.198  cts. 

(about  the  same). 

All  the  above  is  for  1883,  except  the  rates,  which  are  for  1885.     The  earnings  and 
rates  given  are  for  the  national  aggregates,  and  not  merely  for  the  ten  roads  above. 


l6o     CHAP,    v.— OPERATING  EXPENSES— REPAIRS   OF  CARS. 


Table  69. 

Total  Number  of  Locomotives  in  Different  Countries,  Number  of 
Train-Miles  which  they  have  accomplished,  and  the  Average  Miles 
Per  Day  and  Per  Year  Per  Locomotive. 

[Abstracted  from  "Railway  Problems,"  by  J.  S.  Jeans,  Secretary  British  Iron  and  Steel  Asso- 
ciation, with  some  modifications.] 


Countries. 


United  States.. . . 
United  Kingdom 

Germany 

Austria 

Belgium 

France 

Italy 

Luxembourg 

Norway 

Netherlands  .... 

Roumania 

Russia 

Finland 

Switzerland 

India 


Number 

of 
Locomo- 
tives, 


23,823 
14,827 
11,330 
3,671 
1,790 
8,088 
1,630 

34 
III 

519 
211 

5,844 

98 

595 

1,730 


Train- 
Miles. 
I  =  1,000. 


Average 

Miles 
Per  Loco- 
motive 
Per  Annum. 


538,011 

272,803 

134,489 

47,144 

23,870 

135,860 

24,642 

433 

1,557 

11,435 

2,207 

61,940 

1,177 

7,674 

33,919 


22,583 

18,395 
11,870 
12,842 

13.335 
16,798 
15,118 
12.735 
14.027 
22,033 
10,460 

10,599 
12,010 
12,897 
19,606 


Average 

Miles 
Per  Loco- 
motive 
Per  Day. 


62 
50 
33 

35 
37 
46 

41 

35 
38 
60 
29 
29 
33 
35 
54 


The  above  statistics  are  for  1883  for  the  United  States  and  Great  Britain,  and  for  1882 
for  the  other  countries.  Some  American  roads  (see  Fig.  4)  run  up  to  an  average  for  large 
numbers  of  engines  of  100  miles  per  day. 

143.  Repairs  of  Cars  can  be  estimated  with  most  correctness  per 
car-mile,  and  not  per  train-mile.  They  may  be  roughly  placed,  with  a 
very  fair  degree  of  correctness,  at  \  cent  per  freight  car-mile  and  i^ 
cents  per  passenger  car-mile,  on  the  larger  roads.  On  small  roads  \  cent 
per  car-mile  for  freight-car  repairs  is  more  nearly  correct.  Figures  indi- 
cating much  less  than  this  require  allowances.  This,  however,  as  in  the 
case  of  engine  repairs,  includes  only  labor  and  material  directly  applied 
to  the  cars  themselves,  and  there  is  a  considerable  amount  of  incidental 
expenditure,  which  is  really  a  part  of  the  actual  cost  of  maintaining  the 
cars,  but  which  is  yet,  for  very  proper  reasons,  already  stated,  not  gen- 
erally included  in  the  reported  cost  of  car  repairs. 

Such  general  and  incidental  expenses  amount  to  from  10  to  25  per 
cent  of  the  total  cost  of  car  repairs  proper. 


CHAP,    v.— OPERATING  EXPENSES— REPAIRS  OF  CARS.     l6l 


Table  70. 

Average  Cost  of  Car  Repairs  on  Western  &  Atlantic  Railroad  for 
Different  Kinds  of  Cars. 

Cost  Per  Car  Per  Year. 


Cost  Per  Car  Mile. 


■ 

Passenger. 

Local  Box. 

Stock. 

Coal  and 
Flat. 

Line. 

Running  gear 

Interior  fittings 

Miscellan's  material. . 

$64.80 
23-45 
41-75 

$6.78 
12.10 

$7.46 
8.50 

$6.76 
6.50 

$19.09 
13-49 

Total  material 

Labor 

$130.00 
III. 50 

$18.88 
11. 12 

$15-96 
9-35 

$13.26 
4.48 

$32.58 
10  62 

Total 

$241.50 

$30.00 

$25-31 

$17.74 

$43.20 

Miles  per  car 

No.  of  cars  in  use..  . . 

36,480 
138 

7,780 
194 

5.601 
40 

5,420 

4S9 

10,043 
648 

Running  gear. 

Interior  fittings 

Miscellan's  material. . 

cts. 

.178 
.064 

.114 

cts. 

.087 

.155 

cts. 

.133 
.152 

cts. 

.125 

.120 

cts. 

.191 

.135 

Total  material 

Labor 

.356 

.306 

•  243 

-143 

.285 
.167 

•  245 

.083 

.326 

106 

Total 

.662 

.386 

.452 

.328 

.432 

The  above  includes,  whether  by  chance  or  otherwise,  no  charges  whatever  for  seats  or 
upholstery  of  passeng-er  cars.  Otherwise  it  includes  all  work  done  in  the  car  department 
for  maintenance  of  cars,  both  repairs  and  renewals.  The  cost  per  passenger  car  is  very- 
low. 

Tables  70,  71,  72,  73  were  computed  from  data  given  in  a  very  careful  paper 
on  car  mileage  and  repairs  by  E.  C.  Spalding,  Car  Accountant  W.  &  A.  R.  R., 
and  afford  about  the  most  trustworthy  data  on  the  details  of  car  repairs  which  is 
extant.  Such  information  is  very  difficult  to  obtain,  and  even  this  affords  no 
means  of  distributing  expenses  to  different  parts  of  the  car  body.  Making  a 
proper  allowance  for  labor,  it  will  be  seen  that  somewhat  over  40  per  cent  of 
car  repairs  arises  from  running-gear  maintenance,  and  nearly  75  per  cent  from 
truck  repairs.  By  far  the  larger  part  of  the  remainder  is  for  draw-gear  re- 
pairs.    Other  repairs  of  body  are  a  very  small  expense. 

These  statistics  give  the  true  average  cost  of  car  repairs  for  a  stock  which 
II 


1 62     CHAP.    V  — OPERATING  EXPENSES— REPAIRS  OF  CARS. 


is  being  neither  increased  nor  decreased.  They  are  almost  the  only  records  of 
the  kind  which  have  been  published. 

One  very  notable  fact  in  Table  70  is  that,  contrary  to  what  might  be 
expected,  the  cars  which  make  the  largest  mileage  per  year  cost  the  most  per 
mile  for  maintenance.'  The  chief  reason  for  this  is,  probably,  that  they  are 
maintained  up  to  a  higher  standard;  but  as  the  cars  in  local  service  are  (i)  sub- 
jected to  more  banging  and  more  frequent  use  of  brakes,  and  (2)  make  a  smaller 
mileage  per  year,  so  that  the  rotting  and  other  effects  of  time  and  age  are 
divided  up  among  a  smaller  number  of  miles,  we  should  expect  to  see  a  some- 
what higher  cost  per  mile  run  for  such  cars.  On  the  contrary,  it  is  smaller,  both 
for  running  gear  only  and  for  the  aggregate  of  all  items. 

Table  74  gives  the  cost  of  car  repairs  on  the  Lake  Shore  &  Michigan  Southern 
Railway  for  repairs  proper  and  renewals  separately.  In  former  years  the  cost 
of  Lake  Shore  car  repairs  was  much  higher  than  that  shown  ;  $50  per  year  is 
perhaps  a  fair  permanent  average  at  present  prices.  The  reason  why  no  dis- 
tinction is  even  attempted  between  renewals  and  repairs  in  either  locomotive  or 
car  maintenance  is  clear  from  the  note  to  the  table. 


Table  71. 

Cost   of  Freight-Car    Repairs  Per   Mile  Run  by  Items  for  Cars  of 
Various  Ages — Western  &  Atlantic  Railroad. 


Box  Cars. 

Coal  Cars. 

Items. 

Cars. 

I  to  5 
years. 

6  to   TO 

years. 

II  to  16 
years. 

Av'ge 

all 
Cars. 

I  to  5 
years. 

6  to  10 
years. 

II  to  16 
years. 

Axles 

•  035 
.101 
.073 

.022 
.081 
•  052 

.042 
.112 
.077 

.051 
.123 
.110 

.031 
•073 
•  063 

.016 
.042 
.032 

.CAS 

Brasses      

099 
091 

.083 

Wheels 

.071 

Runninsf  tfear.         .... 

.209 

•155 

.231 

.284 

.167 

.090 

235 

.188 

.030 
.054 
.052 
.021 
.022 

.CX59 

•  135 

.012 

.020 
.036 
.017 
.022 
.017 
.002 
•075 

.007 

.030 
.066 

•073 
.020 
.022 
.016 
•154 

.018 

.050 
.074 
.090 
.022 

•033 
.011 
.227 

.013 

.032 
.070 
.065 
.011 
.016 
.... 
.141 

.004 

.021 
.028 
.007 
.011 
.016 

.046 
.002 

031 
100 
116 
006 
018 

220 
005 

■043 
.086 

Lumber    

.081 

.014 
.016 

Bolts          

Paint 

Labor             .          

.170 
.006 

Nails,  chains,  and  metal- 
lic sundries 

•544 

•351 

.630 

.804 

.506 

.221 

731 

.604 

Av,  miles  run  per  year.. 

9,238 

11,767 

8,904 

6,996 
$56.26 

4,970 

5,541 

4,336 

5,091 

Av.  total  cost  per  year. . 

Sso.33 

S39.82 

Ss6-io 

$25.24 

$12.25 

$ 

31-67 

$30.72 

CHAP,    v.— OPERA  TING  EXPENSES— REPAIRS  OF  CARS.     1 63 


Table  72. 
Cost  of  New  Box  Car  in  Detail,  1883. 

[Deduced  from  data  given  in  a  paper  by  E.  C.  Spalding,  Car  Accountant,  Western  &  Atlantic 

Railroad.] 


Material. 

Labor. 

Total. 

Per  Cent. 

Lumber 3,987  ft. 

Wrought-iron. .  .704  lbs. 

Cast-iron 606    " 

Nails,  etc 

$79-74 
35 -20 
18.18 

5-21 

4.14 
12.60 
3-28 

1 

i 

)■  20  days  carpenter. 

$45.00 

$183.33 

4.14 
16.60 
6.28 

\ 
36.1 

Draw-springs 46  lbs. 

Tin  roof 

0.8 

4  days  tinner 

ij^  days  painter 

4.00 
3.00 

3-3 
1.2 

Total  body 

$158.35 
31.2 

$52.00 
10.2 

$210.35 
41.4 

41.4 

Truck. 


Wheels 4,200  lbs. 

>  $160.00 

14.08 
16.56 
9-74 
50.00 
39.18 
•79 

$160.00 
14.08 
16.56 

104.57 
1.29 

31-5 
2.8 

Axles 1,400    " 

Brasses 64    " 

Springs 184    " 

Lumber. 487  ft. 

Wroughl-iron.  1,000  lbs. 

Cast-iron 1,306    " 

Painting 

3-3 

20.7 

•3 

1-  Carpenter 

Painter 

$5.65 
•50 

Total  truck 

$290.35 

$6.15 

$296.50 

58.6 

Total  car 

$448.70 
88.5 

$58.15 
11-5 

$506.85 
100.00 

Per  cent 

The  weight  of  metal  in  a  standard  New  York  Central  40,000-lb.  box-car  is  given  as 
follows  : 

Wrought-iron  in  car  body  2,552    lbs. 

Cast-iron  in  " 797      " 

Steel  in  "  104      " 

Malleable  iron  in      "  13^4 " 

Wr't-iron  in  trucks,  includ'g  axles,  3,144      " 


Cast-iron  in  trucks,  includ'gwheels, 

Malleable  iron  in  trucks 

Journal-bearings 

Wheels,  each 

Axles  (M.  C.  B.  Standard) 


5,366  lbs. 

48  ■" 

80  " 

525   " 

347    " 


The  TOTAL  COST  PER  TRAIN-MILE  of  passenger-car  repairs  and  freight- 
car  repairs  is  very  nearly  the  same  in  the  aggregate,  as  may  be  seen  from 
Tables  75-80,  although  the  proportion  of  the  constituent  elements  differs 
considerably.     (See  par.  150,) 


164     CHAP.    V— OPERATING  EXPENSES^REPAIRS  OF  CARS. 


Table  73. 

Average  Cost  in  Detail  of  Keeping  in  Repair  Trucks  and  Bodies 

Separately  of  Box  Cars. 

Age  of  cars  three  years.     Built  at  cost  of  $515.00  each.     (Compare  Table  87.) 


Trucks. 
Original  Cost,  8315. 

Body. 
Original  Cost,  S200. 

Items. 

Cost  Per 
Year. 

Per  Cent 
of  Total. 

Items. 

Cost  Per 
Year. 

Per  Cent 
of  Total. 

Axles 

$3.04 
12.44 
6.06 

6.3 
25.8 
12.6 

Labor  

«5.45 
1-33 
1.40 
I. II 
1.70 
1.26 

X.19 

"•3 

2  6 

Brasses  

Cast-iron                . 

Wheels . 

Wrought-iron 

Bolts 

2.9 

S21.54 

44-7 

2-3 

3-5 

Running  gear 

Lumber 

Springs 

$4.97 

2.72 

2.66 

2.10 

.67 

.11 

.02 

.02 

10.3 
5-6 
5-5 
4.4 

•       1-7 

Springs 

Chains,    nails,    nuts, 
paint,  screws,  sol- 
der, tin 

2.6 

Cast-iron  . 

Wrought-iron 

Bolts 

Lumber 

2.6 

Nuts 

Paint 

Total  

S34.81 

72.2 

$13-44 

27.8 

Total  cost  per  car                                                                     .         

$48.25 

100  0 

The  expenditures  for  wheels  are  extremely  low  in  all  the  Western  &  Atlantic  records.. 
Many  roads  show  as  high  as  40  per  cent  of  car  repairs  expended  in  wheels  alone. 


144.  The  established  mileage  rate  for  interchange  of  traffic  is  f  cent 
per  car-mile,  this  rate  having  been  attained  by  a  gradual  drop  from 
3  cents  to  2  cents,  to  if  cent,  to  i  cent,  and  at  last  to  the  present  rate, 
f  cent,  and  including  (or  being  intended  to  include)  a  certain  profit  on 
the  use  of  the  cars  sufficient  to  take  awa}^  all  inducement  for  keeping 
foreign  cars  in  home  service,  if  not  to  place  a  certain  penalty  on  such 
use.  It  is  probable  that,  as  an  average  of  several  years,  the  price  stated 
is  sufficient  to  do  this,  especially  as  in  addition  to  this  sum  the  road 
using  foreign  cars  is  required  to  make  good,  at  its  own  expense,  any 
deterioration  which  parts  of  the  car  other  than  the  wheels  and  axles  may 


CHAP,    v.— OPERATING   EXPENSES— REPAIRS   OF  CARS.      1 65 

suffer  while  on  its  lines.  Nevertheless,  whenever  business  is  brisk  and 
cars  are  scarce,  which  may  be  one  half  to  two  thirds  of  the  time,  the  price 
fixed  is  not  sufficient  to  cause  cars  to  be  sent  home,  and  earnest  efforts 
are  now  making  to  bring  about  a  change. 

145.  This  effort  is  more  particularly  directed  to  the  fixing  of  some  per-diem 
rate,  to  cure  the  great  present  evil,  that  when  cars  are  kept  on  hand,  on  a  side- 
track, instead  of  being  sent  home,  sometimes  for  weeks,  the  offending  road  loses 
nothing,  since  it  pays  nothing  for  the  car  except  vvnen  it  is  in  motion.  The 
most  favored  plan  is  a  change  to  a  mixed  per-diem  and  mileage  rate,  approxi- 
mating to  25  cents  per  day-|--i^  cent  per  mile.  If  the  car  were  kept  faithfully  in 
service,  there  would  probably  be  no  dispute  that  f  cent  per  car-mile  is  sufficient 
to  cover  (i)  maintenance  and  renewal  charges,  (2)  interest  on  the  value  of  the 
car,  and  (3)  a  fair  business  and  punitory  profit  in  addition. 


Table  74. 

Cost  of  Freight-Car  Repairs  Per  Car  Per  Year,  on  Lake  Shore  & 
Michigan  Southern  Railway,  for  Six  Years. 

(Average  mileage  of  cars  per  year,  about  12,500  miles.) 


1880. 

1881. 
1882. 
1883. 
1884. 
1885. 


Year. 


Total,  6  years. 
Av.  per  year. . 


Cost  Car  Per  Year. 


Repairs  only. 


$47.80 
43-46 
38.90 
30.64 
21.24 
35-30 


217-34 
36.22 


New  cars  built 

for  acct. 

"  repairs." 


;4.oo 
2.74 

1-59 

5.56 
3.17 
1.05 


;ib.ii 
3.02 


Total  repairs 
and  ren'ls. 


$51.80 
46.20 
40.49 
36.20 
24.41 
36.35 


$235-45 
39-24 


No.  OF  Cars. 


Total  in  use. 


12,107 
14,663 
16,796 
16,649 

16.355 
16,629 


15,520 


Built  new 

for 
renewals. 


107 

66 

53 

197 

108 

38 


574 
95-7 


For  the  ten  years  1870-79  preceding  this  table,  the  Lake  Shore  built  in  all  2,233  cars 
entirely  new  on  renewal  account,  making  the  total  number  rebuilt  entirely  new  in  sixteen 
years,  2,807.  The  stock  of  cars,  beginning  with  6,077  in  1870,  was  increased  to  10,185  in 
1S74,  and  then  remained  practically  stationary  until  the  middle  of  1879,  when  the  increase 
began  to  the  figures  above.  Except  that  a  large  majority  of  cars  are  rebuilt  piecemeal, 
and  maintain  a  kind  of  continuous  existence,  at  least  10,000  cars  should  have  been  rebuilt 
during  this  period  instead  of  2,807.  It  is  probable  that  most  of  the  latter  were  broken 
up  entirely,  chiefly  because  they  had  become  of  too  antiquated  design  to  be  serviceable. 


l66     CHAP,    v.— OPERATING  EXPENSES— REPAIRS   OF   CARS. 

146.  The  repairs  which  the  road  using  foreign  cars  has  to  pay  for  in  addi- 
tion to  paying  f  cent  per  mile  are  not  of  great  importance,  and  are  determined 
in  this  wise:  At  every  junction  point  there  is  an  inspector,  usually  a  joint  in- 
spector, who  admits  cars  on  to  the  road  only  when  "  in  good  running  order,"  as 
determined  by  minute  specifications  revised  yearly  by  the  Master  Car-Builders' 
Association.  Once  on  the  road  it  must  be  passed  off  as  fulfilling  all  the  same 
specified  conditions,  or  be  sent  to  the  shop  for  repairs.  Failures  of  the  wheels  or 
axles  are  assumed  to  be  (in  default  of  evidence  to  the  contrary)  from  the  nor- 
mal wear  paid  for  by  the  f  cent  per  mile.  Other  failures,  broken  draw-timber 
castings,  sills,  doors,  roofs,  trucks,  etc.,  are  assumed  to  result  from  bad  usage, 
and  are  made  good  in  addition  to  the  mileage  payments.  In  this  way  a  road 
may  often  have  to  pay  for  repairs  due  to  gradual  deterioration,  for  which  it  is 
not  at  fault;  but  the  average  is  about  fair:  and  since  no  general  repairs  are 
made,  but  the  car  is  simply  patched  up  so  as  to  barely  pass  inspection,  it  does 
not  amount  to  a  very  heavy  addition  to  the  established  mileage  rate. 

147.  The  apparent  cost  of  car  repairs,  to  an  even  greater  extent  than 
the  cost  of  engine  repairs,  has  been  and  will  continue  to  be  far  smaller 
than  it  really  is  because  of  the  constant  additions  of  new  stock,  made 
necessary  by  the  rapid  growth  of  traffic.  As  the  repairs  on  new  cars  are 
small  for  many  years,  if  the  stock  of  cars  be  doubling  every  four  or  five 
years,  as  has  been  the  case  in  the  United  States  for  the  past  twenty  years, 
the  apparent  cost  of  repairs  cannot  but  be  greatly  affected.  Table  74 
shows  how  great  an  effect  this  cause  may  have,  in  many  cases.  Any 
figures  seeming  to  be  much  below  those  here  given  will  be  apt  to  be 
largely  affected  b}'-  this  cause,  or  by  the  one  above  alluded  to — omission 
of  general  and  incidental  shop  expenses. 

148.  We  are  less  concerned,  however,  as  in  the  case  of  engine  repairs, 
with  the  total  cost  of  car  repairs  than  with  its  origin  and  subdivisions ; 
as  in  that  way  only  can  we  properly  determine  what  effect  differences  of 
grade  and  line,  or  other  specific  causes,  will  have  upon  the  cost  of  this 
item.  Few  railways  keep,  and  none  publish,  any  detailed  record  of  the 
cost  of  the  various  items  which  make  up  the  enormous  aggregate  of 
"  repairs  of  cars,"  that  being  the  only  one  which  appears  in  the  reports, 
or,  as  a  rule,  on  the  books.  It  is  therefore  difficult  to  determine  pre- 
cisely the  ratio  of  the  various  items  to  each  other.  Nevertheless,  from 
the  information  given  in  Tables  70  to  73  and  other  data  (compare 
especially. Table  87)  we  may  conclude  that  the  actual  cost  of  repairs  and 
renewals  of  freight  cars  is  divided  very  nearly  as  follows : 


CHAP,    v.— OPERATING  EXPENSES— REPAIRS   OF  CARS.      1 6/ 


Wheels, 30  per  cent. 

Axles,  brasses,  and  axle-boxes, 30 

Springs, 10  " 

Truck  frame  and  fittings, 5  " 

Total  truck,      .     .     .     .     o 70  " 

Brakes, » 5  " 

Draw-bars,    , 10 

Sills  and  attachments, 5  " 

Car  body,  painting,  etc., 5  " 

Total, .100 


149.  Passenger-car  repairs  are,  for  wheels,  axles,  and  brasses,  but 
slightly  more  than  for  a  freight  car  per  mile.  Exact  information  as  to 
the  comparative  mileage  of  passenger  and  freight  wheels  is  difficult  to 
obtain,  owing  to  the  fact  that  as  soon  as  wheels  show  any  noticeable  de- 
fect, which  yet  does  not  make  them  unsafe,  they  are  withdrawn  from  pas- 
senger service  and  put  under  freight  cars,  often  making  a  large  mileage 
before  being  finally  scrapped.  The  general  tendency  of  the  available 
evidence  is  that  there  is  but  little  difference,  and  that  difference  in  favor 
of  passenger  cars,  the  effect  of  the  higher  speed  being  counterbalanced 
by  less  injurious  brakes  and  better  springs.  The  extra  cost  of  repairs  and 
renewals  of  passenger  cars  is  mainly  in  its  decorations,  better  painting, 
and  interior  fittings  ;  and  bearing  in  mind  that  passenger  cars  are  not 
exposed  to  anything  like  the  rough  service,  blows,  and  shocks  which 
come  upon  freight  cars,  we  may  say,  without  any  error  of  moment,  that 
the  average  cost  per  passenger  car-mile  is  about  as  follows  : 

Frt.  Car.    Pass.  Car. 
Cts.  Per  Mile. 

Running  gear,  draw-bars,  etc., 0.3  0.5 

Sills,  frames,  etc., o.i  0.2 

Painting  and  varnishing  car  body, 0,2 

Interior  fittings  and  upholstery, 0.5 

Total, 0.4  1.4 

150.  In  other  words,  the  cost  of  maintaining  a  passenger  car  for  those 
items  or  parts  of  items  which  are  affected  by  differences  of  distance,  cur- 
vature, and  gradients   is  not  so  much  greater  than  for  freight  cars,  but 


1 68     CHAP,    v.— OPERATING  EXPENSES— TRAIN  WAGES. 

that  it  is  noticeably  smaller  per  passenger  train-mile,  but  the  total  cost 
of  repairs  per  train-mile  is  about  the  same.     (See  note  foot  of  page  163.) 

151.  The  average  mileage  of  freight  cars  per  year,  taking  the  whole 
equipment  of  a  road  together,  ranges  from  11,000  to  15,000  miles,  some- 
times even  higher,  but  very  frequently  considerably  less.  On  short  roads 
with  heavy  local  business  it  is  often  smaller  than  this,  averaging  10,000 
miles  per  year,  or  even  less.  The  tendency  in  recent  years  has  been  to 
decrease.  The  mileage  made  by  different  cars,  however,  varies  enor- 
mously :  "line"  cars,  so  called,  belonging  to  the  independent  or  semi- 
independent  organizations,  which  now  conduct  a  very  large  proportion 
of  the  through-freight  business  passing  over  several  lines,  make  the 
greatest  mileage,  as  is  but  natural;  both  because  they  are  exclusively 
used  in  long-trip  through-business  and  because  they  are  most  sharply 
looked  after.  The  general  average  of  all  classes  of  cars  (see  also  Table 
70)  is  about  as  follows  : 

Miles  Per  Day.  Miles  Per  Year. 

Coal  and  flat  cars, 15  to    20  5,000  to    7,500 

Boxcars, 25  to    40  9,000  to  15,000 

"  Line"  cars, 70  to  100  25,000  to  35,000 

Average, 35  to    45  12,000  to  16,500 

The  average  mileage  of  passenger  cars  ranges  from  40,000  to  60,000 
miles  per  year,  these  being  about  the  two  extremes.  Through  coaches, 
sleeping-cars,  etc.,  run  much  higher  than  this — up  to,  in  some  cases, 
150,000  miles,  averaging  about  100,000. 

152.  Train  Wages,  the  sole  remaining  considerable  item  affected  by 
line  and  grades,  are  less  difficult  than  the  preceding  to  state  with  correct- 
ness. The  following  are  a  close  approximation  to  the  rates  which  now 
prevail  in  this  country  for  average  runs  of  a  hundred  miles.  In  1870-74 
they  were  naturally  higher  than  this,  say  25  per  cent,  and  higher  yet  in 
the  preceding  decade.  In  1875-78  they  were  about  10  per  cent  lower. 
They  vary  considerably  in  different  parts  of  the  country,  but  less  than 
any  other  item  of  train  expenses  : 

Freight.  Passenger. 

Engineman, $3.50  to  $3.75  $3-50  to  $4.00 

Firemen, 1.75  to  2.00  1.75  to  2.00 

Conductor, 2.75  to  3.00  3.75  to  5.00 

Brakeman  (each,  $1.75),     3-5o  to  5.25  3.50  to  3.50 

Baggage-men, ...  2.00  to  3.00 

$11.50  to  I14.00         $14.50  to  $16.50 


CHAP,    v.— OPERATING   EXPENSES— TRAIN  WAGES.      1 69 


153.  The  system  by  which  train  wages  are  fixed  varies  materially.  It 
is  sometimes  strictly  by  the  month  or  day,  especially  in  passenger  ser- 
vice— a  certain  run  being  called  a  day's  work,  independent  of  the  time 
actually  employed.  These  runs  may  vary  anywhere  from  75  to  no  or 
120  miles  ;  but  if  it  constitutes  de facto  a  day's  work,  it  is  rated  a  day, 
independent  both  of  time  and  distance  run. 

This  system  was  formerly  universal,  and  is  still  very  common  for  pas- 
senger service  ;  but  with  increase  of  traffic,  and  especially  with  the  con- 
solidation of  lines  into  great  systems,  with  runs  of  widely  varying  length, 
the  practice  is  coming  more  and  more  into  vogue  of  paying  strictly  ac- 
cording to  mileage,  in  the  manner  specified  in  par.  191.  The  chances 
are  that  the  tendency  to  pay  in  close  accordance  with  mileage  will  be- 
come stronger  and  stronger  with  the  great  organizations,  especially  in 
freight  service,  while  the  former  plan  will  always  prevail  with  the  smaller 
independent  lines,  and  even  on  many  of  the  larger  lines  for  passenger 
service. 

154.  A  compromise  plan,  intermediate  between  these  two  extremes, 
is  at  present  more  usual  than  any  other.  The  runs  over  various  divisions 
are  graduated  as  i  day,  \\  day,  i^^  day,  sometimes,  though  rarely,  \  day, 
etc.,  etc.,  so  as  to  have  a  close  correspondence  with  the  real  distance,  but 
not  to  be  in  exact  ratio  thereto ;  other  circumstances,  such  as  number  of 
stops,  etc.,  being  often  taken  into  account.  This  appears  to  be  not  only 
fairer  than  an  exact  mileage  basis,  but  more  acceptable  to  employes.  The 
present  system  of  handling  traffic,  by  which  the  freight  crews  not  only 
know  no  distinction  of  night  or  day  or  week-day  and  Sunday,  but  do  not 
even  recognize  the  day  of  twenty-four  hours,  tends  to  facilitate  this  basis 
of  payment;  the  crews  being  "on"  or  "off "  at  intervals  determined  by 
the  pressure  of  traffic,  and  not  at  all  by  the  number  of  hours  in  the  day 
or  days  in  the  week.  In  passenger  service,  or  wherever  the  freight  ser- 
vice is  tolerably  regular  in  its  character,  the  deference  paid  to  an  exact 
mileage  basis  is  much  less  marked.     (See  also  par.  191.) 

155.  The  tendency  is  strong  to  increase  the  length  both  of  locomotive 
runs  and  of  divisions.  Locomotive  runs  were  formerly  from  80  to  100 
miles.  At  present  they  range  by  preference  from  120  to  150  miles,  the 
gradients  being  often,  of  course,  a  controlling  condition.  The  prevailing 
tendency  is  well  illustrated  by  the  locomotive  divisions  on  the  Canada 
Pacific,  of  which  there  are  19  on  the  2445  miles  between  Montreal  and 
the  Pacific,  an  average  run  per  locomotive  of  I28f  miles.  The  shortest 
and  longest  runs  are  :     (See  page  178.) 


I/O 


CHAP,    v.— OPERATING  EXPENSES— SUMMARY. 


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CHA  P.    V. — OPERA  TING  EXPENSE  S—  S  UMMA  R  Y. 


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176 


CHAP,    v.— OPERATING  EXPENSES— SUMMARY. 


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CHAP,    v.— OPERATING  EXPENSES—SUMMARY. 


177 


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178 


CHAP,    v.— OPERATING  EXPENSES— SUMMARY, 


6  (ii2,  113,  114,  116,  and  two  of  118  miles)  under  120  miles. 
4  (120,  121,  125,  and  126  miles)  between  120  and  130  miles. 
6  (130,  131,  133,  133,  134,  134  miles)  between  130  and  140  miles. 

1  (145  miles)  between  140  and  150  miles. 

2  (150,  152  miles)  over  150  miles. 

Thus  the  minimum  is   112  and  the  maximum  152  miles.     This  practice 
tends  strongly  to  economy. 

156.  General  and  Station  Expenses  are  but  slightly  affected  by 
any  probable  variations  in  the  line  and  grades,  so  that  it  is  unnecessary 
to  consider  them  in  detail,  although,  for  many  questions  connected  with 
the  operations  of  railways,  such  analysis  is  highly  important.  They 
amount  altogether  to  about  thirty  per  cent  of  the  total  operating  ex- 
penses, ranging  from  twenty  to  forty  per  cent  in  extreme  cases. 

157.  In.  Tables  75,  76,  ^-j,  'jZ  are  given  various  details  as  to  expendi- 
tures for  the  railways  of  the  entire  United  States  and  the  several  interior 
groups  thereof,  for  the  four  great  trunk  lines,  for  four  minor  trunk  lines, 
and  for  the  six  leading  Chicago  lines.  These  details  are  all  computed 
from  the  census  statistics  of  1880,  which  were  the  first  which  gave  an 
available  source  for  obtaining  these  statistics,  on  an  approximately  sim- 


Table  79. 
Operating  Expenses  of  British  Railways,  1884-85. 


Cents  per 
Train-mile. 

Per  Cent. 

Maintenance  of  way 

11.32 

16.55 
6.05 

19-77 

2.87 
3-45 
0.68 

0.27 

0.34 

•      0.51 

0.79 

18. 1 
26.4 

9-7 

31.6 

4.6 

5.5 
I.I 

0.4 

0.5 
0.8 

1-3 

Locomotive  power..  

Rolling  stock 

Traffic  expenses 

General  charges 

Government  duty 

Compensation: 

Personal  injuries 

Damage  to  goods 

Legal  and  parliamentary  expenses.. . 
Miscellaneous , . . . 

Totals 

62.60 

100. 0 

No  material  change  in  the  percentages  of  these  various  expenses  has  taken  place  since 
1870,  but  the  cost  per  train-mile  has  fallen  from  an  average  of  77  cents  to  62.6. 


CHAP,    v.— OPERATING  EXPENSES— SUMMARY. 


179 


Table  80. 

Approximate  Estimate  of  the  Details  of  Operating  Expenses  for  an 
Average  American  Road. 

[Liable  to  considerable  variations  in  individual  instances,  especially  when  the  traffic  is 
very  great  or  very  small,  but  to  much  less  extensive  variations  than  might  be  imagined, 
even  in  extreme  cases.  The  average  total  cost  per  revenue  train-mile  is  still  not  very 
much  below  $i.oo,  and  by  taking  it  at  that  even  figure  the  following  become  either 
percentages  or  cents  per  train-mile,  which  we  shall  hereafter  assume  them 
to  be.] 


Train  Expenses. 
47-op.c. 


Maintenance  of  Way. 
23.0  p.  c. 


Engines. 
18.0  p.  c. 


Train 

Wages  and 

Supplies. 

17.0  p.  c. 


Cars. 
12.0  p.  c. 

Track 

between 

Stations. 

8.0  p.  c. 


Road 
engines. 
14.4  p.  c. 


'  Fuel 7. 

Water o. 

Oil  and 
waste o. 

Repairs —  en- 
gines  5. 


6  p.  c. 

4    " 


6    " 


Switching  engines 3 

Switching  engine  wages.  ...i. 


Train 
wages  and 

supplies.      \    r^  T 

15:4  p.  c.     [Car  supplies,  o. 


Engine  w'ges.6, 
Car  wages . . 


6  p.  c. 
6    " 


4  p.  c. 

5  " 
5     " 


Repairs  and  renewals..    .  .10.0  p.  c. 
Mileage  (a  practical  equiv- 
alent for  repairs) 2.0    " 


Renewals  of  rails 2 

Adjusting  track 6. 


Road-bed.    j   Renewing  ties 3, 

7.0  p.  c.        {   Earthwork,  ballasting,  etc.. 4. 


Yards  and 

Structures. 

8.5  p.  c. 


Switches,    frogs,    and    sid- 
ings    1. 

Bridges  and  masonry 3. 

1^  Station  and  other  buildings.  2. 


o  p.  c. 

o     " 


o  p.  c. 
o    " 


5  p.  c. 

5     " 
o    " 


Total  "  Line"  or  Transportation  Expenses 70. 

Station,  Terminal,  and  General  Expenses  and  Taxes 30. 


o  p.  c. 
o    " 


Total  Operating  Expenses 100 .  o  p.  c. 


See  Table  8i  for  similar  estimate  from  former  edition. 


l80  CHAP,    v.  — OPERATING  EXPENSES— SUMMARY. 

ilar  basis  of  distribution  of  expenses.  Many  minor  errors  plainly  oc- 
curred in  making  over  the  accounts  according  to  the  census  form ;  but 
the  result  is  more  likely  to  afford  a  uniform  basis  of  comparison  than 
any  individual  attempts  to  do  the  same  thing  with  later  statistics. 

In  Table  78  are  likewise  repeated  the  final  results  of  a  large  table, 
which  the  writer  computed  for  his  former  edition,  from  the  accounts  of 
seventeen  different  roads,  each  averaged  for  from  three  to  ten  years.  It 
will  be  seen  that  the  correspondence  between  these  various  statistics  is 
singularly  close— quite  enough  so  to  afford  a  pretty  accurate  basis  for 
estimating  the  expenses  of  any  road.  In  Table  79  are  given  some  corre- 
sponding statistics  for  English  railways. 

158.  Summarizing  the  ground  gone  over,  we  may  estimate 
the  operating  expenses  of  a  railway  in  the  North  Central  States, 
laid  throughout  with  steel,  and  of  good  average  character,  about 
as  in  Table  80,  on  the  previous  page.  With  less  accuracy  this 
table  will  apply  to  railways  in  any  part  of  the  United  States,  the 
principal  cause  of  variation  being  volume  of  traffic. 

This  estimate,  however,  is  merely  an  average,  as  should  al- 
ways be  remembered,  to  be  corrected  in  each  individual  case  ac- 
cording to  local  circumstances.  It  has  been  endeavored  in  this 
chapter  to  furnish  a  guide  for  such  corrections,  as  far  as  possible, 
but  nothing  will  fully  take  the  place  of  intelligent  examination 

Table  81" 

Classification  of  Operating  Expenses  Adopted  in  the  Former  Edition 

OF  THIS  Treatise. 

f  (Fuel 10  p.  c. 

I   Engines 21  p.  c.  -i^  Oil,  waste,  etc 2      " 

Train  Expenses.         I  (Repairs 9      " 

43  p.  c.  I   Cars 10    "         Repairs,  inspection,  etc lo 

Train  wages 12 


(  Engineman  and  firemen 6 

I  Conductor  and  brakemen 6 

f  Tr;,rlr  t-    "       \  Renewal  of  rails 7 


Track 13 


)  Adjusting  track,  etc 6 


Maintenance  OF  AV AY.    I    r„„h  hed  -,    "       *  Renewal  of  ties  3 

27P.C.  ^  Koad  Dea ,     7  ,  Earthwork,  ballast,  etc 4      " 

i  Switches,  frogs,  and  sidings..  3  " 
I  Yards  and  structures  7  "  -  Bridges  and  bridge  masonry.  2.5  " 
1^  (  Station  and  other  buildings. ..  1.5  " 

Total  "  Line"  or  Transport.ation  Expenses 70    p.  c. 

Station,  Terminal,  and  General  Expenses  and  Taxes 30      " 

Total  Operating  Expenses 100    p.  c. 


CHAP,    v.— OPERATING  EXPENSES— SUMMARY. 


i8i 


of  the  facts  on  neighboring  roads.  This  table  gives  merely  a 
rude  average  for  use  in  the  remainder  of  this  volume  for  com- 
puting examples. 


Table  82. 

Percentage  of  Total  Revenue- Mileage  (assumed  as  ioo.)  of  Revenue- 
Passenger  Trains,  Revenue  Freight  Trains,  ''Switching  Trains,"  and 
"Other"  (mostly  Work)  Trains  in  the  United  States  and  Each 
Group  of  States. 


[Computed  from  the  Statistics  of  the  Census  of 


For  Census  Groups  see  Table  75.] 


Group  of  States. 

Miles 
Oper- 
ated. 

Revenue  Train-Mile- 
age. 

Other  Mileage. 
(Per  Cent  of  Rev.  Miles.) 

Pas- 
senger. 

Freig't. 

Total. 

Switch- 
ing. 

Other. 

Total. 

5,887 
28,693 
14,243 
25,038 
877 
13,044 

51.8 
35.6 
34-3 

31-2 

16.9 
34-8 

48.2 
64.4 
65.7 
68.8 
83.1 
65.2 

100. 0 
100. 0 
100. 0 
100. 0 
100. 0 
100. 0 

12.6 
16.5 

7.2 
16. 1 

4.4 
10.8 

14.4 

3-5 
4-5 
5-6 
5-9 
1.9 
9.0 

5-1 

16  I 

Middle,  Ind.,  and  Mich 

12  8 

111.,  la..  Wis.,  Mo.,  Minn 

La.,  Ark.,  Ind.  T 

22.0 

6.3 
19.8 

Far  West  and  Pacific 

87,782 

35-5 

64-5 

100. 0 

19-5 

It  is  quite  certain  from  the  statistics  that  the  actual  proportion  of  switching  mileage 
is  larger  than  the  above,  both  because  fully  one  third  of  the  roads  do  not  report  switching 
at  all,  and  because  many  include  switching  with  train-mileage.  The  per  cent  of  switching 
to  revenue-mileage  of  a  few  single  roads  runs  as  follows  : 


Eastern. 

Per  Cent. 

Middle. 

Per  Cent. 

Boston  &  Albany 

12.9 

18. 

13-8 

29. 

21. 

31-4 

32.4 

14.8 

37-3 

Allegheny  Valley 

35-5 
21.8 

5-6 
25-7 
33-7 
21. 1 

4.0 
24.7 
33-5 

Atl.  &  Gt.  Western 

Bait   &'  Ohio 

Cent.  Vermont 

Eastern         .... 

01.,  Col.,  C.  &  Indianapolis 

CI.  &  Pittsburg         

Col.,Ch.  &Ind.  Central.... 
Del.,  Lack.  &>  Western  .... 

N.  v.,  L.  Erie  &  W 

N.Y.  Central  &  H.  R 

Maine  Central 

Nashua  &  Lowell 

Old  Colony 

Prov.  &  Worcester 

The  two  roads  given  in  italics  above  are  among  those  which  show  an  extraordinarily 
low  cost  per  train-mile.     The  main  cause  therefor  is  clearly  indicated  in  the  above  figures. 


1 82  CHAP,    v.— OPERATING  EXPENSES— SUMMARY. 

In  Table  80  one  fifth  of  the  total  cost  of  motive-power  has  been 
allotted  to  switching-engines.  In  most  cases  there  is  a  larger 
proportion  than  this,  independent  of  the  switching  done  by  reg- 
ular trains  in  tra^isitu,  as  is  partly  indicated  by  the  following 
Table  82. 

In  Table  81  is  given  the  table  corresponding  to  Table  80, 
which  was  used  in  the  former  edition  of  this  treatise  as  the  as- 
sumed average  distribution  of  expenses  for  computing  examples. 


PART  II, 


THE  MINOR   DETAILS  OF  ALIGNMENT. 


"Despise  not  small  things,  for  therefrom  comes  sorrow  and  disap- 
pointment. Yet  remember  that  they  are  small,  and  fix  your  aims  and 
your  thoughts  chiefly  on  the  great  ends  of  life." — Horace  Mann. 


PART   II. 
THE  MINOR  DETAILS  OF  ALIGNMENT, 


CHAPTER   VI. 


THE    NATURE    AND    RELATIVE    IMPORTANCE    OF    THE   MINOR   DETAILS 

OF    ALIGNMENT. 

159.  The  three  details  of  alignment  which  are  properly  to  be 
classed  as  minor  details  are  the  following: 

1.  Distance,  or  length  of  line. 

2.  Curvature,  not  sharp  or  so  ill-placed  as  to  limit  the  length 
or  necessary  speed  of  trains,  but  only  to  increase  the  expense  of 
running  trains. 

3.  Rise  and  Fall,  or  elevations  overcome  by  the  engine  on 
gradients  not  exceeding  in  resistance  the  maximum  of  the  road, 
and  hence  not  limiting  the  length  of  the  train. 

160.  These  are  termed,  collectively,  the  minor  details,  for  the 
reason  that  their  influence  is  comparatively  trifling  upon  the 
future  of  the  property  in  comparison  with  two  other  details  of 
overwhelming  importance,  viz.: 

1.  The  amount  of  traffic  which  the  line  has  been  or  may  be 
adapted  to  secure  (often  very  largely  and  even  ruinously  affected 
by  the  location,  for  reasons  discussed  in  Chapter  III.,  the  fol- 
lowing Chapter  VII.,  and  Chapter  XXL),  and 

2.  The  RULING  GRADIENTS  or  Other  causes,  whatever  they  may 
he,  which  limit  the  weight  and  length  of  trains,  and  so  play  the 
chief  part  in  fixing  the  cost  of  handling  the  traffic.  These  causes 
are  considered  in  Part  III.  of  this  volume,  under  the  general 
head  of  "Limiting  Gradients  and  Curvature." 

To  characterize  three  such  details  as  distance,  curvature,  and 
rise  and  fall  as  minor  details,  either  separately  or  collectively, 
does   some  violence  to  popular   impressions,  which   exist  even 


1 86    CH.    VI.— RELATIVE  IMPORTANCE   OF  MINOR  DETAILS. 

among  engineers.  It  will  therefore  be  well  that  we  should  first 
see,  by  a  "  bird's-eye  view"  of  the  subject,  free  from  all  detail, 
why  the  designation  is  a  proper  one,  nevertheless. 

161.  The  ideal  line  for  a  railway  between  any  two  points   is 
^j^y-po'^MXdirly  felt  to  be  a  rigfetJine  between  the  two  termini.     This 

(y^  may  even  be  found  stated  as  an  axiom  in  some  engineering  works, 

and  in  a  strictly  engineering  sense  it  is  true.  If  it  were  true  in 
every  sense,  it  should  follow  that,  in  proportion  as  a  line  deviates 
therefrom,  it  is  bad  ;  and  since  the  three  details  classified  as 
"  minor"  include  every  possible  deviation  therefrom  in  either  of 
the  three  dimensions  of  space, — curvature  representing  lateral 
deviations;  rise  and  fall,  vertical  deviations;  and  distance,  lon- 
gitudinal deviations, — the  three  together,  far  from  being  minor 
details,  seem  naturally  to  represent  or  include  all  the  conditions 
which  make  a  line  good  or  bad.  This  view  is  so  far  plausible, 
that  it  is  asserted  or  implied  to  be  the  true  one,  not  only  in  com- 
mon talk,  but  in  technical  discussions  or  writings,  "A  short, 
straight  line  was  obtained,  with  few  curves  or  high  elevations," 
will  pass  very  generally  as  a  description  of  what  must  be  an  ex- 
cellent line. 

Yet,  as  a  matter  of  fact,  this  view  is  wholly  erroneous — so 
gravely  erroneous  that  the  excellence  or  badness  of  the  line  in 
all  the  minor  details  put  together,  within  wide  limits,  has  com- 
paratively a  very  slight  influence  on  its  value  as  an  investment 
or  on  its  usefulness  to  the  public. 

162.  We  shall  see  why  this  is  true  of  each  detail  separately,  as 
we  come  to  consider  each  in  detail.  To  see  why  it  is  true  of  all 
three  put  together,  let  us  take  the  case  of  two  railways  be- 
tween the  same  points — one  a  little  shorter,  a  little  less  crooked, 
and  with  a  little  less  up  and  down  in  its  gradients;  but  suppose 
them  both  to  have  cost  the  same  money,  to  have  the  same  tribu- 
tary population,  to  be  able  to  haul  the  same  trains  with  the  same 
engines,  and  to  make  the  same  time  between  termini.  These 
conditions  obtain  in  many  instances,  and  may  conceivably  in  all. 
Na}^,  we  might  even  extend  our  parallel,  and  assume  that  there 
are  considerable  differences  in  one   or   the   other  of   the  minor 


CH.    VI.— RELATIVE  IMPORTANCE   OF  MINOR  DETAILS.    1 8/ 

details  between  the  two  lines,  but  always  on  the  condition  that 
they  still  remain  minor  details  as  already  defined,  in  that  they 
do  not  affect  the  sources  of  traffic  nor  the  amount  of  traffic  which 
can  be  handled  by  one  train. 

163.  Which  of  these  two  lines  is  the  best  property  ?  It  is  a 
matter  of  the  merest  chance — a  mere  question  of  management, 
or  of  business  shrewdness  in  effecting  connections.  The  differ- 
ence in  the  minor  details  will  beyond  doubt  be  of  large  absolute 
importance,  but  will  have  so  trivial  an  effect  comparatively  that 
it  will  hardly  enter  into  the  question  at  all. 

164.  This  results  simply  from  the  broad  general  fact  that  those 
details  affect  only  the  cost  per  trip  of  riin?ii?ig  trains,  and  that  but 
slightly.,  while  they  do  not  reduce,  nor  in  any  manner  affect 
(within  wide  limits),  either  the  work  done  or  the  revenue  earned 
by  each  train.  It  is  now  abundantly  established  by  experience 
that  the  effect  of  those  details  on  the  direct  cost  per  trip  or  per 
mile  of  running  trains  is  an  exceedingly  small  percentage  of  the 
aggregate,  within  the  widest  limits  of  deviation  which  exist  in 
practice.  As  for  distance  :  the  additional  cost  of  running  a  few 
more  miles  is  but  a  small  portion  of  the  average  cost,  and  is 
always  counterbalanced  by  the  receipts  of  some  additional 
revenue — often  enough  to  make  the  advantage  greater  than  the 
disadvantage,  and  always  enough  to  greatly  reduce  the  disad- 
vantage. As  for  curvature,  and  rise  and  fall  :  it  is  now  estab- 
lished beyond  all  question  that  no  considerable  difference  in  the 
aggregate  expenses  per  train-mile  on  different  railways,  or  on 
different  divisions  of  the  same  railway,  can  be  detected,  which  is 
clearly  due  to  differences  in  the  amount  of  curvature,  or  rise  and 
fall,  even  when  very  marked  differences  in  those  details  exist. 
Tables  75  to  80,  as  well  as  Table  83,  afford  cumulative  evidence 
of  this  fact,  which  has  been  commented  on  at  intervals  from  the 
very  beginning  of  railroad  history.  One  of  the  earliest  records 
of  the  fact  is  the  following  statement  of  the  eminent  English 
engineer  Mr.  Charles  B.  Vignoles,  formerly  President  of  the  In- 
stitution of  Civil  Engineers,  as  quoted  with  approval  in  Demp- 
sey's  *' Practical  Railway  Engineer"  (p.  11). 


1 88    CH,    VI  — RELATIVE  IMPORTANCE   OF  MINOR  DETAILS. 

165.  "  Mr.  Vignoles  stated  in  a  paper  before  the  British  Association 
for  the  Advancement  of  Science  that  he  had  analyzed  railway  expenses 
of  working,  and  the  average  expenses  of  a  train-mile,  as  deduced  from 
several  years'  experience  and  observation  on  various  railways  operating 
under  different  circumstances  and  with  greatly  different  gradients.  The 
result  was  that  on  passenger  and  light  traffic  lines  the  total  cost  of  atrain- 

Table  83 

Average  Cost  Per  Train-Mile  of  running  Engines  on  the  several 
Divisions  (differing  widely  in  the  Amount  of  Curvature  and  Rise 
AND  Fall)  of  the  Pennsylvania  and  Philadelphia  &  Erie  Railroads. 

Averaged  on  the  Pennsylvania  Railroad  for  a  period  of  four  years  (1859-66-70-73),  and 
on  the  Philadelphia  &  Erie  for  three  years  (1866-70-73). 

[Reproduced  from  first  edition  of  this  Treatise.] 
PENNSYLVANIA   RAILROAD. 


Passenger  Engines. 

Freight  Engines. 

Average  op  Passenger 

AND  Freight. 

Divisions. 

Re- 
pairs. 

Fuel. 

Stores 

Total 

Re- 
pairs. 

Fuel. 

Stores 

Total 

Re- 
pairs. 

Fuel. 

Stores 

Total 

Eastern 

Middle 

6.32 
10.08 

6.08 
6.33 

1.03 
1.03 

i3^43 
17^44 

6.53 
7.67 

7.78 
7.67 

1.26 
1. 10 

15-56 
16.44 

6.42 
8.87 

6.93 
7.00 

I-I5 
1.07 

14  •so 
16.94 

Av.  Eastern 
and  Middle 

Western 

Mountain  and 
Tyrone  .... 

8.20 
7-97 

3-91 

6.20 
6.38 

6.70 

1.03 
1. 17 

•73 

i5^43 
i5^52 

"•34 

7.10 
IO-54 

9.29 

7.72 
8.-79 

7.38 

1. 18 
1. 61 

•93 

16.00 
20.94 

17.60 

7.65     6.96 
9-25      7-59 

6.60      7.04 

I. II 

1-39 

.83 

15-73 
18.23 

i4^47 

Av.  Western, 
M  0  u  n  tain 
and  Tyrone 

5-94 

6.54 

•95 

13-43 

9.91 

8.09 

1.27 

19.27 

7.92 

7-32 

I. II 

16.35 

Av.  of  entire 
road 

7.07 

6.37 

•99 

14-43 

S.50 

7.91 

1.22 

17-63 

7.78 

7.14 

I. II 

16.03 

PHILADELPHIA  &  ERIE  RAILROAD. 


Divisions. 

Average  of  all 
Engines. 

Re- 
pairs. 

Fuel. 

Stores 

Total 

Eastern 

Middle.. 

Western 

10.64 
II. I 
10.49 

9.91 

9^77 
9.92 

1. 19 
1. 19 
i^i5 

21.74 
22.06 
21.56 

Average . . . 

10.74 

9.87 

1. 18 

21.79 

On  the  Philadelphia  &  Erie  the  expenses  of  en- 
gines are  not  kept  separate  for  the  different  classes. 
The  difference  in  the  cost  of  repairs  from  that  on  the 
Pennsylvania  Railroad  is  due,  as  the  writer  learns, 
to  the  very  different  character  and  condition  of  en- 
gines. 


CH.    VI.— RELATIVE  IMPORTANCE   OF  MINOR  DETAILS.    1 89 

mile  averaged  35.  per  mile — 2s.  6d.  being  the  least,  and  35-.  4^.  the  great- 
est ;  and  that  this  average  seemed  to  hold  good  irrespective  of  grades  mtd 
curves  [in  italics  as  quoted].  It  was  not  found  practicable  to  distinguish 
the  additional  expense,  if  any;  but  as  three  fourths  of  railway  expenses 
were  quite  independent  of  these  curves,  such  additions  must  be  small." 

166.  The  essential  truth  of  this  statement  has  been  growing 
better  and  better  established  with  time  to  the  present  day,  and 
we  shall  readily  find  evidence  that  it  even  understates  the  facts 
when  we  come  to  consider  the  effect  of  these  details  in  the 
separate  items  of  railway  expenditure.  From  this  it  does  not 
follow  that  these  details  have  no  important  effect  on  expenses. 
They  do  have  an  important  effect,  which  increases  by  a  large 
percentage  certain  single  items  of  expenses,  and  is  readily  traced 
therein.  But  they  always  add  only  a  trifling  percentage  to  the 
aggregate  expenses,  even  when  very  marked  differences  exist. 

167.  And,  moreover,  the  important  further  fact  must  be 
remembered  that,  as  respects  any  one  line,  there  can  be  at  most, 
as  we  began  by  assuming   (par.  162),  only  a  "little"  difference  in 

/; 

■'    ^  '    ^^         V      . 

Fig.  5. 

the  minor  details,  for  the  vastest  expenditure  cannot  effect  much 
more.  No  possible  expenditure  can  eliminate  curvature  alto- 
gether and  give  a  continuous  right  line  AB,  Fig.  5,  of  any  con- 


FiG.  6. 


siderable  length,  in  place  of  the  curved  line  shown,  nor  make 
much  more  reduction  in  it  than  is  indicated  by  the  dotted  line  in 
Fig.  5;  nor  can  we  make  more  than  a  small  difference  in  distance 


190    CH.   VI.— RELATIVE  IMPORTANCE   OF  MINOR  DETAILS, 

ordinarily,  nor  have  we  more  than  the  choice  between  the  grade- 
lines  b  and  c^  Fig.  6  saving  a  mere  fraction  of  the  rise  and  fall. 
The  grade-line  a^  taking  out  all  the  rise  and  fall  between  A  and 
B,  is  rarely  a  financial  or  physical  possibility. 

168.  For  these  reasons,  assuming  what  cannot  always  be 
assumed,  that  the  engineer  has  first  done  well  in  putting  his  line 
upon  the  ground  so  as  to  avoid  unnecessary  distance,  curvature, 
and  rise  and  fall  (i.e.,  that  which  might  have  been  eliminated 
without  expense),  to  eliminate  altogether  even  "  little"  differences 
in  the  minor  details  will  ordinarily  involve  an  immense  expense. 
But  grant  them  all  to  have  been  eliminated,  without  expense, 
from  the  least  favored  of  the  two  lines  which  we  began  by  assum- 
ing (par.  162),  and  let  us  see  with  somewhat  more  detail  to  what 
extent  it  will  be  benefited  thereby.  (For  a  more  exact  estimate 
see  Chap.  X.) 

It  will  not  reduce  the  interest  charge,  even  if  it  do  not  (as  it 
ordinarily  must)  increase  it,  and  that  takes,  say,  one  third  of  the 
receipts.  As  respects  the  remaining  two  thirds  of  the  receipts, 
which  includes  what  are  ordinarily  termed  "  operating  expenses:" 
It  will  not  reduce  the  number  of  trains,  for  the  length  of  trains 
is  not  affected  by  them.     Consequently, 

It  will  not  reduce  train  wages  and  supplies,  which  are  (Table 
80)  some  17  per  cent  of  the  expenses  ; 

It  will  not  reduce  station-agent's  wages,  nor  station  labor, 
nor  the  salaries  of  the  general  officers  and  clerks,  nor  taxes,  nor 
terminal  expenses,  and  these  constitute  some  30  per  cent  of  the 
expenses ; 

It  will  somewhat  affect  repairs  of  engines  and  cars,  fuel,  oil 
and  water,  and  maintenance  of  way,  aggregating  some  53  per 
cent  of  the  operating  expenses  ;  but 

169.  It  will  not  affect  that  portion  of  the  cost  of  fuel  and 
engine  and  car  repairs  which  is  due  to  yard  and  station  work, 
stopping  and  starting,  wear  of  paint  and  rotting  of  wood,  natural 
running  wear  over  the  rest  of  the  possible  line,  injury  to  boilers 
from  cooling  off,  care  and  maintenance  of  shops  (except  in  an 
indirect  and  trivial  way),  etc.,  etc.  These  causes  together  in- 
clude an  immense  proportion  of  the  total  of  these  items. 


CH.   VI.— RELATIVE  IMPORTANCE   OF  MINOR  DETAILS.    IQI 

We  have  seen  (par.  142)  that  something  like  28  per  cent  of 
the  locomotives  of  New  York  State  are  used  for  yard  work  only, 
besides  which  a  large  proportion  of  the  wear  and  tear  and  waste 
of  power  of  engines  in  regular  service  comes  from  yard  work 
and  stopping  and  starting.  Precisely  how  much,  we  will  not 
now  consider ;  but  it  will  be  plain  in  a  general  way  that  only  a 
minute  percentage  of  even  the  cost  of  engine  and  car  repairs  can 
be  saved  by  improvements  of  line  which  do  not  reduce  the  num- 
ber of  trains  required. 

Then  as  to  maintenance  of  way:  All  that  degeneration  which 
comes  from  the  elements,  from  the  decay  of  ties,  from  the  growth 
of  weeds  ;  expenses  for  maintaining  frogs,  switches,  sidings, 
yards,  stations,  bridges,  culverts,  crossings,  signals,  track-walkers 
(for  the  most  part),  track-watchmen,  hand-cars,  fences,  etc.,  are 
virtually  unaffected,  or  nearly  so,  by  any  modifications  of  line 
(except  distance)  wliich  are  within  the  power  of  the  engineer  to 
effect,  as  is  likewise  that  portion  of  the  wear  of  rails,  ties,  and 
surfacing  which  would  exist  on  the  best  possible  line,  and  which 
is  on  any  long  line  (for  none  are  everywhere  unfavorable)  by  far 
the  larger  part  of  it. 

170.  There  remains,  therefore,  only  a  very  small  fraction  of 
about  half  the  operating  expenses,  or  a  very  small  fraction  of 
one  third  of  the  revenue,  which  varies  directly  with  the  minor 
details  of  alignment,  whereas  a  full  half  (m  round  figures)  of  the 
operating  expenses  or  a  full  third  of  the  revenue  varies  directly 
with  the  number  of  trains.  The  smaller  loss  is  still  enough  to 
justify  and  require  the  utmost  care  of  the  engineer  to  avoid  it, 
but  it  is  not  enough  to  make  it,  ordinarily,  anything  but  the 
worst  of  bad  judgment  to  sacrifice  the  securing  of  good  limiting 
gradients,  or  the  reaching  of  more  traffic  points,  to  get  "a  short, 
straight,  and  level  line,"  which  may  or  may  not  mean  a  good  line, 
for  we  shall  see  (Part  III.)  that,  although  a  tolerably  "  level  "  line 
passing  over  low  summits  ordinarily  means  one  with  low  ruling 
grades,  yet  that  the  two  have  no  very  exact  relation  to  each 
other. 

171,  We  may  further  enforce  the  very  important  moral  of  the 


192    CH.    VI.— RELATIVE  IMPORTANCE   OF  MINOR  DETAILS. 

comparative  unimportance  of  the  minor  details  of  alignment  by 
what  is  really  a  close  parallel  from  ordinary  business  life  : 

Let  us  assume  the  case  of  a  large  wholesale  house  which 
sends  out  its  "drummers"  to  all  parts  of  the  country  to  obtain 
business.  Every  time  it  sends  one  out  it  has  a  reasonable  cer- 
tainty of  selling  something  and  a  possibility  of  selling  a  good 
deal.  Such  a  house  may  be  compared  to  a  railway  corporation, 
which  sends  out  its  trains  to  secure  a  certain  minimum  but 
varying  maximum  of  traffic. 

Now  in  the  conduct  of  such  a  business  there  are  three 
ends  : 

1.  To  sell  all  the  goods  possible. 

2.  To  dispense  with  all  the  miles  of  travel  possible. 

3.  To  reduce  the  cost  of  travel  per  mile. 

So  in  planning  a  railway  there  are  these  three  ends,  precisely 
analogous  to  the  former  in  their  nature,  and  as  nearly  as  may  be 
in  degree  : 

1.  To  sell  all  the  transportation  possible. 

2.  To  dispense  with  all  the  train-miles  possible^ 

3.  To  reduce  the  cost  of  running  trains  per  mile. 

172.  Of  all  the  three  ends  sought  in  the  drumming  business, 
the  least  important — the  minor  detail  of  the  drumming  busi- 
ness— is  to  reduce  the  direct  cost  of  travelling;  the  expenditures 
for  railway  and  sleeping-car  fares  and  to  hotels.  Not  that 
they  are  unimportant,  for  the  firm  which  was  reckless  about 
them  might  readily  be  ruined  ;  but  they  are  a  minor  detail,  of 
small  effect  upon  the  ultimate  result,  whether  they  be  large  or 
small,  if  the  business  as  a  whole  be  well  planned  and  well  con- 
ducted ;  and  the  firm  which  should  concentrate  its  attention 
upon  them,  giving  its  thought  to  selecting  routes  where  the 
travelling  expenses  per  day  or  per  mile  were  small,  to  the  neglect 
of  the  more  important  question  of  securing  more  business  or 
reducing  the  amount  of  travel  required,  whether  its  cost  per  mile 
or  per  day  were  large  or  small,  would  be  justly  deemed  on  the 
road  to  ruin. 

No  doubt  many  have  been  so  ruined,  for  the  petty  end  which 


CH.   VI.~RELATIVE  IMPORTANCE   OF  MINOR  DETAILS.    1 93 

the  dullest  mind  cannot  fail  to  perceive  and  comprehend  may- 
fill,  from  that  fact,  an  unduly  large  arc  in  the  mental  horizon  of 
many. 

173.  And  so  not  only  some  but  many  railways  may  be,  as 
they  have  been,  ruined  as  productive  properties  by  the  undue 
importance  given  by  engineers  to  the  minor  details  of  align- 
ment :  those  details  which  do  not  add  at  all  to  the  traffic  of  the 
line,  and  which  do  not  reduce  at  all  the  number  of  trains  needed 
to  handle  it,  but  which  simply  effect  a  "picayune  "  saving  in  the 
cost  per  mile  run  ;  a  saving  which  is  often  so  slight  as  to  be 
imperceptible,  which  still  more  often  adds  to  the  interest  charge 
more  than  it  saves,  and  not  infrequently,  as  we  shall  see,  results 
in  a  negative  saving,  or  absolute  loss  from  the  larger  expendi- 
ture. 

As  a  matter  of  fact,  the  first  and  most  important  end  in  the 
conduct  of  the  drumming  business  is  to  get  all  the  business  possible : 
everything  else — both  the  drummer's  time  and  his  expendi- 
tures— is  subordinate  to  that,  because  if  the  end  is  not  secured 
the  means  must  necessarily  be  bad.  So  with  a  railway  corpora- 
tion :  the  first  and  most  important  end,  when  there  is  any  great 
difference  between  routes,  is  to  put  the  line  where  there  will  most 
business  come  to  it. 

174,  And,  finally,  the  second  most  important  end  in  the  drum- 
ming business  is  to  obtain  the  most  business  with  the  least 
possible  aggregate  of  travel,  because  avoidable  travelling  is 
expensive,  not  only  from  its  direct  cost,  but  from  its  waste  of 
the  drummer's  tim.e  and  possible  earnings  in  more  productive 
localities.  If  in  any  possible  way  one  drummer  can  be  made  to 
do  the  work  of  two,  or  two  drummers  the  work  of  three,  the 
economy  is  so  great  that  any  probable  or  possible  difference  in 
the  drummer's  expenses  per  mile  will  hardly  affect  the  question 
at  all.  So  with  a  railway  corporation:  the  second  most  important 
end  is  to  do  their  business  with  the  least  number  of  trains  per 
mile,  because  making  one  train  do  what  two  did  before  saves  all 
the  expense  of  the  extra  train,  whereas  cutting  out  some  curva- 
ture or  distance  will  only  save  a  part  of  it — ^and  a  very  small 

13 


194    CH.    VI.— RELATIVE  IMPORTANCE   OF  MINOR  DETAILS. 

f — • 

part.  Until  all  has  been  done  which  can  be  done,  therefore,  to 
reduce  the  number  of  trains  required,  it  is  hardly  worth  while  to 
give  a  thought  to  reducing  the  expenses  per  train-mile.  After- 
wards it  becomes  proper  and  important  to  reduce  the  latter  also, 
to  the  extent  that  is  permissible  without  encroaching  on  the  two 
more  important  ends  ;  to  get  the  business  to  carry  and  to  make 
a  few  trains  carry  it. 

175.  The  student  can  do  no  more  profitable  thing  to  qualify 
himself  for  the  correct  conduct  of  location  than  to  ponder  over 
the  parallel  thus  drawn  until  it  is  clearly  perceived  to  be  essen- 
tially true,  not  only  in  substance  but  in  degree;  until  he  clearly 
perceives  that  the  three  ends  of  getting  business,  of  saving  need- 
less travel,  and  of  reducing  the  direct  mileage  expenditures 
should  occupy  about  an  equal  proportion  of  the  attention  of  an 
engineer  building  a  railway  and  a  drummer  building  up  trade. 
Each  is  important.  No  one  of  them  can  be  safely  neglected  ; 
but  each  in  the  order  given  is  far  more  important  than  the  other. 

Why  this  is  so  in  railway  business  appears  more  in  detail  in 
the  three  following  chapters. 


CHAPTER  VII. 


DISTANCE. 


176,  The  effect  of  a  variation  in  the  length  of  a  railway  on  the 
value  of  the  property  we  have  seen  (Chap.  III.)  to  be  peculiar  in 
this — that,  alone  among  all  the  details  of  alignment,  it  has  a 
direct  and  material  effect,  not  only  on  expenses,  but  on  the  reve- 
nue or  receipts,  which  tends  very  materially  to  reduce  its  finan- 
cial disadvantage.  As  a  contrary  view,  leading  to  a  feeling  that 
that  a  longer  distance  between  termini  is  an  unmitigated  mis- 
fortune, and  a  great  one,  is  common  even  with  engineers  and 
practical  railroad  men,  and  as  this  view  is  as  mistaken  as  it  is 
common,  and  leads  to  much  mistaken  action,  it  will  be  well,  be- 
fore proving  affirmatively  that  this  view  is  an  error,  to  point  out 
the  nature  and  source  of  the  error  (which  is  easily  enough  seen), 
since  the  presumption  is  strong  that  any  view  which  is  widely 
held  is  a  true  one. 

177.  Its  origin  lies  in  a  series  of  plausible  non-sequiturs,  which 
are,  in  a  few  Words,  these — no  one  of  them  being  true  : 

1.  Rates  are  (usually  and  whenever  possible)  fixed  at  so  much 
per  mile,  because  (fallacy  i)  it  costs  so  much  per  mile  to  transport 
the  passenger  or  freight.  Ten  per  cent  more  or  less  distance 
means  ten  per  cent  more  or  less  fare,  and  "  necessarily"  (fallacy 

2)  ten  per  cent  more  or  less  expense. 

2.  But  on  our  particular  railway  the  service  rendered  is  just 
as  valuable,  if  transportation  be  furnished  from  the  point  desired 
to  the  point  desired,  whether  the  intermediate  distance  be  90 
miles  or  100  miles,  and  hence  (by  a  long  but  unconscious  jump 
over  a  vast  hiatus  in  the  reasoning)  we  shall  ''  of  course"  (fallacy 

3)  receive  the  same  money  for  it.     Therefore,  necessarily. 


196   VII.— DISTANCE— RELATION   TO  RATES  AND  EXPENSES-. 

3.  All  extra  distance  adds  greatly  to  the  cost  of  the  service 
(fallacy  i  and  2);  adds  nothing  to  the  value  of  the  service  (true 
enough  with  certain  limitations);  hence  adds  nothing  to  revenue 
(fallacv  3),  and  hence  is  among  the  greatest  of  disadvantages: 
Q.  E.  b. 

The  truth  is,  not  one  single  item  of  railway  expenditure,  large 
or  small,  not  even  fuel  or  wear  of  wheels,  varies  in  direct  ratio 
with  distance,  or  in  anything  like  direct  ratio,  and  more  than, 
half  of  them  are  very  slightly  if  at  all  affected  thereby.  On  the 
other  hand,  a  very  large  proportion — on  some  railways  almost  the 
whole — of  the  receipts  does  vary  directly  with  the  distance. 

178.  The  reason  why  rates  are  so  generally  based  more  or  less 
directly  on  distance  hauled,  and  on  nothing  else  except  necessity, 
is  not  in  the  least  that  it  is  a  primary  factor  in  the  cost  of  the 
service,  but  simply  this:  The  sale  of  transportation,  like  the 
sale  of  any  other  commodity,  is  governed  by  the  one  universal 
business  law  of  selling  whatever  is  salable  as  dearly  as  possible 
(or  at  least  as  dearly  as  is  prudent  and  wise),  regardless  of  the 
cost  of  production.  The  selling  price  of  no  marketable  com- 
modity, whether  transportation  or  houses  or  cotton  cloth,  is  fixed. 
by  the  cost  of  production,  except  that  if  it  will  not  bring  a  pro- 
fit on  its  cost  it  is  no  longer  produced  ;  and  for  railways  any 
such  attempt  would  be  particularly  senseless,  for  the  reason  that, 
as  we  have  elsewhere  seen  (par.  40,  181),  the  cost  of  any  par- 
ticular sale  of  transportation  may  be  considered  as  varying  any- 
where from  zero  upwards  ;  depending,  to  a  far  greater  extent 
than  in  any  other  commercial  transaction,  simply  upon  the 
amount  that  can  be  sold. 

179.  Thus  it  has  happened  that  the  distance  transported  has 
been  made  the  basis  for  tariffs  (when  they  have  any  basis  what- 
ever other  than  the  amount  which  it  is  possible  to  collect),  as 
measuring  in  a  rude  way,  not  the  cost  of  the  service,  but  the 
consumer's  idea  of  its  value.  In  point  of  fact,  the  distance  trans- 
ported is  but  one  of  many  circumstances — and  certainly  not 
the    most    important — which    fix    the    cost   of    transportation* 


VII.— DISTANCE— RELATION   TO  RATES  AND  EXPENSES,   1 97 

Grades,  curvature,  cost  of  construction,  terminal  expenses,  vol- 
ume of  traffic,  whether  the  cars  return  full  or  empty — all  these 
have  very  much  more  to  do  with  the  cost  of  service  than  the 
mere  distance  transported,  but  they  are  entirely  neglected  in  fix- 
ing schedules  of  rates,  simply  because  the  consumer  is  not  con- 
scious of  receiving  any  value  when  he  is  transported  over  curva- 
ture or  grades,  but  is  conscious  of  receiving  value  when  he  is 
transported  over  distance.  For  this  very  humble  reason  only, 
and  not  because  there  is  any  natural  equity  in  it,  the  railway 
taxes  him  for  the  one  service  and  not  for  the  other,  so  that  it  may 
even,  to  a  certain  extent  and  under  certain  circumstances,  and  so 
long  as  those  circumstances  continue,  be  a  positive  advantage  to 
a  line  to  have  a  few  miles  of  extra  distance,  especially  when  ad- 
ditional way  traffic  is  thereby  secured. 

180.  The  mere  possibility  of  such  effect  makes  it  invariably 
necessary,  in  considering  the  effect  of  distance,  to  consider  its 
effect  on  revenue  as  well  as  on  expenses,  even  if  the  former  be 
considered  only  to  be  disregarded.  To  disregard  it  is  often  the 
only  proper  course,  for  this  reason  if  no  other  :  As  a  question 
purely  of  public  policy — that  is  to  say,  if  the  interests  of  the 
corporation  were  in  all  respects  strictly  identical  with  the  in- 
terests of  the  community  as  a  whole — the  effect  of  distance 
upon  operating  expenses  would  be  the  only  one  which  there 
would  be  need  to  consider,  and  its  effect  on  revenue  should  not 
be  considered  at  all.  For  since  the  real  service  rendered  and 
paid  for  is  the  transportation  of  persons  or  property  from  one 
terminus  to  another,  the  precise  length  of  track  between  the  two 
should  have  no  more  effect  upon  the  price  paid  than  the  precise 
amount  of  curvature  or  rise  and  fall,  and  much  less  than  the  rates 
of  ruling  grades.  All  should  be  considered  or  none  should  be. 
And  even  in  the  case  of  railways  constructed  by  private  en- 
terprise for  pecuniary  profit,  although  the  fact  that,  both  by  law 
and  by  fixed  custom,  there  is  a  certain  credit  side  to  the  disad- 
vantages of  a  circuitous  route  and  not  to  other  disadvantages 
is  entitled  to  a  certain  legitimate  weight,  yet  the  nature  of  this 


1 98   VII.— DISTANCE— RELATION   TO  RATES  AND  EXPENSES. 

credit  side  greatly  affects  the  expediency  of  relying  on  it  ;  for 
it  is  obtained,  not  by  rendering  more  valuable  service,  nor  by 
decreasing  the  cost  of  the  service,  but  by  the  corporation  avail- 
ing itself  of  an  arbitrary  custom  to  transfer  a  portion  of  the 
burden  arising  from  one  element  of  an  unfavorable  line  (and 
not  of  others)  from  its  own  shoulders  to  the  public  at  large,  or 
to  its  connecting  companies. 

Moreover,  this  is  a  variable  power,  which  does  not  always  exist 
at  all.  We  will  therefore,  for  the  present,  postpone  all  discussion 
of  that  side  of  the  question,  and  neglect  it  wholly,  until  we  have 
determined  the  effect  of  distance  upon  operating  expenses. 

181.  As  illustrating  the  vastly  greater  effect  of  other  causes  than  distance  on 
the  cost  of  transportation: 

Wm.  von  Nordling,  one  of  the  most  eminent  of  Austrian  engineers,  in  a 
study  on  the  cost  of  railway  transportation,  apropos  of  a  proposition  for  con- 
structing large  canals  to  connect  the  Danube  with  the  Oder  and  the  Elbe, 
submits  some  interesting  calculations,  in  which  he  avoids  the  mistake  so 
commonly  made  in  such  calculations  (and  oftener  in  Europe  than  elsewhere) 
of  calculating  the  average  cost  per  mile  of  transportation  on  the  railroad,  and 
assuming  that  to  be  the  measure  of  the  cost  of  transporting  any  greater  or  less 
amount  of  traffic  any  greater  or  less  distance. 

After  calculating  that  the  average  cost  per  ton  per  mile  on  the  Theiss  Rail- 
way of  Austria,  in  1875,  was  0,98  cent,  exclusive  of  loading  and  unloading,  he 
finds  that  additional  freight  under  ordinary  conditions  would  have  cost  0.457 
cent;  with  cars  full  one  way  and  returning  empty,  0.392  cent;  and  full  both 
ways,  0.286  cent  per  ton  per  mile;  while  back  load  for  cars  that  otherwise  would 
return  empty' would  have  added  only  0.180  cent  per  ton  per  mile  to  the  expenses. 


THE    EFFECT    OF    DISTANCE    ON    OPERATING    EXPENSES. 

182.  The  cost  of  operating  additional  distance  not  only  is 
not  the  same  per  mile  as  the  average  cost,  but  is  not  even  a  con- 
stant quantity  per  unit  of  additional  length  ;  that  is  to  say,  is 
by  no  means  the  same  per  mile  when  the  addition  to  be  consid- 
ered is  one  mile  as  when  it  is  twenty.  With  the  small  changes 
of  distance  which  most  frequently  occur,  the  number  of  yearly 
trips  of  rolling-stock,  the  number  of  buildings  and  sidings,  and 


CHAP.    VII.— DISTANCE— EFFECT  ON  EXPENSES.         1 99 

the  considerable  class  of  expenditures  which  vary  therewith,  re- 
main practically  constant,  as  well  as  (very  frequently)  train 
wages,  and  are  not  perceptibly  affected  until  the  change  of 
length  amounts  to  a  considerable  percentage.      How  much  such 

RELATIVELY    SMALL    CHANGES    OF    LENGTH  affcCt  CXpenseS  We  shall 

first  consider. 

183.  Maintenance  of  Way. — The  entire  cost  of  maintenance  of 
way  proper  (excluding  yards  and  structures)  may,  without  any  serious 
exaggeration,  be  considered  as  varying  with  changes  of  distance  as  great 
as  2  or  3  miles ;  but  it  is  not  true,  even  of  such  items  as  track  labor  and 
track  watchmen,  that  they  are  appreciably  affected  by  variations  of  a  few 
hundred  feet,  or  even,  sometimes,  of  as  much  as  half  a  mile  in  distance. 
This  results  from  the  fact  that  the  cost  of  track  labor  is,  and  will  be  still 
more  in  the  future,  fixed  by  other  causes  than  the  precise  amount  of  labor 
to  be  performed.  It  is  essential  for  safety  that  there  should  be  a  gang  of' 
men,  large  enough  to  handle  a  hand-car  and  put  in  a  rail,  every  5  or  6 
miles;  and  to  this  end,  in  practice,  the  road  is  divided  up  into  an  even 
number  of  sections  of  about  that  length,  and  a  minimum  number  of  men 
assigned  to  each,  whose  duty  during  a  large  portion  of  the  year  is  simply 
watchfulness  and  "tinkering."  It  is  only  during  a  few  months  in  the 
spring  and  summer  that  the  amount  of  labor  put  upon  the  track  varies 
strictly  with  the  distance. 

It  is  safer,  however,  to  consider  that  all  track  and  road-bed  expenses 
(15  cts.  or  per  cent — Table  80)  will  vary  directly  with  distances  large 
enough  to  be  measured  by  miles  or  quarter-miles,  as  they  will  certainly 
do  when  the  distances  become  as  great  as  of  2  or  3  miles  ;  but  for  dis- 
tances of  a  few  feet  or  stations  there  is  no  reasonable  possibility  that 
other  items  than  rail  wear,  tie  renewals,  ballast,  and  fencing  will  increase 
m  direct  ratio. 

184.  Fuel. — A  very  considerable  percentage  of  the  consumption  of 
fuel  is  a  constant  wastage  independent  of  the  exact  distance  run.  The 
cost  of  kindling  fires  alone  averages  8  or  10  per  cent  of  the  total,  as 
shown  in  Table  84.  A  fire-box  full  of  coal  is  wasted  every  time  the  fire 
is  drawn,  which  was  formerly  about  every  100  miles  run,  but  is  now,  on 
an  average  of  a  whole  road,  nearer  to  every  1000  miles,  owing  to  the  m- 
troduction  of  the  practice  of  banking  fires,  especially  with  the  long-trip 
system.  This  practice  saves  no  fuel,  however,  but  rather  wastes  some, 
its  advantage  being  wholly  in  saving  of  time  and  of  injury  to  the  loca- 


200         CHAP.    VII.— DISTANCE— EFFECT  ON  EXPENSES. 


Table  84. 

Showing  the  Relative  Cost  of  Wood  for  Kindling  on  the  Philadel- 
phia &  Reading  Railroad  for  a  Series  of  Years. 


Year. 

Percentage  of  the  < 
Kindling-wood  tc 
MAiNiNG  Cost  of  ] 

30ST  OF 

Re- 

f'UEL. 

Prices  of  Fuel. 

Average  Consumption  of 
Wood  for  Kindling. 

Passenger 
Trains. 

Freight 
Trains. 

Coal 
Trains. 

Wood 
per  Cord. 

Coal 
per  Ton. 

1867 

lS6g 

1873 

14.2 
8.8 
9-7 

10. 
6.4 
6.2 

5-1 
3.6 

4.1 

$5  79 
5  50 
5  94 

$3  15 
3  So 
3  25 

Passenger  trains,  .13  c'd. 
Freight          "        .15    " 
Coal               "        .22    " 

Average. 

10.9 

7-5 

4-3 

$5  74 

$3  40 

The  above  does  not  include  the  cost  of  any  coal  used  in  kindling.  The  consumption 
of  wood  seems  very  small ;  Mr.  Trautwine  ("Engineers'  Pocket  Book,"  p.  411)  gives  ]/i 
cord  as  the  average  consumption. 

When  this  road  was  using  wood  fuel  entirely,  passenger  trains  used  2. 7  cords  per  100 
miles,  or  about  2%  cords  per  daily  run  of  93  miles.  Allowing  J4  cord  for  getting  up 
steam  would  amount  to  exactly  10  per  cent. 

Mr.  William  Stroudley,  Loc.  Supt.  London,  Brighton  &  South  Coast  Railway, 
in  a  paper  before  the  Institution  of  Civil  Engineers  (1885)  shows  that  the  number  of 
pounds  of  coal  burned  to  raise  100  lbs.  of  steam  from  water  at  70°  F.  was  about  450  lbs., 
equivalent  to  from  3  to  4  lbs.  of  coal  per  train-mile  when  kindling  fires  once  a  week,  or 
every  650  to  800  miles  run.  This  amounts  to  almost  exactly  10  per  cent  of  the  total 
quantity  of  coal  burned  per  mile.  He  gives  also  tables  showing  that  his  passenger  engines 
spend  nearly  half  the  time  that  they  are  nominally  in  service  either  in  switching  or  standing 
still  (mostly  the  latter),  and  only  half  the  time  running. 


motive  from  expansion  and  contraction.  This  terminal  wastage  alone 
will  average,  therefore,  some  400  or  500  pounds  per  100  miles,  sufficient 
to  run  a  locomotive  5  to  10  miles,  or  5  to  10  per  cent  of  the  total  con- 
sumption. Whether  the  fires  are  drawn  or  not,  a  fire-box  full  of  coal  at 
least,  and  usually  more,  is  wasted  at  the  end  of  every  trip. 

185.  The  consumption  due  to  stoppmg  and  starting  and  to  standing 
idle  in  yards  and  on  side  tracks  is  also  a  heavy  item,  and  may  be  considered 
as  nearly  independent  of  distance  in  the  case  of  two  nearly  equal  lines 
operated  with  the  same  number  of  steps  and  sidings  between  the  same 
termini.  The  direct  amount  of  loss  of  power  m  stopping  a  train  run- 
ning at  15  miles  an  hour  is  sufficient  to  lift  it  vertically  nearly  8  feet,  as  will 


CHAP.    VII.— DISTANCE— EFFECT  ON  EXPENSES.         20 T 

be  seen  in  Table  ii8,  and  at  30  miles  an  hour  four  times  that  height,  or 
nearly  32  feet.  The  rolling  resistance  of  a  loaded  freight  or  passenger 
train  in  motion  on  a  level  being,  as  will  be  seen  hereafter,  equivalent  to 
that  of  a  grade  of  less  than  16  feet  per  mile,  we  have,  from  stopping  and 
starting  only,  a  waste  of  power  sufficient  to  run  the  train  one  half  mile 
in  the  one  case  and  two  miles  in  the  other,  causing  a  loss  for  an  average 
number  of  stops  for  stations  and  crossings  of  something  very  close  to  10 
per  cent  of  the  total  consumption.  In  such  extreme  cases  as  the  Manhat- 
tan (elevated)  Railway  of  New  York,  where  there  are  stations  about  every 
three  eighths  of  a  mile,  very  nearly  three  quarters  of  the  total  consump- 
tion of  fuel  has  been  shown  to  be  due  to  this  cause.  As  to  the  wastage 
while  standing  idle,  experiments  made  by  Mr.  Reuben  Wells  show  that 
an  engine  with  jacketing  in  perfect  order,  standing  idle  all  day  long  in  a 
yard,  wholly  protected  from  wind  and  using  no  steam  in  the  cylinders, 
requires  from  25  to  32  lbs.  of  coal  per  hour  to  keep  up  steam  in  the 
boiler,  or  nearly  enough  to  run  it  a  mile  in  service.  For  the  short  stops 
in  actual  service  at  least  twice  this  amount  per  hour  is  probably  wasted, 
including  what  is  blown  out  of  the  safety  valve,  owing  to  all  parts  of  the 
engine  being  hot,  and  a  surprisingly  great  amount  of  time  is  spent  on  an 
average  freight  trip,  and  even  passenger  trips,  in  simply  standing  still. 
It  will  average  over  4  hours  per  day,  if  not  more,  in  freight  service  on 
single-track  roads,  not  including  the  time  lost  at  the  beginning  and  end 
of  the  trip;  and  on  the  very  fastest  express  runs  experience  has  shown 
that  fully  one  fourth  of  the  time  between  termini  is  lost  by  stops.  This 
amounts  to  a  further  waste  of  3  to  6  per  cent. 

186.  From  all  these  causes  together  it  is  a  very  moderate  estimate  that 
about  one  third  of  the  total  cost  of  fuel  is  not  affected  by  a  slight  change 
more  or  less  in  the  length  of  the  line.  The  average  consumption  of  fuel 
per  train-mile  in  both  directions  is  not  so  greatly  affected  by  grade  that 
we  need  consider  the  question  of  whether  the  additional  distance  is  on  a 
grade  or  on  a  level.  Going  up  grade  the  consumption  is  greatly  in- 
creased, but  there  is  no  consumption  of  steam  at  all  in  going  down 
grade,  so  that  the  average  is  only  slightly  increased. 

187.  Repairs  of  Engines  and  Cars. — It  is  exceedingly  common, 
and  for  certam  purposes  proper  enough,  to  assume  these  expenses  to 
vary  directly  with  distance,  but  for  our  present  purpose  this  is  very  erro- 
neous. The  wear  and  tear  of  rolling-stock,  it  is  plain,  arises  from  several 
distinct  causes,  of  which  the  regular  running  wear  when  m  motion  is 
only  one.     These  causes  are : 


^202         CHAP.    VII.— DISTANCE— EFFECT  ON  EXPENSES. 

1.  Deterioration  from  time  and  age :    Varying  with  time. 

2.  Stopping  and  starting:    Varying  with  number  of  stops. 

3.  Terminal  service,  getting  up  steam  and  drawing  fires,  switching, 
making  up  trains,  etc.:  Varying  with  the  nuinber  of  trips,  independent  of 
their  length. 

4.  Effect  of  curvature  and  heavy  grades:  Varying  with  the  character 
of  the  alig7iment.     And,  finally,  we  come  to 

5;  Effect  of  regular  running  between  stations  on  a  tangent :  Varying 
with  distance  (the  additional  effect  of  any  curvature  on  a  given  distance 
being  a  separate  matter). 

All  of  these  causes  contribute  to  increase  the  cost  of  maintaining  roll- 
ing-stock, and  as  the  whole  cannot  be  greater  than  the  sum  of  all  its 
parts,  the  effect  of  any  one  of  them  alone  must  be  much  less  than  the 
total  cost  unless  the  effect  of  the  other  four  is  insignificant.  Each  item 
will  be  seen  to  vary  with  a  different  cause  and  only  with  that,  and  only 
one  of  these  causes  is  the  exact  length  of  track. 

188.  The  mere  statement  of  these  facts  at  once  makes  probable  that 
rolling-stock  repairs  cannot  vary  very  directly  with  distance  alone  when 
the  other  causes  of  deterioration  remain  the  same,  although  precisely 
how  much  each  cause  contributes  to  the  total  will  probably  always  re- 
main an  indeterminate  problem.  Nothing  but  the  most  exhaustive  ex- 
periments could  settle  it  accurately.  Hence  we  find  that  when  men's 
attention  is  specially  fixed  upon  the  disadvantages  of  some  one  of  these 
causes  they  are  very  apt,  with  entire  good  faith,  to  exaggerate  the  effect 
of  that  one  cause,  simply  from  momentary  forgetfulness  of  how  many  other 
causes  are  also  co-operating  to  make  up  the  aggregate.  If  the  effect  of 
distance  is  under  discussion,  the  whole  cost  of  rolling-stock  repairs  will  be 
charged  off  as  so  much  pei  mile  run,  as  if  no  other  cause  but  mileage  had 
any  effect ;  but,  on  the  other  hand,  if  the  disadvantages  of  some  grade 
crossing  is  in  question,  we  shall  have  the  wear  and  tear  resulting  from 
that  cause  spoken  of  as  something  fabulous.  And  so  about  the  injurious 
effect  of  some  particularly  crowded  yard  or  objectionable  curvature. 
But  starting  from  the  premise  that  the  total  effect  of  all  these  causes 
cannot  be  more  than  100  per  cent,  we  have  in  Table  8$  a  subdivision  of 
this  total,  item  by  item,  between  the  above  five  causes.  As  this  has  been 
done  with  great  care  to  get  the  best  attainable  authority  for  each  (which 
it  would  occupy  too  much  space  to  give  in  detail),  the  margin  for  possible 
error  is  not  great  enough  to  be  of  moment,  although  no  absolute  exact- 
ness can  be  claimed  for  it. 


CHAP.    VII.— DISTANCE— EFFECT  ON  EXPENSES. 


203 


Table  85. 

Distribution  of  the  Cost  of  Engine  Repairs  to  its  Various  Contrib- 
uting Causes. 


Total 

Cost  of 

Item. 

Distribution. 

Item. 

Effect  of 

Time, 

Age, 

and 

Exposure. 

Stopping 

and 
Starting 
at  Way 
Stations. 

Terminal : 
Getting 

Up  Steam, 
Making 

Up  Trains. 

Curvature 

and 
Grades. 
(Approx. 
Average.) 

P.c. 

4- 
7- 
5. 

Distance 
on 

Tangent 
between 
Stations. 

Boiler 

p.  C. 
20.0 
20.0 
30.0 

p.  C. 
I. 

p.  C. 
2. 

4. 

7. 

p.  C. 

7. 
2. 

3. 

p.  C. 

7- 

1- 

14. 

Machinery 

Mountings.. 

Lagging  and  painting — 
Smoke-box,  etc 

12.0 

10. 0 
3.0 

4. 

I. 
I. 

2. 

2. 
I. 

I. 
I. 

3. 

6.    . 
3. 

4- 
I . 

Tender: 
Running  gear 

Body  and  tank 

Total 

100. 0 

7. 

15. 

17. 

19. 

42. 

Table  86. 

Distribution  of  the  Cost  of  Freight-Car  Repairs  to  its  Various  Con- 
tributing Causes. 


Distribution. 

Item. 

Total 

Cost  of 

Item. 

Effect  of 
Time  and 
Age,  in- 
dependent 
of  Work 

and 
Mileage. 

Stopping 

and 
Starting. 

Terminal : 
Making 

up 

Trains, 

etc. 

Curvature 

and 

Grades. 

Distance 

only 
between 
Stations 

on 
Straight 
Track. 

Wheels 

p.  c 
30 
30 
10 
5 
5 
10 

5 
5 

p.  c. 

2. 

I. 

3- 

p.  C. 
5- 
5- 
2. 
I. 
2. 

4. 
2. 

0.5 

p.  C. 
2. 
2. 

I- 
I. 
I. 

4- 
2. 

0.5 

p.  C. 
13- 

5- 

I. 

2. 

2. 

p.c 

10. 

Axles,  brasses,  and  boxes 
Springs 

18. 
6. 

Truck  frame  and  fittings. 
Brakes 

I. 

Draw-bars 

Sills  and  attachments.. . . 

Car  body,  painting,  etc. . 

I. 

Total 

100, 

6.0 

21.5 

13-5 

23.0 

36.0 

The  proportionate  cost  of  wheels,  axles,  and  brasses  above  is  perhaps  large,  and  that 
of  brakes  and  draw-bars  small,  but  it  is  in  accordance  with  the  best  attainable  information. 


204        CHAP.   VII.— DISTANCE— EFFECT  ON  EXPENSES. 


189.  In  Table  85  each  of  the  smaller  items  is  as  small  as  it  can  rea- 
sonably be  made.  Consequently  not  more  than  42  per  cent  of  the  cost 
of  the  engine  repairs  appears  to  vary  with  the  minor  changes  of  length. 
The  distribution  to  curvature  and  grades  will  be  spoken  of  hereafter.  It 
will,  of  course,  vary  greatly  on  different  roads.  Table  86  is  a  similar  dis- 
tribution of  the  cost  of  freight-car  repairs  based  in  part  upon  Tables  71 
to  75,  and  in  part  on  Table  87. 

190.  It  will  be  seen  that  a  considerably  larger  proportion  of  car  re- 
pairs than  of  engine  repairs  is  independent  of  distance,  as  is  but  natural. 
The  cost  of  passenger-car  repairs  may  be  considered  as  not  greatly  differ- 
ent per  train  from  that  of  freight  trains,  but  the  maintenance  of  the  seats, 
furniture,  and  inside  and  outside  ornamentation  make  up  much  more 
than  half  the  cost  of  passenger-car  repairs,  so  that  the  cost  per  train  of 
all  kinds  of  running  wear  is  much  less  considerable. 

Table  87, 

Estimated    Cost    New,   Scrap  Value,  and    Rate   of    Depreciation    of 
Freight  Cars  of  Various  Kinds. 


[Deduced  from  data  published  in  the  National  Car-Builder  of  April,  1880.] 
Box  Cars. 


Labor. 

Material. 

Total. 

Scrap 
Value. 

Total 
Deprec'n. 

Average 
Life 
Years. 

Annual 
Deprec'n. 

Wheels 

$90.00 
45-00 
10.00 
94-94 

$35-00 

15.00 

4.00 

25.00 

$55. 

30. 

6. 

70. 

4 

8 

3 
35 

$13-75 

3-75 

Br3,sses        • 

2.00 

Fr3,nic         .  • . 

2.00 

$227.82 

7-33 
26.08 

52.85 

25-49 
10.76 
36,78 
5.25 
13.29 

5-89 

Truck 

Brakes .  • 

Draw-bars — 

Frame 

Roof 

Floor 

Sides 

Painting 

Trimmings.. . 
Trusses 

$12.12 
2.16 
2.95 
6.79 
3-34 
1. 12 
7-58 
2.16 
6.23 
I -13 

239.94 

9.49 

29.03 

59-64 
28.83 
11.88 

44-31 
7.41 

19.52 
6.02 

79.00 
2.00 
6.00 

10.00 
4.00 
1. 00 
2.00 

3-00 
3.00 

161. 

7-50 
23- 
50. 
25. 
II. 
42. 

7.50 
16. 

3- 

6 

15 

8 

10 
20 

7 
20 
20 

$21.50 
1.25 
3.83 
3.33 
3.12 

I.IO 

2.10 

1.07 

.80 

•15 

Total,  box  c. 

410.54 

45-58 

456.12 

110.00 

346. 

$38.25 

Stock  cars.... 

388.72 

42.68 

431.40 

(ov 

tx.) 

CHAP,    VII.— DISTANCE— EFFECT  ON  EXPENSES, 


205 


Table  87. — Continued. 

Flat  a7td  Coal  Cars. 


Total  Cost 
New. 

Scrap 
Value. 

Total 
Depreciat'n. 

Average 
Life. 
Years. 

Annual 
Depreciat'n. 

Truck  (as  above) 

Brakes ... 

Draw-bars 

$239-94 
9.49 

29.03 
45.00 
12.00 
8.00 
5-00 
6.00 
6.00 

$79 

'    2 

6 

10 
I 
I 
I 
3 

$161 

7 

23 

35 

II 

7 

4 

3 

6 

50 

6 
15 

TO 
20 
20 
20 

7 

$21.50 
1.25 
3.83 
2.33 

Frame 

Floor 

1. 10 

Sides 

0.35 
0.20 

Fittings 

Trusses 

0.  15 

Painting. 

0.88 

Total 

$360.46 

^lO"^, 

^2=;7.  e;o 

$31-59 

Per  Cent  of  Total  Depreciation. 


Flat  Cars. 

Box  Cars. 

Average. 

Wheels     

43-5 

18.2 

6.3 

36.0 

I5-0 

5.2 

40. 
16.6 

5.7 

Axles  and  brasses 

Truck  frame 

Total  truck 

68.0 

4.0 

12. 1 

7.4 

8.5 

56.2 

3-3 
10. 0 

8.7 
21. 8 

62.3 
3.6 

II. 0 
8.0 

15-1 

Brakes 

Draw-bars 

Frame 

Other  parts 

Total 

100. 0 

100. 0 

100. 0 

With  this  table  compare  Table  73.  The  principal  discrepancy  between  the  two  is  that 
the  cost  of  wheels  is  much  less,  and  of  brasses  much  more,  in  the  latter.  On  the  whole, 
this  table  is  at  least  equally  trustworthy. 

The  rule  of  the  Master  Car-Builders'  Association  is  that  6  per  cent  per  year,  or  say  $30, 
shall  be  allowed  for  depreciation  in  value  of  freight  cars,  down  to  a  minimum  of  40  per 
cent  of  their  original  cost. 


191.  Train  Wages. — The  tendency,  as  already  stated  (par.  152),  is 
more  and  more  to  fix  all  train  wages  directly  by  the  mile,  especially  on 
the  larger  lines  made  up  of  several  divisions  and  with  heavy  traffic, 
where  the  total  number  of  trips  a  crew  can  run  per  month  is,  in  fact, 
proportioned  almost  exactly  to  the  length  of  the  run.     Some  arbitrary 


206         CHAP,    VII.— DISTANCE— EFFECT  ON  EXPENSES. 

limit  is  fixed,  varying  from  26,000  to  35,000  miles,  as  a  month's  work. 
Dividing  this  by  the  length  of  each  division  gives  the  number  of  trips 
to  constitute  a  month's  work,  the  fraction  being  disregarded  in  favor  of 
the  employe.  On  a  division  100  miles  long  260  trips  is  a  month's  work; 
on  a  division  90  or  105  miles  long  288.89  ^'^^  247.62  trips  would  be  exactly 
a  month's  work,  but  the  fraction  would  be  dropped  in  favor  of  the  em- 
ploye, and  288  and  247  trips,  respectively,  called  a  month's  work. 

192.  Many  of  the  smaller  lines  still  pay  no  attention  to  the  exact 
mileage  run,  and  others  (including  probably  over  half  the  mileage  of  the 
United  States)  adopt  the  compromise  plan  already  described  (par.  154); 
but  under  any  circumstances  it  will  be  seen  that  it  is  extremely  unlikely 
that  slight  changes  of  length  of  a  few  hundred  feet  will  affect  train 
wages  in  any  manner  or  under  any  circumstances  whatever.  The  circum- 
stances, and  the  probable  standard  of  train  wages,  must  be  considered 
in  each  case,  and  in  the  summary  below  train  wages  are  both  included 
and  excluded. 

193.  Station  and  General  Expenses  and  Taxes. — Taxes  are 
nominally  assumed  at  so  much  per  mile,  and  no  doubt  really  vary  with 
mileage  to  some  extent,  in  fact  as  well  as  in  form.  As  they  are  in  the 
long-run,  however,  based  on  value  and  not  on  cost,  it  can  hardly  be 
proper  to  consider  them  as  varying  with  distance  to  any  important  extent, 
and  unless  a  longer  line  between  two  given  points  increases  the  value  of 
the  property,  they  should  not  increase  with  distance  at  all.  Station, 
terminal,  and  general  expenses  are  of  course  entirely  unaffected  by  any 
small  changes  of  length,  unless  the  volume  of  business  or  number  of 
stations  and  side  tracks  is  also  increased. 

194.  Summing  up  the  effect  of  distance  on  the  various  items 
of  operating  expenses,  as  in  Table  88,  we  obtain  as  a  final  result, 
that  fractional  changes  of  distance  increase  or  decrease  expenses 
by  only  25  to  40  per  cent  of  the  average  cost  of  operating  an 
equal  distance,  according  as  train  wages  are  affected  or  un- 
affected. The  limit  of  possible  variation  or  error  in  this,  as  in 
all  other  such  estimates,  is  no  doubt  a  considerable  percentage, 
but  this  is  unavoidable.  Exactitude  enough  to  make  us  certain 
of  having  avoided  grave  error  and  hopeful  of  having  avoided  all 
error,  is  the  utmost  that  is  possible. 


CHAP.    VII.— DISTANCE— EFFECT  ON  EXPENSES. 


207 


Table  88. 

Effect    on    Operating    Expenses    of    Minor 
Measured  by  Feet  or  Stations,  and  Not  by 


Estimated    Approximate 

Changes  of  Distances 

Miles. 

[Cost  of  train-mile  assumed  at  $1.00,] 


Item. 


Total  Cost 

by 

Table  80. 

Cts.  or  p.  c. 


Proportion  of  Same 

Increasing  with 

Distance. 


Cost  of 
Running 

One 
Additional 
Train-Mile. 


Fuel 

Water 

Oil  and  waste 

Engine  repairs 

Switching-engines 

Train  wages , 

Train  supplies 

Car  repairs 

Car  mileage 

Rail  renewals 

Adjusting  track 

Tie  renewals 

Earthwork  and  ballast 

Yards  and  structures 

Station,  terminal,  general,  and  taxes. 


7.6 
0.4 
0.8 
5.6 
5.2 
14.9 

0.5 

10.  o 

2.0 

'2  ' 
6 
3 
4 


30. 


67  per  cent, 
unaffected. 
50  per  cent; 
40 
unaffected. 


35  per  cent, 
100 

80 

50 
100 
too 

unaffect 


5-1 


0.4 
2.2 


ed. 


Total. 


24.8  per  cent. 


24.8 


If  train  wages  vary  exactly  with  distance. 


39-7 


For  more  considerable  changes  of  distance  see  Table  89. 

In  the  first  edition  of  this  treatise  the  cost  of  small  additions  to  distance  was  estimated 
as  follows : 


Total  Cost  of 

Item  at  $1  Per 

Train-Mile. 

Proportion  of  Same 

Increasing  with 

Distance. 

Cost  of  Runn'g 

One  Additional 

Mile. 

Fuel 

10  cts. 
2    " 

1 
30 " 

70  per  ct. 

so      " 
70      " 
unaffected  by  small  1 
changes.           J 
all  but  yards  and    1 
structures.          ) 
unaffected. 

7  cts. 
I    " 
14    " 

Oil,  waste,  and  water 

Train  wages 

Station  and  general  expenses 

Total 

$1.00 

42  per  ct. 

42  cts. 

The  difference  between  this  and  the  above  estimate  is  partly  owing  to  changes  in 
operating  conditions  and  partly  to  more  correct  estimate  of  the  actual  effect  of  shght  ad- 
ditions of  distance.  At  the  time  the  first  edition  of  this  work  was  published  an  estimate 
that  the  cost  of  operating  additional  distance  was  only  about  42  per  cent  of  the  average 
cost  was  something  of  a  novelty,  yet  it  really  was  an  over-estimate. 


208         CHAP.    VII.— DISTANCE— EFFECT  ON  EXPENSES. 

COMPARATIVE    VALUE    OF    GREAT    AND    SMALL    REDUCTIONS     OF 

DISTANCE. 

195.  When  the  saving  or  loss  of  distance  is  more  considerable 
than  we  have  been  considering,  or  at  some  point  varying  from  2 
to  10  or  15  miles,  according  to  the  practice  and  conditions  of  the 
road,  a  considerably  larger  proportion  of  expenses  will  vary  with 
distance.  The  train  wages  and  number  of  track  sections  will 
almost  certainly  do  so.  The  cost  of  stopping  and  starting, 
maintenance  of  yards  and  sidingSj  and  track  labor  generally  will 
also  be  increased.  This  increase  will  be  in  detail  about  as  com- 
puted in  Table  89. 


Table  89. 

Estimated  Approximate  Effect  of  Great  and  Small  Differences  of 

Distance, 
The  smaller  percentage  is  as  in  Table  51,  for  small  differences  of  distance,  and  the 
table  gives  the  estimated  increased  effect  on  each  item  of  a  greater  difference  of  distance. 
[Cost  of  train-mile  assumed  at  $i.oo.] 


Item. 


Total  Cost 
by  Table  80. 

Cts.  or  p.  c. 


Increase  for  Greater 

Differences  of  Distance  of 

Per  Cent  varying  with 

Distance- 


Total  Am'nt 
Per  Train- 
Mile 
for  Greater 
Differences 
of  Distance. 


Fuel 

Water 

Oil  and  waste 

Engine  repairs 

Sviritching-engines 

Train  wages 

Train  supplies 

Car  repairs 

Car  mileage 

Rail  renewals 

Adjusting  track 

Tie  renewals 

Earthwork  and  ballast 

Yards  and  structures 

Station,     terminal,     general, 
and  taxes 


7.6 
0.4 
0.8 
5.6 
5-2 

14.9 
0.5 

10. o 
2.0 
2.0 

6.0 

3-0 


from 


4.0 

8.0 

30.0 


67  p, 

o 
50 
40 

o 

o 

o 

35 
100 

80 

50 

100 

100 

o 


c.  to 


85  p. 

50 

50 

57  ' 

o  ' 

100  ' 

40  ' 

50  ' 

100  ' 

100  ' 

100  ' 

100  ' 

100  ' 

50  ' 


6.5 
0.2 
0.4 

3-2 


14.9 

0.2 
5-0 
2.0 
2.0 
6.0 
3-0 
4  o 
4.0 


Total, 


from  24.8  p.  c.  to  51.4  p.  c. 


51.4 


If  train  wages  are  not  affected,  we  have. 


36.5 


CHAP.    VII.— DISTANCE— EFFECT  ON  EXPENSES.         209 

196.  From  the  aggregates  at  the  foot  of  Tables  88  and  89, 
we  find  that  the  total  cost  per  train-mile  for  great  and  small 
changes  of  length  compare  about  as  follows  : 

COST   PER   TRAIN-MILE. 

Minor  Changes.  Greater  Changes. 

(Measured,  in  Feet.)  (Measured  in  Miles.) 

If  train  wages  are  affected^,    .     39.7  cts.  or  per  cent.  51.4  cts.  or  per  cent 
If  train  wages  are  not  affected,  24.8  cts.  or  per  cent.  36.5  cts.  or  per  cent. 

Multiply  these  sums  by  365X2,  and  dividing  the  product  by 
5280  in  the  first  column  only,  we  obtain  the  following  : 

YEARLY   COST   PER  DAILY  TRAIN    (ROUND   TRIP)    OF  GREAT  AND   SMALL 
CHANGES   OF   LENGTH. 


Minor  Changes. 
Per  Foot.        Per  Mile. 

Greater  Changes. 
Per  Mile. 

Train  wages  affected,    .     . 

.     5.49  cts.        $290 

$375 

Train  wages  not  affected,  . 

.     3.43  Cts.         $181 

266.50 

These  sums,  divided  by  the  assumed  or  actual  rate  per  cent 
which  must  be  paid  for  capital,  .05,  .06,  .08,  .10,  etc.,  will  give  the 
justifiable  expenditure  to  save  one  foot  or  one  mile  of  distance,  as 
respects  its  effect  on  expenses  only.     Thus  at  10  per  cent  cost  of 

capital  we  may  spend  '^^1^  =  $3750  per  mile  to  save  considerable 

additions  to  distance. 

These  exact  figures  are  of  course  hypothetical,  to  illustrate 
the  general  law,  and  need  to  be  made  up  anew  for  any  particular 
case — at  least  to  the  extent  of  correcting  the  assumed  cost  per 
train-mile,  which  averages  80  to  90  cts.  rather  than  $1.00. 

197.  For  very  large  and  considerable  differences  of 
DISTANCES,  amounting  to  20  to  30  miles  in  100,  the  value  of  sav- 
ing distance  may  properly  be  still  further  increased,  even  up  to 
the  figures  at  which  all  saving  of  distance  without  distinction  is 
sometimes  estimated.  The  conditions  are  then  very  greatly 
modified.  The  number  of  yearly  trips  of  rolling-stock  is  then 
affected,  and  their  number  must  be  correspondingly  increased  or 
diminished,  whereas  smaller  changes  have  no  such  effect.  Gen- 
14 


2IO         CHAP.    VII.— DISTANCE— EFFECT  ON  EXPENSES. 

eral  expenses  even  will  then  be  perceptibly  affected,  and  almost 
every  item  of  expenditure  except  the  cost  of  making  up  trains 
and  getting  up  steam  will  be  very  largely  increased  by  the  extra 
distance.  The  total  cost  of  all  train  and  maintenance  of  way 
expenses  amounts  in  our  assumed  average  (Table  80)  to  70  cents 
or  per  cent  ;  but  as  all  experience  seems  to  indicate  that  even 
direct  train  expenses  cannot  be  reduced  in  practice,  and  will  not 
increase  in  direct  ratio  to  distance,  even  if  the  difference  of  dis- 
tance were  as  much  as  50  per  cent  (although  it  may  appear  that 
they  should  in  theory),  it  is  probable  that  80  or  90  per  cent  of 
the  above-mentioned  total  of  way  and  train  expenses,  or  say 
56  cents  per  train-mile,  is  the  maximum  effect  of  the  most  con- 
siderable changes  of  distance.  Or  to  put  the  whole  thing  into 
even  figures  :  the  average  cost  of  a  train-mile  being  taken  for 
even  figures  at  $1.00  (it  is  now  usually  less)— 

The  minimum  effect  of  extra  distance,  measured 

in  feet,  is  per  train-mile 25  per  cent  or  \ 

The  minimum  effect  of   distance,   measured   in 

miles,  not  affecting  train  wages,  is    ...     .  36.5  "       "     or  f 

The  maximum  effect  of  the  most  considerable 

change  of  distance  is „     .     56  to  63  "       "     or  f 

198.  Between  the  extremes  above  given,  the  true  valuation 
may  be  almost  anywhere  under  different  circumstances.  There 
are  even  certain  conceivable  cases,  which  have  sometimes 
occurred  in  practice,  where  the  assumed  maximum  is  not  ade- 
quate, as  for  instance,  in  comparing  two  routes  for  a  transconti- 
nental line  differing  by  100  to  800  miles.  The  number  of  operat- 
ing divisions  will  then  vary,  and  with  it  a  very  large  proportion 
of  the  general  and  station  expenses,  so  that  the  extra  distance 
may  cost  (or  may  not)  90  or  even  100  per  cent  of  the  average 
cost;  but  such  extreme  cases  are  too  exceptional  for  discussion. 

199.  The  effect  per  year  upon  operating  expenses  of  any  given 
distance  having  been  thus  determined,  the  capital  sum  for  which 
this  yearly  cost  represents  the  interest  will  plainly  be  the  sum 
which  (neglecting  all  effect  on  revenue)  we  are  justified  in  ex- 
pending to  cut  out  that  distance.     Thus,  if  distance  be  found,  as 


CHAP,   VII.— DISTANCE— EFFECT  ON  RECEIPTS.         211 

above,  to  cost  3.43  cents  per  daily  train  per  foot,  during  one 
year,  a  road  running  10  trains  per  day  each  way,  and  paying  8 
per  cent  for  capital^  can  afford  to  spend,  to  save  one  foot  of  dis- 
tance, $42.87  lessXh^  value  of  the  counterbalancing  considerations 
which  we  have  yet  to  consider.  To  this  we  may  add,  if  we  please, 
$2.00  per  foot,  more  or  less  as  the  case  may  be,  as  the  cost  of 
superstructure,  right  of  way,  and  fencing ;  or  we  may  include 
that  sum  with  the  other  items  of  construction.  This  value  hav- 
ing been  determined,  the  difference  in  cost  of  construction  to 
sub-grade  then  enters  in,  to  determine  whether  or  not  the  given 
improvement  will  cost  more  than  it  is  worth. 

200.  Errors  have  been  committed,  resulting  in  a  great  exaggeration  of  the 
value  of  saving  distance,  by  assuming  that  the  whole  average  cost  of  con- 
structing a  mile  of  line  complete  is  to  be  added  to  the  operating  advantage  of 
saving  a  mile  of  line  to  determine  its  total  value.  But  the  value  of  distance, 
like  the  value  of  everything  else,  is  independent  of  its  cost.  Whether  the  per- 
manent works  beneath  the  track  be  costly  or  cheap,  the  value  of  cutting  out 
that  part  of  the  length  of  the  road  will  be  the  same  for  the  same  road  with  the 
same  traffic.  We  therefore  first  estimate  the  value  of  the  saving,  and  then 
estimate  both  alternate  lines  to  see  whether  or  not  the  value  exceeds  the  cost. 

•All  the  preceding  has  been  on  the  supposition  that  distance, 
like  other  advantages  of  alignment,  is  a  pure  source  of  expense 
and  has  no  effect  upon  receipts — an  entirely  false  supposition. 
We  proceed  now  to  consider  the  other  side  of  the  question. 

THE    EFFECT    OF    DISTANCE    ON    RECEIPTS. 

201.  All  railway  traffic  is  in  common  parlance  roughly  divided 
into  "through"  and  "local,"  but  what  is  through  and  what  is 
local  is  a  matter  of  varying  definition.  The  literal  interpretation 
of  the  word  "  through" 'freight  would  be  freight  passing  over 
the  entire  distance  between  termini,  whether  exchanged  with 
other  lines  or  not,  and  this  definition  is  often  followed  in  classi- 
fying. Another  basis  for  subdividing  traffic  into  through  and 
local  is  that  adopted  in  the  Massachusetts  Railroad  Reports  ; 
viz.,  to  call  all  traffic  "  local  "  which  is  confined  to  the  home  road, 
and  simply  passes  from  one  station  of  the  road  to  another, 
whether  those  stations   are   the    termini  or  not ;  and  all  traffic 


212 


CHAP.    VII.— DISTANCE— EFFECT  ON  RECEIPTS, 


"  through"  which  is  (under  this  definition)  not  local,  but  passes 
over  parts  of  two  or  more  lines,  although  the  total  haul  may  be 
only  a  few  miles  between  small  non-competitive  stations  ;  where- 
as "  local "  traffic  may  be  hauled  the  entire  length  of  the  road  at 
competitive  rates,  and  be  for  all  practical  purposes  what  is  ordi- 
narily understood  as  "  through"  business. 

202.  Neither  basis  of  division,  therefore,  is  a  particularly 
happy  one  for  accomplishing  the  end  sought,  and  the  reason 
why  neither  can  be  is  easy  to  see.  The  difficulty  is  that  each  of 
them  is  an  attempt  to  include  under  only  two  classifications  ^z;^ 
distinct  classes  of  traffic,  each  one  governed  by  different  laws  as 
respects  rates  and  other  business  considerations.  These  classes 
are  : 

Non-competitive  local. 

Non-competive  exchange. 

Competitive  local. 

Competitive  exchange. 

Partially  competitive  (i.e.,  competitive  only  with  the 
disadvantage  of  a  local  haul  in  addition). 

More  in  detail,  the  nature  of  these  sub-classifications  are  as 

follows : 

^  I.  Local  or  home  traffic  proper^  having  no 

choice  of   route  and   confined  to 

one  line. 

\  2.  Exchange  traffic^  or  (by  Massachusetts 

classification)    "  through"    traffic, 

having   no    choice    of   route,    but 

passing  from  one  line  to  another. 

Local  or  home  traffic^  confined  to  one 
line,  but  having  a  choice  of  an- 
other route  (a  class  of  traffic  once 
small,  but  rapidly  increasing  with 
the  multiplication  of  railways). 

Exchange  or  ^^ through''  traffic  proper^ 
passing  between  the  more  impor- 
tant railway  centres,  and  with  a 
choice  of  two  or  more  routes. 


-1:: 

-U: 

c.  j'- 

A.  Non-Competitive. 

(The  whole  of  it  being  what 
is  ordinarily  referred  to 
by  the  term  *  *  local "  traf- 
fic.) 


B.  Competitive. 

(The  whole  of  it  being  what 
is  ordinarily  referred  to 
by  the  term  "through 
traffic") 


CHAP,    VII,— DISTANCE— EFFECT  ON  RECEIPTS,         213 


C.  Partially 

Competitive. 


Traffic  (usually  exchange  or 
'' through")  between  non-competitive 
local  points  and  tjnportant  railway 
centres  having  a  choice  of  route 
only  at  disadvantage,  by  paying 
a  local  rate  in  addition  to  the 
"through."  This  class  does  not 
exist,  practically,  for  passenger 
service. 

203.  Out  of  all  these  five  classes  there  is  only  one — viz., 
Class  B,  3  ;  traffic  confined  to  the  home  road  and  therefore 
purely  local,  but  having  a  choice  of  route  by  some  other  line 
and  therefore  competitive — on  which  a  longer  haul  has  no  effect 
vsrhatever  to  increase  receipts,  but  is  a  pure  disadvantage.  This 
class  is  also,  on  most  roads,  the  smallest  class  of  all,  and  on  very 
many  it  is  entirely  non-existent.  On  others,  however,  as  for  in- 
stance on  a  new  line  between  New  York  and  Philadelphia,  it 
would  be  the  bulk  of  the  traffic.  It  is  rapidly  increasing  in  im- 
portance, moreover,  from  the  prevalent  tendency  to  consolidate 
lines  into  great  systems,  and  even  when  this  consolidation  is  not 
formal  and  complete,  there  is  often  such  community  of  interest 
from  common  ownership  as  to  amount  to  very  nearly  the  same 
thing. 

Receipts  from  all  the  other  classes  are  affected  materially  by 
the  distance  ;  but  in  different  ways,  which  we  proceed  to  con- 
sider : 

204.  A.  Non-competitive  (Class  i  and  2).  Traffic  between 
non-competitive  way  points,  whether  these  points  are  on  the 
same  or  different  roads. 

There  is  no  real  need  for  making  a  distinction  between  these 
two  classes  in  respect  to  rates,  the  "  through"  being  made 
simply  by  the  addition  of  the  two  local  rates,  and  divided  in  the 
same  proportion. 

This  class  of  traffic,  which  is  what  is  popularly  meant  by 
**way"  traffic,  is  an  immense  factor  in  the  freight  revenue  of  any 


214         CHAP.    VII,— DISTANCE— EFFECT  ON  RECEIPTS. 

railway,  varying  ordinarily  from  50  to  75  per  cent  of  it ;  and 
rarely  falling  below  50  per  cent,  except  on  lines  of  heavy  through 
traffic  running  through  sparsely  settled  districts.  The  old 
Canada  Southern  (now  Michigan  Central)  is  a  peculiar  and  very 
exceptional  example  of  a  line  of  the  latter  character,  its  local 
ton-mileage  having  averaged,  before  its  consolidation,  below  8 
per  cent  of  the  total.  Even  in  this  extreme  case,  however,  its 
revenue  from  local  freight  appears  to  have  been  from  25  to  30 
per  cent  of  the  total.  The  Cleveland,  Columbus,  Cincinnati  & 
Indianapolis  Railway,  which  carries  perhaps  as  small  a  propor- 
tion of  non-competitive  freight  as  any  other  line  for  which  precise 
statistics  are  available,  and  which  is  certainly  exceeded  in  that 
respect  by  very  few,  derives,  as  an  average  of  9  years  (1873-81),, 
36  per  cent  of  its  tonnage,  23  per  cent  of  its  ton-mileage,  and 
about  2i^  per  cent  of  its  freight  receipts  from  "  local  freight," 
which  in  this  case  includes,  practically,  non-competitive  of  all 
classes.  In  its  passenger  traffic  this  line  enjoys  an  even  larger 
proportion  of  non-competitive  traffic,  being  at  much  less  disad- 
vantage in  that  respect,  and  in  fact  representing  as  nearly  as 
may  be  the  average  condition  of  the  whole  American  railway 
system.  This  is  the  more  fortunate  as  it  is  one  of  the  very  few 
lines  which  give  statistics  of  the  passenger  or  any  other  traffic 
in  such  form  that  it  can  be  accurately  separated  into  at  least  four 
of  the  five  classes  of  traffic  which  actually  exist,  as  above  speci- 
fied. The  following  Table  90  gives  the  percentage  of  each  of 
these  classes  (omitting  fractions  and  distributing  a  trifling  sum 
for  miscellaneous  receipts)  for  the  average  for  the  9  years  1873- 
1881.  The  table  may  be  accepted  as  giving,  in  a  rough  way, 
about  the  general  average  of  the  whole  American  railway  system 
for  passenger  service. 

205.  Table  91  gives  some  corresponding  details  for  the 
freight  traffic  of  the  same  road,  which  can  hardly  be  accepted  as 
so  representative,  and  in  Table  92  (as  also  in  various  other  tables  ; 
— see  Index)  are  given  data  as  to  average  train  loads.  The 
variations  in  such  matters  are  limited  only  by  the  number  of 
roads,  and  are  often  very  great. 


CH.  VIL— DISTANCE— EFFECT  ON  COMPETITIVE  TRAFFIC.  21$ 

There  is  a  certain  portion  of  even  non-competitive  traffic, 
it  must  alwa5^s  be  remembered,  on  which  rates  are  governed 
solely  by  what  it  will  bear,  without  any  reference  to  distance, 
and  on  many  roads  a  very  large  proportion,  as  where  there  is 
much  suburban  traffic;  yet  in  the  main  the  rates  are  nominally 
fixed  by  the  mile  on  all  this  traffic,  and  on  a  certain  large  pro- 
portion they  are  by  law  or  fixed  custom  actually  so  fixed. 

Before  considering  what  weight  should  be  given  to  these 
facts  in  estimating  the  value  of  distance  (for  which  see  par.  227) 
we  will  consider  the  conditions  which  exist  with  the  three  re- 
maining classes  of  traffic. 

206.  Competitive  traffic,  whether  confined  to  one  line  or  not; 
(classes  3,  4,  and  5,  above).  The  total  through  rates  on  all  com- 
petitive traffic  are,  in  nearly  all  cases,  arbitrarily  fixed,  with 
little  regard  to  the  mileage.  For  this  reason  it  may  appear,  and 
may  be  too  readily  taken  for  granted  by  engineers  not  familiar 

Table  90. 


Comparative  Magnitude  of  the  Separate  Classes  of  Through  and 
Local  Competitive  and  Non-Competitive  Passenger  Traffic  on  the 
Cleveland,  Columbus,  Cincinnati  &  Indianapolis  Railway. 

Average  of  9  years,  1 873-1881. 

[This  table  may  be  accepted,  in  a  rude  way,  as  not  far  from  the  general  average  of  the  whole 
American  Railway  System.] 


Class  of  Traffic  as  Subdivided  on  page  122. 

Per  Cent  of 
No.  of  Pas- 
sengers. 

Per  Cent 
of  Pass. 
Mileage. 

Per  Cent 
Contributed 
to  Revenue. 

A.  Non-Competitive ■ 

74" 
14. 

-88 

r 

1 

M 
-  \ 

48  ~ 

13. 

2.  Local  or  exchange  between 
local   points  in  different 
roads  

B.  Competitive - 

3.  Local  traffic  between  com- 
petitive termini  (only  par- 
tially in  this  case) 

.  4.  Competitive  through 

(Non-existent  in  pass,  service.) 

8^^ 

C.  Partially  Competitive. 

'3) 

100 

p.  c. 

100  p.  c. 

100  p.  c. 

2\6  CH,  VII.— DISTANCE— EFFECT  ON  COMPETITIVE  TRAFFIC. 


Table  91. 

Fluctuations  and  Distribution  of  the  Different  Classes  of  Freight 
Traffic;  Cleveland,  Columbus,  Cincinnati  &  Indianapolis  Railway, 

local  Freight. 


East-Bound.               I 

West-Bound. 

Total. 

Year. 

Tons. 

I  = 
1,000. 

Ton- 
Miles. 
I  = 

1,000,000. 

Rev. 

Si,ooo. 

Tons. 
1,000. 

Ton- 
Miles. 

1,000,000. 

Rev. 

Si,^o. 

Tons. 

Ton- 
Miles. 

Rev. 

1873... 

1875... 
1880.. . 

18S5... 

419 
401 

564 
451 

50.0 
43-3 
74.6 
43-3 

908.9 
686.7 

749-8 
469.7 

211 
253 
311 

355 

20.8 

27-7 

33-6 
41.0 

434-8 
465.0 
451.6 
406.3 

630 
654 
874 
806 

70.8 

71.0 

108.2 

84.3 

1344. 
II52. 
I20I. 

876. 

Through 

Freight. 

1873-.. 

870 

166.5 

1895. 

181 

37.1 

i 
496.8! 

1050 

203.5 

2392. 

1875... 

747 

145-5 

1093. 

209 

46.8 

402.8 

957 

192.3 

1495. 

1880... 

1189 

232.0 

1539- 

378 

80.3 

588.0' 

1567 

312.2 

2127. 

1S85... 

1 140 

226.9 

997- 

1 

569 

117. 4 

598.6 

1 

1708 

344-4 

1596. 

The  above  indicates  the  nature  and  extent  of  the  fluctuations  which  have  occurred 
during  the  thirteen  years  covered  by  the  table.  The  following  are  averages  for  the 
ten  years  1876-1885 : 


Percentages  of  Total  Tons  Carried. 

Percentages 

OF  Total  Ton-Miles. 

Through. 

Local. 

Total. 

Through. 

Local. 

Total. 

East-bound. .  . 
West-bound.  . . 

48.4 
17.7 

19.9 
14.0 

68.3 
31.7 

East-bound. .  . 
West-bound. . . 

Total 

56.5 
21.8 

12.5 
9.2 

69.0 
31.0 

Total 

66.1 

33-9 

100. 0 

78.3 

21.7 

100. 0 

Percentages  of  Total  Revenue. 

Average  Receipts  Per  Ton-Mile. 

Through. 

Local. 

Total. 

Through. 

Local. 

Total. 

East-bound. .  . 
West-bound.  . . 

44-5 
20.0 

20.3 
15-2 

64.8 
35-2 

100. 0 

East-bound. 
West-bound 

Total.... 

.556  Ct. 
.656    " 

1. 161  cts. 
1. 210   " 

.674  Ct. 

.818    " 

Total 

64.5 

35-5 

.591  Ct. 

1. 182  cts. 

.719  Ct. 

CH.   VII.— DISTANCE— EFFECT  ON  COMPETITIVE  TRAFFIC.  217 


Table  92. 

Average  Train-Load  of  Freight  and  Passengers  in  the  United  States, 
Groups  of  States,  and  on  Trunk  Lines. 

LComputed  from  the  Census  Statistics  of  1880.] 


L  New  England 

n.  Middle,  with  Md.,  Mich.,  Ind, 

IIL  Southern 

IV.  111.,  la.,  Wise,  Mo.,  Minn... 

V.  La.,  Ark.,  Ind.  T 

VI.  Tex.,  Kan.,  Dak.,  and  Far  W 

Total  United  States 

Trunk  Lines. 

Boston  &  Albany 

New  York  Central 

N.  Y.,  L.  Erie  &  W 

Pennsylvania 

Baltimore  &  Ohio 

N.  Y.,  Penna.  &  O 

N.  Y.,  N.  Haven  &  Hartf 


Passenger  Traffic. 


Av.  Train- 
Load. 
No. 


53-3 
44.2 
21.3 
37-1 
18.3 
48.0 


41-5 


72. 

65. 

55- 

52.4 

38. 

41. 

90. 


Av.  Haul. 

Miles. 


16.8 

go. 

17.4 

163. 

44.1 

55- 

41.9 

122. 

39-8 

61. 

44.8 

95. 

21, 


Freight  Traffic. 


Av.  Train- 
Load. 
Tons. 


129. 


IIO. 
218. 
211. 

233- 
185.5 
113- 
113  = 


Av.  Haul. 

Miles. 


55-7 
106. 1 
103.7 
153-3 

34-6 
166.9 


III 


with  operating  practices,  that,  for  this  class  of  traffic  at  least,  any- 
additional  distance  must  be  a  pure  disadvantage,  increasing  ex- 
pense, but  not  affecting  revenue.  And  this  is  literally  true  with 
respect  to  such  competitive  traffic  as  begins  and  ends  on  one 
line,  or  on  one  system  of  lines  with  interests  wholly  in  common. 
But,  in  spite  of  the  present  tendency  to  consolidation,  a  very 
large  proportion  of  such  traffic  on  all  lines,  and  practically  the 
whole  of  it  on  the  smaller  lines,  is  through  freight  proper,  which 
passes  over  parts  of  several  lines.  On  all  such  traffic  the  total 
rate  from  shipping  point  to  destination  is  indeed  arbitrarily 
fixed,  without  regard  to  mileage,  and  often  in  fact  in  inverse 
ratio  to  it;  but  of  the  division  of  this  total  rate  between  Jhe  par- 
ticipating companies,  which  is  what  practically  concerns  us,  this 
is  by  no  means  the  case. 


2l8  CH.   VII.— DISTANCE— EFFECT  ON  COMPETITIVE  TRAFFIC, 

207.  The  division  in  all  such  cases  is  by  a  percentage  which  is 
regulated  strictly  in  accordance  with  the  relative  distance  hauled, 
although  not  necessarily  in  direct  ratio  to  that  distance  ;  for 
there  are  frequently  "  Arbitraries"  of  various  kinds,  and  granted 
for  various  reasons,  as  for  terminal  expenses,  to  be  first  deducted 
before  the  final  division  or  percentage  is  distributed  according 
to  mileage. 

208.  So,  too,  it  is  not  uncommon  for  some  line  to  have  some 
strategic  advantage  of  another,  so  that  it  can  exact  from  it  cer- 
tain special  concessions,  in  excess  of  its  exact  mileage  propor- 
tion, such  as  allowances  for  "  constructive  mileage,"  etc.,  etc. 

The  Erie  Railway  formerly  bad  a  great  strategic  advantage  of  this  kind  over 
the  old  Atlantic  &  Great  Western  Railway  (New  York,  Pennsylvania  &  Ohio), 
the  nature  and  effect  of  which  we  shall  shortly  see  (par.  216). 

209.  Again,  when  shipments  are  for  extremely  long  dis- 
tances they  are  quite  frequently  subject  not  to  one,  but  to  the 
sum  of  two  competitive  rates,  and  the  total  is  divided  accord- 
ingly. All  freight  passing  through  Chicago  is  a  remarkable 
example  of  this.  It  is  not  common  to  make  rates  past  Chicago 
to  points  on  either  side  otherwise  than  by  adding  the  two 
Chicago  rates  (which  latter  is  very  common),  except  when,  as  to 
''Missouri  River  points,"  special  circumstances  make  it  abso- 
lutely unavoidable.  The  tendency  to  make  Chicago  a  terminal 
point  for  competition  and  start  afresh  from  there,  is  strong. 

There  are  some  apparent  partial  exceptions  to  this  rule,  but  they  are  hardly 
real  ones.  Thus  in  1886,  after  considerable  controversy  and  irregularity, 
rates  from  New  York  to  "  Mississippi  River  points,"  including  a  large  number 
of  points  north  of  St.  Louis,  were  by  agreement  adjusted  at  the  fixed  rate  of  116 
for  100  to  Chicago.  This  was  then  divided  between  the  lines  east  and  west 
of  Chicago  (there  being  half  a  dozen  or  more  lines  interested  on  each  side),  by 
assuming  the  distance  for  all  lines  to  be  220  miles  west  of  Chicago  and  970 
miles  east,  these  being  about  the  average  of  the  actual  distances,  which  of 
course  varied  with  each  road.  The  total  rate  was  then  divided  in  exact  propor- 
tion (as  nearly  as  might  be)  to  these  distances,  viz.,  18^  per  cent  west  and  81-^ 
per  cent  east  of  Chicago.  Exactly  these  divisions  would  have  been  18.487  and 
81.513,  so  that  the  rate  on  0.15  mile  of  haul  west  of  Chicago  was  given  away  to 
the  lines  east  to  obtain  a  round-numbered  percentage. 


CH,   VIL— DISTANCE— EFFECT  ON  COMPETITIVE  TRAFFIC  219 

In  this  exceptional  instance  the  general  rule  that  through  competitive  rates 
are  regardless  of  distance  is  extended  likewise  to  a  first  division  of  those  rates 
into  two  parts.  What  the  arrangement  really  means,  however,  is  that,  although 
a  common  aggregate  rate  to  the  Mississippi  River  points  was  desirable  in  the 
interest  of  peace  and  good-will,  yet  the  distance  was  so  great  and  the  conflict- 
ing interests  so  multifarious  that  it  was  more  convenient  to  regard  this  rate  as 
made  up  of  two  separate  and  distinct  through  rates,  than  to  regard  it  as  a  single 
through  rate  to  be  divided  in  the  usual  manner. 

Compacts  of  this  kind  may  increase,  but  at  present  they  are  too  exceptional 
to  merit  more  than  passing  notice. 

As  one  example  of  "  arbitrary"  allowances,  a  large  part  of  the  business  from 
and  to  local  points  near  large  cities  really  comes  under  the  head  of  through 
traffic  ;  the  through  rates  from  the  West  to  points  within  a  hundred  miles  more 
or  less,  of  New  York,  for  instance,  being  usually  made  the  same  as  to  New 
York,  and  divided  as  if  the  freight  or  passengers  were  actually  taken  to  and 
delivered  there. 

In  such  case  the  division  is  not  exactly  as  the  mileage,  but  it  is  the  same  in 
its  effect  upon  the  receipts  of  the  connecting  lines  as  if  it  were. 

210.  Certain  considerable  allowances  for  terminal  charges  at 
points  where  such  charges  are  heavy  are  very  commonly  and 
very  justly  deducted  from  the  through  rate  before  the  latter  is 
distributed,  as  notably  at  New  York,  where  the  terminal  allow- 
ances are  very  heavy  (4  to  5  cents  per  100  lbs.),  although  hardly 
enough  to  cover  the  direct  and  indirect  expense  to  the  terminal 
road. 

In  fact  the  variations  and  exceptions  in  the  fixing  and  division 
of  rates  are  endless,  but  through  them  all  the  general  law  holds 
good  that  all  "  through"  rates  between  connecting  lines  are 
divided  precisely  according  to  the  actual  mileage,  and  to  a  very 
large  extent  directly  as  the  mileage. 

211.  These  facts  result  in  a  curious  and  apparently  contradic- 
tory law,  as  respects  the  through  traffic  of  a  new  or  old  road, 
which  it  may  be  highly  important  that  the  engineer  should 
understand.     That  law  may  be  thus  expressed  : 

1.  It  is  extremely  desirable  that  any  new  line  should 

FORM    A    PART     OF    THE    SHORTEST    ROUTES     BETWEEN     IMPORTANT 
CENTRES  OF  TRAFFIC. 

2.  It  IS  NOT  DESIRABLE,  AND  OFTEN  THE  REVERSE  OF  DESIRABLE, 


220  CH.   VII.— DISTANCE— EFFECT  ON  COMPETITIVE  TRAFFIC, 

THAT  IT  SHOULD  MAKE  ANY  EFFORT  TO  BRING  ABOUT  THIS    RESULT, 
EXCEPT  IN  SELECTING  ITS  CONNECTIONS. 

The  reason  for  each  half  of  this  law  is  not  difficult  to  see. 

212.  As  respects  the  first  part  of  it : 

The  through  rate  being  altogether  independent  of  distance, 
the  receipts  per  ton-mile  or  per  passenger-mile  on  competitive 
traffic  will  be  the  greater  the  shorter  the  line  is — a  consideration 
plainly  of  immense  importance. 

We  may  see  a  striking  proof  of  this  by  comparing  the  New 
York  Central,  Erie,  and  Pennsylvania  lines.  The  operating  ex- 
penses of  the  Central  and  Erie,  as  shown  in  Tables  37  and  76, 
average  continually  a  much  heavier  percentage  of  their  receipts 
than  on  the  Pennsylvania,  yet  they  are  operated  with  substantially 
equal  efficiency — at  least  there  is  far  less  difference  than  super- 
ficial observers  often  conclude  from  this  very  fact.  The  true 
cause  of  it  (with  which  other  causes  may  co-operate,  but  only  to  a 
minor  extent)  is  simply  this  :  that  the  Pennsylvania  has  the  short- 
est line  from  almost  every  point  in  the  West  to  New  York  and 
Philadelphia,  and  hence  its  receipts  per  mile — from  the  same 
through  rates — are  unavoidably  materially  larger  than  the  Cen- 
tral's or  Erie's.  This  fact,  however,  does  not  show  so  much  as 
it  otherwise  would  in  the  average  receipts  per  ton-mile  of  these 
roads,  as  published,  simply  because  the  Central  and  in  less 
degree  the  Erie  have  an  immense  local  business,  which  both  pays 
more  and  costs  more,  thus  bringing  up  the  average  receipts  ;  but 
the  through  business  proper  leaves,  and  must  continue  to  leave, 
a  very  small  margin  per  mile  to  both  lines  compared  with  what 
the  Pennsylvania  obtains.  No  ingenuity  or  skill  will  ever  be 
able  to  materially  decrease  the  large  percentage  of  advantage 
for  through  business  which  its  geographical  position  gives  to  the 
latter  road  ;  because  the  total  through  rate  will  always  be  the 
same  by  all  competing  lines,  and  the  long  lines  must  conse- 
quently forever  suffer  in  receipts  per  mile,  unless  causes  not 
now  possible  to  foresee  shall  change  the  conditions. 

213.  But  notwithstanding  this  fact,  we  have  in  these  same 
roads  a  striking  illustration   of  the   truth  of  the  second  half  of 


CH.   VII,— DISTANCE— EFFECT  ON  COMPETITIVE  TRAFFIC.  221 

our  contradictory  law.     Neither  the  New  York  Central  nor  the 

Erie  have  any  interest  whatever  in  shortening  their  own  lines  (if 

we   consider   the  interests   of   both  as   terminating  at   Buffalo), 

notwithstanding   that   they  suffer  so  much   from   the   fact  that 

they  are  links  in  a  long  route.      Thus  the  Erie  now  constitutes 

423-963    of    its    New    York-Chicago    connection    via  the    Lake 

Shore  &  Michigan  Southern  Railway,  and  receives  on  a  15-ton 

car-load  at  a  30-cent  rate  $39.55  out  of  $90,  assuming  the  through 

rate  to  be  divided  according  to  distance  only,  without  arbitrary 

or  terminal  allowances.     If  its   length  were   10  miles  shorter  it 

1     423  —  10         413      .    „  „  ,  ^ 

would  receive  onlv  -^ or of  Sqo,  or  S39.00 — a  loss  of 

^   963-10        953         ^^  "^^^ 

$0.55  per  car-load,  which  is  about  three  times  what  would  be  the 

actual  extra  cost  of  hauling  the  car  over  that  extra  distance. 

214.   On  the   other  hand,  if  some  of  its  Western  connections 

were  to  shorten    their  line  ten  miles  the   Erie  would  be  greatly 

benefited;  for  then,  for  the  very  same   service,  it  would    receive 

from  the  Lake  Shore  &  Michigan  Southern  Railway,  for  example, 

42  X  A.2.  'X 

instead  of  -— -  of  $90,  or  $39.95  instead  of  $39.55 — an  increase 

of  40  cents,  or  about  i  per  cent, /^r  nothing. 

Spending  money  to  shorten  one's  own  line  for  through  busi- 
ness, therefore,  must,  except  under  peculiar  circumstances,  be 
classed  among  those  charitable  actions  for  which  a  reward  may 
possibly  be  hoped  for  in  the  next  world,  but  hardly  in  this.  The 
only  important  exceptions  are  : 

First,  When  a  road  reaches  all  important  points  over  its 
own  lines,  as  the  Pennsylvania  ;  or. 

Secondly,  When  it  is  built  for  other  reasons  than  direct 
profit  to  the  investors,  as  the  Cincinnati  Southern  Railway,  or 
lines  built  by  the  State. 

Even  these  exceptions  are  in  all  cases  only  partial.  There  is 
always  some  credit  side  to  the  disadvantage  of  distance,  whereas 
there  is  never  any  credit  side  to  bad  gradients  or  curvature. 
Bad  curvature  and  gradients  may  indirectly  have  a  credit  side 
to  them,  from  being  necessary  to  reach  certain  traffic  points,  but 


222  CH.  VII.— DISTANCE— EFFECT  ON  COMPETITIVE  TRAFFIC, 

in  themselves  they  are  wholly  harmful,  whereas   extra  distance 
is  not. 

215.  A  notable  example  of  these  antithetic  effects  of  distance, 
and  of  the  danger  of  disregarding  them,  may  be  found,  among 
many  others,  in  the  old  Atlantic  &  Great  Western  (now  New 
York,  Pennsylvania  &  Ohio)  Railroad.  It  enjoys  the  unique  dis- 
tinction of  being  now,  as  it  was  when  first  built,  the  longest  line 
in  existence  even  between  its  three  termini — New  York  in  the 
East,  Cincinnati  and  Cleveland  in  the  West.  It  has  always  two^ 
and  generally  three  or  four,  more  favored  rivals  between  each 
considerable  point  in  the  East  and  every  considerable  point  in 
the  West.  Yet  even  in  this  extreme  case,  if  its  own  line  had 
been  ten  miles  longer  between  Cleveland  and  Cincinnati  and 
New  York  it  would  have  been  better  off.      It  would  then  have 

received  ^^  or  46  per  cent  (see  par.  220)  instead  of  -— —  or  45 

2  2'? 

per  cent  on  all  Cincinnati  and  New  York  business,  and  - —  or 

637 

2  I  "2 

35  per  cent  instead  of  -- —  or  34  per  cent  on  all  Cleveland-New 

York  business,  assuming  in  both  cases  that  receipts  were  divided 
strictly  according  to  distance. 

216.  As  it  happens,  this  is,  or  was  until  within  a  few  years  (the 
old  Atlantic  &  Great  Western  is  now  leased  to  the  Erie),  one  of 
the  cases  in  which  the  division  was  not  strictly  as  the  distance  ; 
the  Erie  Railway  having  formerly  insisted  on  being  allowed  a 
CONSTRUCTIVE  MILEAGE  of  46  milcs  from  the  junction  point  at 
Salamanca  to  its  terminus  and  junction  with  the  Lake  Shore  & 
Michigan  Southern  Railway  at  Dunkirk  :  an  unjust  exaction, 
which  it  had  power  to  enforce  because  it  was  the  only  eastern 
connection  of  the  Atlantic  &  Great  Western.  Whereas,  there- 
fore, a  division  exactly  according  to  distance  would  have  given 

the  Erie   on    Cleveland-New  York  business  - —  or  66  per  cent, 

627  ^ 

21'? 

and  the  Atlantic  &  Great  Western  --^  or  34  per  cent,  the  actual 

027 


CH.   VII.— DISTANCE— EFFECT  ON  COMPETITIVE  TRAFFIC.  223 

,.    •   •  414+46  460  ,^^  ^  _ 

division  was ■ -,  or  - —  (68  per  cent)  to  the  Erie  and  only 

627  +  40         673  ^       ^  ^ 

'21"? 

— --  (32  per  cent)  to  the  Atlantic  &  Great  Western.  Neverthe- 
less, in  this  as  in  all  other  cases  divisions  were  ultimately  based 
upon,  although  not  in  strict  accordance  with,  the  precise  relative 
hauls, 

217.  From  this  example  the  over-hasty  conclusion  should  not 
by  any  means  be  drawn,  that  a  road  should  lengthen  its  line  of 
set  purpose,  for  this  end  alone,  for  that  would  probably  lead  to 
acts  of  folly  ;  but  it  does  clearly  follow  that  whenever  a  better 
line  in  all  other  respects  can  be  thus  obtained  it  will  ordinarily 
be  folly  not  to  take  it.  As  it  happens,  such  lines  did  exist  at 
several  points  along  the  Atlantic  &  Great  Western,  affording 
better  grades,  more  traffic,  and  cheaper  work,  at  the  cost  of  some 
distance;  but  unfortunately  the  original  projectors  sinned  against 
both  of  the  cardi-nal  principles  laid  down  in  par.  211  :  they  ne- 
glected the  vital  end  of  securing  short  and  favorable  connections, 
but  exerted  themselves  to  shorten  their  own  road  by  striking  an 
air-line  wherever  possible,  at  almost  any  sacrifice  of  gradients  ; 
running  it,  in  literal  truth,  "over  the  hills  and  far  away"  from 
traffic.  The  consequences  of  such  engineering  may  be  read  in 
the  financial  history  of  the  road — a  history  which  might  have 
been  anticipated  with  certainty  in  the  beginning,  and  may  be 
counted  on  w4th  certainty  to  continue  to  the  end.  It  has  now 
found  its  greatest  and  only  real  use  as  a  feeder  and  competing 
weapon  in  the  hands  of  the  Erie,  but  considered  as  a  separate 
property,  apart  from  one  or  two  profitable  leases  which  have 
alone  kept  it  in  as  good  a  position  as  it  has  had  (see  Chap.  XXI.), 
it  can  never  by  possibility  more  than  barely  pay  operating  ex- 
penses for  any  period  of  years  ;  for,  however  great  may  be  the 
growth  of  traffic,  and  however  great  the  future  improvements 
tending  to  reduce  expenses,  other  lines  also  share  these  advan- 
tages, and  through  rates  will  continue  to  fall  in  proportion,  down 
to  the  lowest  point  which  affords  the  most  favored  line  2i  handsome 
but  not  exorbitant  profit,  and  way  rates  likewise  will  continue  to 


224  CH.  VII.— DISTANCE— EFFECT  ON  COMPETITIVE  TRAFFIC. 

fall  in  proportion  down  to  a  reasonable  but  not  excessive  per- 
centage (usually  from  50  to  75  per  cent)  in  excess  of  the  through 
competitive  rates. 

218.  In  a  certain  important  sense,  indeed,  we  may  say  that  all 
rates  are  fixed  by  competition,  for  the  fact  that  non-competitive 
way  rates  do  adjust  themselves  quite  closely  to  the  through  rates 
is  well  determined.     In  illustration  of  this  fact,  which  has  been 


Table  93. 

Statistics  of   Passenger  Traffic,  Cleveland,  Columbus,  Cincinnati  & 
Indianapolis  Railway,  1873-1885. 


Local  Pass. 

Through  Pass. 

Per  Cent 

Year. 

Av.  Haul. 
Miles. 

Rects. 

Per  Mile. 

Cts. 

Av.  Haul. 
Miles. 

Rects. 

Per  Mile. 

Cts. 

Through  of 
Local  Rate. 

1873 

74 

2g.8 

27.8 

3-47 
2.83 

198 

185 

2.53 
2.55 

73-0 
90.0 

1875 

27.1 

2.63 

188 

2.38 

90-5 

1876 

77 

78 

79 

28.3 
27.9 
27-3 
28.6 

2.48 
2.41 
2.42 
2.46 

192 

183 
182 
186 

1.89 
2.24 
2.10 

1.82 

76.2 
93-0 
86.8 
73-9 

1880 

29-5 

2.39 

193 

1.82 

76.1 

1881 

82 

83 

84 

27.6 
28.7 
30.5 
29-5 

2.51 
2.60 

2.51 
2.47 

1S4 
115 
121 
118 

1.77 
1.78 
I. 81 
1.73 

70.5 
68.6 
72.0 
70.0 

1885 

28.9 

2.57 

121 

1. 61 

62.6 

Decrease  per  cent  in  through  rate  in  12  years,  36.4  per  cent. 
"  "         "  local  "  "       "     25.9        " 

Summary  of  Average  Decrease  from  Average  of  1873-5  to  Average  of  1S78-81. 


Through  Freight.. 


A  decrease  of 

Or,  in  percentage . 


3  y'rs,  1873-75,    -979  ct. 
3  y'rs,  1879-81,    .593  " 

386  ct. 

393^  P-  c. 


(3  y'rs,  1873-75,  2.487  cts. 
Through  Passenger]^  y,^g^  ^^^^_^^^  ^  g^^  u 

A  decrease  of 0.686  ct. 

Or,  in  percentage 27^^  p.  c. 


Local  Freight . 


I  3  y'rs,  1873-75,  1-766  cts. 
I  3  y'rs,  1879-81,  1.157  " 

A  decrease  of 609  ct. 

Or,  in  percentage  34^^  p.  c. 


Local  Passenger . 


3  y'rs,  1873-75,  2.978  cts. 
3  y'rs,  1879-81,  2.455  " 


A  decrease  of 523  ct. 

Or,  in  percentage 13.3  p.  c. 


CH.   VII.— DISTANCE— EFFECT  ON  COMPETITIVE  TRAFFIC  22$ 


Table  94. 

Statistics  of  Freight  Traffic,  Cleveland,  Columbus,  Cincinnati 
Indianapolis  Railway,  1873-1885. 
Through  Freight. 


East-Bound. 

West-Bound. 

Per 

Cent 
West- 
Bound. 

Per 

Cent 
Through. 

Average 
Receipts 

Per 
Ton-Mile. 

cts. 

Year. 

Average 
Haul. 

Miles. 

Receipts 

Per"^ 
Ton-Mile. 

cts. 

Average 
Haul. 
Miles. 

P.eceipts 

Per 

Ton-Mile. 

cts. 

iSvq 

191 
215 

1. 14 
.92 

205 
214 

I.  'XA 

23^3 
26.2 

62.5 
59-2 

i^i75 
.984 

74 

I 

24 

i87q 

195 

•75 

223 

86 

28.7 

59-4 

-778 

76 

215 
202 
208 
203 

.64 

.67 
•57    • 
•52 

231 
223 
221 
217 

68 
88 
84 
73 

26.8 
26.2 
22.7 
26.2 

64^7 
64.8 
67.4 
67.6 

.650 
.716 
.613 
.565 

77 

78 

7q 

1880 

195 

.66 

212       1 

73 

28.2 

64.2 

.6S1 

81 

193 
184 
185 
202 

.50 

•59 
.62 

•50 

211 
200 
202 
206 

60 
61 

71 
59 

35-2 
35-4 
35.6 

37^4 

64.9 
68.9 
65.1 
64.9 

•532 
•591 
.652 

•525 

82 

83 

84. 

188=; 

199 

•44 

207 

51 

36.7 

68.0 

.463 

local  Freight. 


East-Bound. 

West-Bound. 

Average 
Receipts 

Per 
Ton-Mile. 

cts. 

Per  Cent  Through 
OF  Local  Rate. 

Year. 

Average 
Haul. 
Miles. 

Receipts 

Per 
Ton-Mile. 

cts. 

Average 
Haul. 
Miles. 

Receipts 

Per 
Ton-Mile. 

cts. 

East- 
Bound 
only. 

Total. 

iS?-?   

119 
120 

1.82 
1.65 

98 
93 

2.09 
2.08 

1.899 
1.776 

62    "7 

61. 9 

55^4 

74. 

187=; 

108 

1.58 

109 

1.68 

1.622 

47 

5 

48.0 

76 

106 
108 
116 

115 

1.42 
1.48 
1^15 
1^15 

107 
102 

98 

TOO 

1.44 
1.64 
1. 61 
1^34 

1.429 
1.538 
1.303 
1. 215 

•• 

; 

45-5 
46.6 
47.0 
46.5 

77 

78    . .  .       . 

7Q 

1880 

132 

I.  GO 

108 

1-34 

I. IIO 

66 

0 

61.3 

81 

105 
97 

lOI 

95 

I.  10 
I. 17 
I.  12 
I.  14 

112 
IIO 
117 
120 

1.20 

1. 18 

1-03 

.91 

1. 146 
1. 176 
1.079 
1. 018 

;; 

• 

46.4 
50.3 
60.3 
51.6 

82 

83    

84 

1885       , 

96 

1.08 

116 

•99 

1.039 

40 

s 

44^5 

Per  Cent  of  Decrease,  187 3- 1885. 

East-bound.  West-bound.  Av'e. 
Through  rates. .  61.4  62.0  60.7 
Local  rates  ... .  40.7         52.7         45^3 

15 


Per  Cent  of  Decrease,  1S75-1885. 

East-bound.  West-bound.  Av'e. 
Through  rates  .  41.3  40.7  39.5 
Local  rates  ... .   31.6         41.0         35-9 


226  CH.  VII.— DISTANCE— EFFECT  ON  COMPETITIVE  TRAFFIC. 


Table  95. 

Comparative  Through  and  Way  Rates,  Lake  Shore  &  Michigan  Southern 

Railway. 

(Cents  per  ton-mile.) 


Year. 

East-Bound. 

West-Bound. 

Total 

Through. 

Way. 

Through. 

Way. 

1868 

1869 

1870 

1871 

1872 

1.56 
1.49 
I.I3 
1. 17 
I-I3 

3.49 
3.68 
2.67 
2.35 
2.04 

2.02 

1.78 

1-53 
1. 18 
1.49 

4.07 
4-05 
2.84 
2.26 
2.01 

2.43 
2.34 
1.50 
1.39 
1-37 

Comparative  Rates,  taking  Rates  of  1868  as  i.oo. 


1868. 
1869. 
1870. 
1871. 
1872. 


.954 
•723 
•  750 
•723 


I-055 
.755 
.673 
.685 


882 
^758 
^585 
.738 


996 
698 
556 
494 


1.00 
.962 
.617 

.572 
•563 


Since  1872  the  rates  have  not  been  made  public  in  this  form,  for  through  and  way 
separately. 

It  will  be  seen  that  the  non-competitive  way  rates  fall  in  close  sympathy  with  the 
competitive  rates,  and  vary  more  directly  with  each  other  than  the  East-bound  and  West- 
bound. 


already  alluded  to  (par.  54),  a  comparison  of  the  course  of 
through  and  local  rates  on  the  Cleveland,  Columbus,  Cincinnati 
&  Indianapolis  Railway  is  given  in  Tables  93  and  94,  and  on 
the  Lake  Shore  &  Michigan  Southern  Railway  in  Table  95,  which 
illustrate  the  fact  very  strikingly.  Few  roads  publish  reports 
from  which  such  statistics  can  be  obtained,  but  the  law  holds 
substantially  true  everywhere. 

219.  From  these  examples  it  takes  no  great  intelligence  to 
perceive  how  inexorable  is  the  law  that  the  line  which  places 
itself  originally  at  any  serious  disadvantage  has  no  escape  from 
the  consequences  of  its  folly  but  to  remedy  those  disadvantages. 


CH.  VII.— DISTANCE— EFFECT  ON  COMPETITIVE  TRAFFIC.  22/ 

Apparent  advantages  from  the  general  progress  in  wealth  and 
population  and  science  do  not  help  it  at  all,  since  all  lines  share 
alike  in  them.  They  simply  enable  it  to  hold  its  own,  and  ''  its 
own"  is  nothing  but  bare  existence.  We  have  in  many  such 
lines,  as  particularly  in  the  line  last  referred  to,  a  striking  evi- 
dence of  how  completely  an  enormous  investment  may  be  thrown 
away  solely  and  only  from  bad  engineering  advice. 

220.  It  may  be  added,  that  the  through  rate  is  nearly  always 
divided  by  some  even  percentage,  and  consequently  trifling  dif- 
ferences are  not  likely  to  affect  the  division  either  way.     Thus  a 

397  403 

line  entitled  by  its  exact  mileage  to  receive  either or 

-^  ^  T.ooo        1000 

would  probably  receive  40  per  cent.  If  its  length  entitled  it  to 
— —  it  would  probably  receive  41  per  cent.     The  fractional  per- 

TOOO 

centages  are  sometimes  insisted  on  by  the  line  which  happens 
to  hold  the  stronger  position,  but  usually  any  advantage  of  that 
kind  takes  the  form  of  some  terminal  or  arbitrary  allowance 
instead  of  a  modification  of  the  percentage. 

221.  Since  the  receipts  of  any  one  road  from  competitive  ex- 
change traffic  vary  (i)  with  the  total  haul  on  each  unit  of  traffic, 
and  (2)  with  the  proportion  thereof  on  the  home  and  foreign 
roads,  the  effect  of  any  given  change  in  the  length  of  the  home 
road  will  be  different  on  traffic  between  all  possible  traffic  points. 
All  that  can  be  done,  therefore  (or  all  that  is  in  the  least  neces- 
sary to  do),  is  to  form  some  rude  idea  of  the  centre  of  gravity 
of  the  initial  and  terminal  points  of  shipment  at  each  end  of  the 
line,  which  will  often  be  quite  different  for  different  parts  of  the 
line. 

Precision  in  such  estimates  is  unimportant,  because  the  future  is  almost  cer- 
tain to  bring  about  great  changes,  and  perhaps  very  speedily.  But  when  two  al- 
ternate lines  are  under  comparison  in  other  respects,  the  approximate  effect  of 
their  differences  in  this  respect  also  should  be  determined,  with  a  view  of  seeing 
whether  they  strengthen  or  weaken,  or  utterly  nullify,  the  conclusions  that  would 
be  otherwise  reached.  That  they  do  the  latter,  so  as  to  in  themselves  alone 
cause  the  selection  of  one  route  instead  of  another,  should  be  admitted  only 
with  the  utmost  caution. 


228  CH.VII.— DISTANCE— EFFECT  ON  COMPETITIVE  TRAFFIC, 

ITln  The  effect  on  the  receipts  of  the  home  road  from 
through  competitive  traffic  of  an  increase  in  its  own  length  only, 
the  haul  on  its  connections  remaining  unchanged,  may  be  stated^ 
with  adequate  exactness,  in  this  very  simple  way: 

The  interpolation  of  additional  distance  by  the  adoption  of  a 
longer  alternate  line  between  the  same  termini  will,  for  all  ordi- 
nary and  moderate  changes  of  length  (under  20  or  25  per  cent 
of  home  haul),  leave  the  earnings  per  mile  of  the  original 
(shorter)  line  unchanged,  and  enable  the  home  road  to  earn  on 
its  extra  mileage  as  large  a  percentage  of  the  average  per  mile  on  the 
shorter  line  as  the  percentage  of  the  foreign  haul  to  the  total  haul. 
This  law  holds  essentially  true,  regardless  of  the  amount  of  the 
added  mileage. 

For  example,  on  traffic  which  has  70  per  cent  foreign  haul, 
if  the  home  road  were  longer  it  would  receive  out  of  its  added 
proportion  of  through  competitive  freight  enough  to  earn  70  per 
cent  as  much  per  mile  on  the  added  mileage  as  on  the  original 
mileage,  the  earnings  on  the  latter  remaining  unchanged. 

223.  To  put  the  rule  in  another  and  shorter  way:  With 
through  competitive  traffic — 

The  per  cent  of  home  haul  in  the  total  haul  -f-  the  \  =:  100  p.  c. 
per  cent  of  average  earnings  per  mile  realized  l  (always  a  lit- 

by  home  road  by  extra  mileage )      tie  less). 

The  maximum  and  minimum  "limits"  to  this  rule  are: 
I.   When  the  home  road  has   100  per  cent  of  the  haul  it  rea- 
lizes o  per  cent,  or  nothing,  on  any  extra  haul. 

3.  When  the  home  road  has  originally  o  per  cent  of  the  haul 
the  gain  to  its  receipts  from  any  haul  it  may  gain  is  100  per  cent 
of  the  average  rate  per  mile. 

224.  A  simple  geometric  demonstration  of  this  law  is  given 
in  Figs.  7  to  12,  with  their  accompanying  explanation.  The  law 
is  only  approximate,  and  for  very  great  changes  of  length  be- 
comes materially  in  error;  but  the  largest  probable  differences 
which  can  come  under  the  consideration  of  the  engineer  are 
from   10  to  25  per  cent  in  the  home  haul,  and  for  such  differ- 


CH.  VII.— DISTANCE— EFFECT  ON  COMPETITIVE  TRAFFIC.  229 

ences  the  law  is  sufficiently  exact,  as  is  evident  in  Table  96, 
which  gives  the  exact  effect  on  receipts  of  modifications  of  10 
and  20  per  cent  in  the  home  haul. 


Table  96, 

Effect  of  Changes  of  Distance  on  Earnings  from  Through  (Exchange) 

Competitive  Traffic. 

Giving  the  exact  effect,  and  illustrating  the  essential  truth  of  and  amount  of  error  in  the 
approximate  rule  in  paragraph  223. 


Effect 

of  \o  per  cent  Increase  of  Distance. 

Per  Cent  of 

Corresponding 

, 

Per  Cent  of 

Sum  of 

Oriofinal 

Receipts  of 

If  the  Home  Road 

extra.  Receipts 

Percentages 

Total  Haul 

Home  Road 

were  Ten  Per  Cent  longer  its 

on 

in  First 

on  the 

out  of  $1.00 

Receipts  would  be— 

extra  Haul 

and  Last 

Home  Road. 

Rate. 

to  Average. 

Columns. 

ID 

10  cts. 

TOT  X  $1.00=     10.891 

8q.i 

99.1 

20 

20    " 

T^^^X     1.00=     21.57 

78.5 

98.5 

30 

30   " 

^  X    1. 00  =    32.04 

68.0 

98.0 

40 

40    '• 

tVi  X    i.oo  =    42.31 

57.8 

97.8 

50 

50    " 

A%x  1.00=   52.38 

47.6 

97.6 

60 

60    " 

3:^6  X      1.00=     62.26 

37-7 

97-7 

70 

70   " 

TT) V  X      1.00=      71.96 

28.0 

98.0 

80 

80    " 

3^8_  X    1. 00  =    81.48 

18.5 

98.5 

90 

90    - 

yVa  X      1.00  —     90.S3 

9.0 

99.0 

IOC 

100    " 

xtB^  X    1. 00  =  100.00 

None. 

lOO.O 

Effect 

of  20  per  cent  Increase  of  Distance. 

10 

10  cts. 

t1j%X$i.oo=     11.765 

88.2 

98.2 

20 

20  " 

T^^X    1.00=    2307 

76.8 

q6 

8 

30 

30  " 

3^\X    roo=    3396 

66.0 

96 

0 

40 

40  " 

y^^  X    1.00  =    44.44 

55.5 

QS 

50 

50  " 

■^  X  1.00  ==  54.545 

45-5 

95 

60 

60  " 

3%  X    1.00  =    64.284 

35.7 

95 

70 

70 " 

■^  X    1.00  =    73.68 

26.3 

96 

80 

80  " 

•3^\X      1.00=      82.80 

17-5 

97 

90 

90  - 

1^  X    1.00  =    91.53 

8.5 

q8 

100 

100  " 

||§  X    1.00  =  100.00 

None. 

100 

0 

230  CH.  VII.— DISTANCE— EFFECT  ON  COMPETITIVE   TRAFFIC^ 


Figs.  7  to  12,  Diagrams  illustrating  the  Effect  on  Receipts  from  Com- 
petitive Through  Traffic  of  a  Longer  Home  Line  between  the  same 
Termini. 

4     £ 


4^ 


Fig.  7.  Fig.  8.  Fig.  9. 

lOn  these  diagrams  the  mterpolated  mileage  on  the  home  road  (/)  is  assumed  to  be  ONE 


Figs.  7-10    One  quarter  of 
total  haul  on  home  road. 


EIGHTH  of  the  total  haul.'] 

Figs.  8-it.  One  half  of  to- 
tal haul  on  home  road. 


Figs.  9-12.  Three  quarters  of 
total  haul  on  home  road. 


s 


Fig.  10. 


Fig.  II. 


Fig.  12. 


[On  these  diagrams  the  interpolated  jnileage  on  the  home  road  ( f)  is  assumed  to  be  ONE' 
quarter  of  the  total  haul.] 

Expla7iatzon  of  diagrams,  ajid  demoiistratioii,  front  Figs.  J  to  12,  of  laiir 

stated  ill  par.  12.2. 

225.  In  each  diagram  let  the  base  DC=  the  total  haul  on  any  given  unit  of 
through  competitive  traffic,  in  part  over  the  home  road,  H,  and  in  part  over  one 
or  more  foreign  roads,  F. 

And  let  the  altitude  AD—  BC=  the  average  receipt  per  mile  on  this  unit 
of  traffic. 

Then  will  the  area  ABCD  =  the  total  through  rate  per  unit  of  traffic  (less 
any  terminal  or  other  constant  deduction),  and  the  areas  ZT  and  F  =  the  frac- 
tions thereof  appertaining  to  the  home  and  foreign  roads,  respectively. 

Assume  the  total  haul  increased  to  D'C  by  the  addition  of  the  distance  DD' 
to  the  home  road.  Then,  since  the  total  through  rate  remains  the  same,  we 
shall  obtain  a  new  average  rate  per  mile,  A'D',  of  such  amount  that  the  area  of 
the  new  rectangle  A' B' CD'  =  area  of  original  rectangle  ABCD. 


CH.  VII.— DISTANCE— EFFECT  ON  COMPETITIVE   TRAFFIC.  23 1 


Furthermore: 

Rectangle  AB'  =  gross  amount  lost  by  both  roads  jointly  on  original  haul 
by  decrea'^e  in  through  rate  per  mile  =  rectangle  A'D  =  gross  amount  gat  7zed  by 
home  road exchisively  from  earnings  at  decreased  average  rate  on  its  extra  mileage. 

But  if  we  assume  the  earnings  of  the  home  road  on  its  original  mileage  to 
be  unaffected  by  the  addition  thereto,  then  will  the  rectangles  EB'  =  the  gross 
amount  lost  by  the  foreign  road  through  the  longer  haul  at  the  same  through 
rate,  and  this  area  only  will  represent  the  extra  receipts  of  the  home  road  on  its 
extra  mileage,  which  let  —  rectangle  A" D. 

Then  we  have,  geometrically, 

A"D  _  EB, 
A'D  ~  AB' 


I.e., 


Net  rate  per  mile   realized 


on    home    road    on    added    j 


f  average 
through 


f  original 

haul  (rate  realized  by  home    \\%  \.o\  rate  per  mile  )-as^  ^^    .  ^'^ 
road    on    original    mileage    |  j  on   new  and  |         '    oreign 

being  supposed  unchanged)  j  (^longer    haul  J 

If  2  = 


haul  on 
[road 


forigi- 
J  nal 
)  total 
I  haul. 


For  example:  If  25,  50,  or  75  per  cent  of  the  original  haul  (before  the  home 
line  was  lengthened)  was  on  the  foreign  road,  the  home  road  will  realize  (within 
a  trifling  error,  shown  in  Table  96)  25,  50,  or  75  per  cent  of  the  new  average 
through  rate  per  mile  on  any  added  mileage,  without  suffering  any  such  reduc- 
tion as  its  connections  have  to  suffer  on  its  original  mileage. 

In  practice,  the  changes  of  length  which  the  engineer  is  called  upon  to  con- 
sider will  ordinarily  be  so  small  that  the  through  rate  per  mile  of  competitive 
freight  will  be  but  little  affected,  so  that  we  may  say  in  Figs.  7  to  12  that  practi- 
cally A' D'  =  AD,  whence  we  have  the  approximate  law  of  par.  222. 


Table  97. 

Proportion  of  Through  and  Local  Freight  in  each  Census  Group  of 

THE  United  States. 

[Computed  from  Census  of  1880.]    (Earnings.) 


Census  Group. 

Through 
Freight. 

Local 
Freight. 

Total. 

I.   New  England 

II.   Middle  to  Indiana 

III.  Southern 

IV.  N.  W.  Central 

V.   Louisiana  and  Ark 

VI.  Far  West 

69.7 
60.5 
58.4 
43-8 
51-5 
39-5 

30.3 
39-5 
41.6 
56.2 
48.5 
61.5 

M     H     H     H     H     H 

888888 

Total  United  States. 

56. 

44- 

100. 

For  more  accurate  desig-nation  of  groups  see  Table  92  and  others.     Not  all  the  freight 
here  classed  as  ' '  through  "  is  competitive  traffic,  by  any  means. 


232  CH.  VII.— DISTANCE— EFFECT  ON  COMPETITIVE   TRAFFIC. 


ABLE  98. 


Freight  Movement,  Through  and   Local,  East  and  West,  on  Pennsyl- 
vania Railroad  (P.  R.  R.  Div.  only)  for  Thirty-five  Years. 

(Paying  freight  only.     Statistics  exist  no  farther  back.) 


Tons  Carried. 

ToN-MlLEAGE. 

I   : 

—  1,000,000. 

I  : 

=  1,000,000. 

Year. 

Through. 

Local. 

Total. 

Through. 

Local. 

Total 

East. 

West. 

East. 

West. 

East. 

West. 

East. 

West. 

1S51.... 
52  — 

.008 
.019 

.008 
.021 

.005 
•015 

.013 

0.069 

2.35 

3 

17 

6 

9 

4-2 

16  8 

53 

.036 

.038 

.049 

•037 

0.160 

8.30 

8 

27 

12 

I 

II. 4 

40.0 

54- •  • 

.050 

•  043 

.089 

•  054 

0.237 

^V" 

10 

b 

2b 

b 

II. 9 

61.6 

55--- 

.106 

.065 

.128 

.065 

0.365 

20.9 

lb 

3 

41 

7 

17-3 

102.2 

1851-5.. 

.051 

.042 

.072 

•043 

0.207 

12.51 

9 

58 

21 

82 

11.20 

55-12 

1856.... 

.089 

.076 

.196 

.092 

0.454 

22.0 

19 

0 

55 

4 

23-4 

119. S 

57 

.094 

.077 

.385 

.406 

0.964 

23-5 

19 

I 

67 

3 

30.8 

140.7 

58.... 

.141 

.080 

.404 

.421 

1.047 

35-0 

19 

8 

75 

6 

31-7 

162. 1 

59 

.130 

.103 

•571 

.366 

1. 170 

46.5 

37 

2 

b9 

5 

27-3 

180.3 

60   ... 

.176 

.100 

.642 

•  429 

1.346 

63.0 

35 

7 

89 

9 

26.4 

215. 1 

1856-60. 

.126 

.087 

.440 

•343 

0.996 

38.0 

26 

16 

71 

54 

27.92 

163.62 

1861.... 

0.31 

0.08 

0.86 

0-37 

1.63 

III. 2 

28 

I 

120 

9 

20.0 

280.3 

62.... 

0-37 

0.13 

1-13 

0-43 

2.06 

131-5 

45 

9 

163 

8 

35-1 

376.2 

63   ... 

0.35 

0.13 

1.23 

0.56 

2.27 

124.9 

45 

5 

177 

7 

45-6 

393-7 

64.... 

0.32 

0.15 

1.48 

0.63 

2.59 

115-5 

53 

0 

200 

0 

52.2 

420.6 

65    ■ 

0.30 

0.16 

1.42 

0.67 

2.56 

108.4 

57 

6 

203 

9 

50.1 

420.1 

1861-5.. 

0-33 

0.13 

1.22 

0.53 

2.22 

118.30 

46 

02 

173 

26 

40.60 

378.18 

1866.... 

0.32 

0.16 

1.84 

0.86 

3-19 

"3- 

58 

8 

276 

65.0 

513- 

67.... 

0.31 

0.17 

2.21 

1.02 

3-71 

no. 

62 

0 

322 

72.1 

566. 

68.... 

0-39 

0.22 

2.58 

1.24 

4-43 

141. 

77 

3 

373 

84.8 

676. 

69... 

0.47 

0.23 

2.82 

1.47 

5.00 

169. 

83 

5 

402 

98.9 

753- 

70.... 

0.54 

0.23 

3-07 

1-58 

5-43 

194. 

83 

439 

no. 

826. 

1866-70. 

0.41 

0.20 

2.50 

1.23 

4-35 

145-4 

72 

9 

362 

86.2 

667.0 

1871 

0.71 

0.31 

3-70 

1.85 

6.58 

254- 

113- 

533 

"3- 

1012. 

72.... 

0.79 

0.36 

4.22 

2.47 

7.84 

283. 

130. 

b25 

1-52 

1100. 

73    ■  •  • 

0.87 

0.32 

5-48 

2.54 

9.21 

312, 

114. 

821 

137 

1385. 

74.... 

1.07 

0.30 

4.92 

2-34 

8.63 

381. 

108. 

IH 

119 

1373- 

75---- 

1. 00 

0.35 

5-39 

2.37 

9.12 

358- 

126. 

803 

133 

1479. 

I87I-5-- 

0.89 

0-33 

4-74 

2.31 

8.27 

317-6 

118. 2 

721 

2 

130 

8 

1287.8 

1876.... 

1.32 

0.29 

5-79 

2.52 

9.92 

473- 

105. 

915 

136 

1630. 

77.... 

1.02 

0.29 

5-71 

2.72 

9-74 

364. 

103. 

8b9 

159 

1495- 

78.... 

1-45 

0.29 

6.20 

3.01 

10.95 

519- 

103. 

93^5 

175 

1732. 

79... 

1.09 

0.38 

7-59 

4.01 

13-68 

605. 

137- 

1138 

257 

2137. 

80 ... . 

1.58 

0.49 

8.51 

4-79 

15-36 

565. 

174. 

1230 

329 

2298. 

1876-80. 

1. 41 

0.35 

6.76 

3-41 

11.03 

505.2 

124.4 

1017 

6 

211 

2 

1858.4 

1881.... 

1.64 

0.57 

10.12 

5-91 

18.23 

586. 

203. 

1452 

414 

2655. 

82.... 

1-35 

0-59 

II. 91 

0.51 

20.  ^56 

483- 

213. 

1755 

430 

2880. 

83.... 

1.38 

0.56 

12.47 

7.27 

21.67 

494- 

199. 

1853 

451 

2997. 

84... 

1.29 

0.53 

'3-3.3 

7-43 

22.58 

468. 

192. 

1938 

484 

3082. 

8s.... 

1.68 

0-57 

13.88 

7.91 

24.05 

612. 

209. 

I9b9 

529 

3318- 

1881-S.. 

1.47 

0.56 

12.34 

7.00 

21.38 

528.6 

20 

3-2 

1793 

4 

461 

6 

2986.4 

CH.  VII.^DISTANCE— EFFECT  ON  COMPETITIVE   TRAFFIC.  233 


Table  98. — Continued. 
Summary  by  Half- Decades. 


Tons  Carried. 

Ton-Mileage. 

I  =  1,000,000. 

I   : 

=  1,000.000. 

Year. 

Through 

.        1           Local. 

Total. 

Through. 

Local. 

Total. 

East.      W 

est. 

East. 

West. 

East. 

West. 

East. 

West. 

1851-5. • 

•  05 

04 

.07 

.04 

0.21 

12.5 

9.6 

21.8 

II. 2 

55-1 

1856-60. 

•13 

09 

•44 

•34 

1. 00 

38.0 

26.2 

71.5 

27.9 

163.6 

1861-5.. 

•33 

13 

1.22 

•53 

2.22 

118. 3 

46.0 

173-3 

40.6 

378.2 

1866-70. 

.41 

20 

2.50 

1.23 

4-35 

145-4 

72.9 

362.4 

86.2 

667.0 

1871-S  • 

.89 

33 

4^74 

2.31 

8.27 

317.6 

118.2 

721.2 

130.8 

1287.8 

1876-80. 

1. 41 

35 

6.76 

3-41 

"•93 

505.2 

124.4 

1017.6 

211. 2 

1858.4 

1S81-5.. 

1-47 

56 

12.34 

7.00 

21.38 

528.6 

203.2 

1793.4 

461.6 

2986.4 

Percentages  and  Average  Local  Haul. 


Per  Cents 

OF  Tot 

AL. 

Year. 

Tons. 

Ton-miles. 

on 
Local  Freight. 

Through. 

Local. 

Through. 

Local. 

East. 

West. 

East. 

West. 

East. 

West. 

East. 

West. 

East.    1   West. 

1851-5  - 

24.5 

20.5 

34^5 

20.5 

22.7 

17.3 

39.6 

20.4 

30^3 

26.0 

1856-60. 

12.7 

8.7 

44.2 

34-4 

23.3 

16.0 

43-7 

17.0 

163 

81.0 

1861-5.. 

15.0 

5-9 

55.1 

24.0 

31.3 

12. 1 

45-7 

10.9 

1  141 

76.5 

1866-70. 

9.4 

4.6 

57-7 

28.3 

21.8 

10.9 

54-4 

12.9 

145 

70.2 

1871-5.- 

10.8 

4.0 

57-3 

27.9 

24.7 

9.1 

56.0 

10.2 

151 

56.6 

1876-80. 

II. 8 

2.9 

56.7 

28.6 

27.1 

6.7 

54.8 

11.4 

150 

61  9 

1S81-5  . 

6.9 

2.6 

57-7 

32.8 

17.6 

6.8 

60.2 

15^4 

145 

66.0 

226.  From  the  additional  receipts  thus  realized  is  to  be  de- 
ducted the  additional  cost  of  earning  it,  which  we  have  seen  may 
vary  anywhere  from  25  to  40  or  (for  great  changes)  50  per  cent 
of  the  average  cost  per  mile.  No  absolute  profit,  therefore,  can 
be  realized  from  longer  home-haul  of  competitive  freight,  unless 
the  foreign  haul  is  greater  than  25  to  40  or  50  per  cent  of  the 
total.  But  with  any  foreign  haul  whatever  there  is  some 
credit  as  well  as  debit  side  to  the  disadvantages  of  distance  for 
this  class  of  traffic. 


234    CHAP.   VII.— DISTANCE— EFFECT  ON  WAY   TRAFFIC. 

227.  Let  us  now  see,  in  continuation  of  par.  205,  how  much 
weight  should  be  probably  given  to  differences  of  distance  as 
RESPECTS  WAY  TRAFFIC.  Table  92  and  various  others  will  show  that 
it  is  a  fairly  low  estimate  to  assume  40  passengers  or  100  tons 
of  freight  as  an  average  train-load,  about  one  half  of  which  (see 
Tables  97  and  98)  will  be  local  traffic,  at  rates  fixed  by  the  mile 
or  at  the  will  of  the  company.  The  fluctuations  from  this  average 
are  very  great  indeed,  and  a  nearer  estimate  can  easily  be  formed 
in  any  particular  case.  Assuming  the  above  average,  however, 
at  i^  cents  per  mile  for  freight  and  2\  cents  for  passengers,  this 
purely  local  traffic  would  net  50  to  62^  cents  per  train-mile.  On 
the  other  hand,  we  have  already  estimated  (Table  89  and  par.  195) 
the  actual  cost  of  running  an  extra  mile  at  from  25  to  50  cents. 
This  sum  includes  all  expenses  for  running  such  distance,  so  that 
any  additional  receipts  arising  therefrom  must  be  created  against 
it  in  full. 

228.  Accordingly,  it  is  plain  that  whenever  way  rates  are 
actually  determined  by  the  distance  alone,  any  reduction  of  dis- 
tance would  be  very  apt  even  to  entail  a  balance  of  loss  upon 
the  company.  For  example,  it  would  undoubtedly  entail  a  net 
loss  on  the  New  York  Central  Railroad,  from  their  way  business 
alone,  to  shorten  their  line  by  several  miles,  even  if  it  could  be 
done  without  cost  to  them,  provided  all  their  business,  "way"  as 
well  as  "through,"  had  to  be  transported  over  the  new  line;  for 
60  cents  would  be  a  very  high  estimate  of  the  actual  cost  of  run- 
ning extra  distance  on  that  road.  On  the  other  hand,  taking  an 
average  train-load  (on  main  line  only)  of  100  passengers,  and 
assuming  the  very  low  proportion  of  one  half  as  that  on  which 
the  receipts  are  fixed  by  the  legal  limit  of  2  cents  per  mile,  we 
have  an  average  gross  loss  of  100  cents  per  train-mile,  or  a  net 
loss  of  40  cents  for  every  mile  cut  out  of  the  line.  And  if  the  gross 
loss  had  been  but  10  cents  instead  of  100,  it  would  have  operated 
to  reduce  the  value  of  any  saving  of  this  di-stance  by  so  much, 
although  not  entirely  destroying  it. 

229.  All  way  traffic,  however,  is  not  by  any  means  rated  solely 
by  the  mile;  nor  would  any  railway  think  of  attempting  to  so 


CHAP.    VII.— DISTANCE— EFFECT  ON  WAY   TRAFFIC.  235 

rate  it,  even  if  it  had  the  power  to  do  so,  without  destroying 
business.  Tables  93-5  clearly  show  this.  Table  98,  showing  the 
enormous  and  growing  proportion  which  local  traffic  makes  of 
the  total  traffic  of  a  line  like  the  Pennsylvania  even,  which  is 
often  thought  of  as  chiefly  a  through  trunk  line,  makes  it  still 
clearer  that  it  is  impossible  that  local  traffic  should  be  all  so 
rated.  And  yet  a  line  no  miles  long  instead  of  too,  between 
two  given  points,  will,  or  can  be  made  to,  derive  some  addition 
to  gross  receipts  without  working  either  hardship  or  injustice. 
The  local  passenger  rates  would  be  perhaps  $3.30  instead  of  $3 
—  a  difference  which  those  who  may  be  called  floating  or  occa- 
sional travellers  (those  making  one  or  two  or  ten  trips  a  year) 
can  well  afford  to  pay,  and  would  pay,  probably  without  feeling 
the  difference.  If  we  estimate  the  total  extra  cost  of  running  the 
10  miles  extra  distance  at  $3,  which  would  ordinarily  be  ample, 
it  would  require  but  10  such  passengers  per  train  to  wholly 
counterbalance  the  cost  of  running  the  extra  distance.  Tliat 
road  would  be  the  exception  perhaps  which  did  not  average  10 
such  passengers  per  train,  and  substantially  the  same  condition 
of  things  exists  on  many  roads  in  freight  business  also. 

For  the  remainder  of  the  traffic,  to  which  the  greater  rate  for 
the  extra  distance  would  be  a  real  hardship  and  burden,  it  is 
entirely  at  the  discretion  of  a  railway  company  to  do  away  with 
the  extra  burden  by  special  rates  based  on  volume  of  business 
furnished;  and  this  is  the  true  and  just  principle  of  fixing  rates 
under  all  circumstances;  for  the  interest  both  of  the  stockholders 
and  the  general  public.  A  man  who  travels  or  makes  a  ship- 
ment over  a  line  once  a  year  is  not  greatly  burdened  by  even  a 
considerable  difference  of  rates,  and  it  may  equitably  be  col- 
lected from  him.  A  constant  patron  of  the  line,  on  the  other 
hand,  finds  the  same  difference  of  rate  a  very  great  burden. 

230.  Thus  we  seem  driven  to  the  conclusion  that  it  is  rather 
worse  than  money  thrown  away  for  any  average  road  to  spend 
money  in  shortening  its  line,  nor  is  there  any  escape  from  the 
conclusion  that  there  is  onh^  one  class  of  road  to  which  it  can, 
under  any  circumstances,  be  any  great  object  to  do  so;— those. 


236     CHAP.    VII.— DISTANCE—EFFECT   ON  WAY   TRAFFIC. 

namely,  whose  traffic  is  mostly  hauled  over  their  own  lines  ex- 
clusively, while  at  the  same  time  the  rates  on  a  large  portion  of 
it  are  directly  or  indirectly  fixed  by  competition,  as  on  two  or 
three  of  the  great  trunk  lines.  A  large  non-competitive  way 
traffic  alone  may  entirely  neutralize  the  pecuniary  value  to  the 
company  of  saving  distance. 

231.  But  these  conclusions,  although  undeniably  true,  sliould 
be  acted  upon  with  even  greater  caution  than  those  already  sug- 
gested with  respect  to  through  business,  and  only  when  there  is 
no  possible  doubt  as  to  the  interests  of  the  company.  For  as  a 
question  of  public  polic}^  the  conditions  which  bring  about  a 
credit  side  to  distance  have  no  force  whatever,  the  ultimate  loss 
to  the  community  from  an  unproductive  and  avoidable  service 
being  the  same  whether  borne  directly  by  the  railway  company 
or  transferred  by  it  to  the  general  public.  And  inasmuch  as  the 
prosperity  of  a  railway  is  intimately  connected  with  that  of  its 
supporting  population,  the  policy  under  certain  circumstances — 
perhaps  under  any  circumstances — of  thus  counting  in  as  a  make- 
weight a  possibly  avoidable  tax  (a  large  fraction  of  which  is,  so 
to  speak,  spent  in  collecting  it),  however  fairly  distributed  and 
lightly  borne,  may  be  questioned,  especially  as  the  ability  to 
collect  it  through  absence  of  competition  is,  by  its  very  nature, 
temporary  and  changeable.  Nevertheless  a  railway  is  a  busi- 
ness enterprise  and  not  a  charitable  institution,  and  it  has  the 
same  right  as  any  private  citizen  to  take  every  reasonable  pre- 
caution to  secure  pecuniary  success. 

232.  The  future  returns  to  the  investors  are  always  more  or 
less  problematical,  while  the  benefit  to  the  public  is  not  prob- 
lematical, and  always  far  ahead  of  any  possible  profit  to  the  in- 
vestors. It  is  hardly  reasonable  to  demand,  therefore,  that  rail- 
ways shall  increase  their  investment  for  the  sake  of  decreasing 
the  return  on  that  investment  paid  by  the  public  ;  and  sound 
policy  requires  and  justifies  this  at  least — that  the  expenditure 
should  be  mainly  directed  not  to  shortening  the  line,  but  to  re- 
ducing the  gradients  or  vertical  distances,  which  we  shall  find  to 
be  immensely  more  important  than  linear  variations  in  their  ef- 


CHAP.    VII.— DISTANCE— SECURING   WAY  BUSINESS.    237 

feet  on  operating  expenses,  but  over  which  a  railway  can  under 
no  circumstances  derive  additional  revenue  by  running  its  trains. 
For  it  is  far  easier  to  collect  pay  from  an  intelligent  public  for 
carrying  them  ten  miles  around  a  mountain  than  for  taking  them 
over  the  top  of  it,  while  it  costs  far  less  to  do  it. 

233.  Especially  when  the  question  comes  up  of  lengthening 
THE  LINE  TO  SECURE  WAY  BUSINESS,  as  Suggested  in  Chapter  III., 
we  may  almost  say  that  where  there  seems  any  room  for  doubt 
it  will  almost  always  be  policy  to  do  so.  Extra  business  to  a 
railway — the  engineer  will  rarely  err  in  thinking — is  almost  all 
clear  profit.  Of  passenger  business  this  is  literally  true  until 
the  increase  becomes  considerable.  Of  freight  business  it  is  so 
nearly  true,  that  80  or  90  per  cent  at  least  of  a  way  rate  is  clear 
profit  over  the  actual  cost  of  any  one  particular  extra  shipment. 
(See  also  par.  181.) 

234.  Let  us  suppose,  for  example,  that  the  A.  &  B.  Railway,  Fig.  13, 
100  miles  long,  is  deflected  10  miles  north  to  strike  some  way  point  C. 
The  increase  of  length,  if 
the  road  were  all  a  straight 
line,  would  be  as  nearly  as 
may  be  two  miles,  and  the 
extra  cost  of  running  those 
two  miles  probably  fifty  to  seventy-five  cents  per  train,  as  already  esti- 
mated. 

235.  The  loss  of  distance  from  even  very  considerable  deviations  from  an 
air-line  is  commonly  absurdly  over-estimated,  even  in  the  minds  of  engineers, 
in  a  way  and  for  reasons  more  fully  discussed  later  (Chap.  XXVIII.).  Young 
engineers  are  rarely  trained  in  such  matters,  and  should  take  pains  to  disabuse 
their  minds  of  impressions  which  often  lead  them  to  take  for  granted  assump- 
tions in  this  respect  which  have  a  mere  shadow  of  foundation  in  fact. 

On  such  a  road,  if  running  ten  trains  daily  each  way,  this  loss  would 
amount  to  S3650  to  $5475  per  year.'  A  very  insignificant  town  will  fur- 
nish as  much  business  as  that,  as  will  be  evident  from  Tables  14  to  28, 
The  average  payment  to  railways  in  the  North  Central  States  being 
about  $13  per  head  per  year,  an  average  village  of  300  to  500  people  would 
be  a  sufficient  inducement  for  such  a  deflection.  There  are,  of  course, 
extreme  fluctuations  in  the  probable  revenue  from  a  village  of  that  size. 


238    CHAP.    VII.— DISTANCE— SECURING   WAY  BUSINESS. 

A  village  of  coal-miners  will  produce  ten  times  that  traffic  at  least,  and 
some  retired  hamlet  not  a  tenth  of  it. 

236.  The  preceding  is  independent  of  the  effect  of  the  two  miles 
extra  distance  to  increase  receipts  as  well  as  expenses  on  the  traffic  as  a 
whole.  Taking  that  into  account,  it  needs  no  further  demonstration  to 
show  that  it  must  in  general  be  a  serious  mistake  to  neglect  way  points 
simply  to  shorten  the  line,  unless  the  grades  are  also  affected.  In  the 
latter  case  it  becomes  more  doubtful ;  but  taking  the  country  as  a  whole, 
not  only  the  private  interests  of  railway  corporations  but  the  interests  of 
the  general  public  as  well  have  suffered  great  disadvantage  and  loss  from 
contrary  practices,  while  the  aggregate  railway  mileage  has  been  unnec- 
essarily increased  ;  for  a  slight  swerve  in  the  main  line  will  often  save  a 
long  branch  or  a  longer  competitive  line. 

237.  The  doubting  engineer  may  safely  take  the  two  following  as 
przma-facie  guides,  to  be  deviated  from  only  as  special  reason  to  the  con- 
trary appears : 

1.  Any  deviation  which  will  increase  the  average  per  mile  of 
ROAD  OF  TRIBUTARY  POPULATION  (weighing  the  latter,  of  course,  in 
proportion  to  their  revenue-producing  capacity)  is  all  but  certainly  ex- 
pedient, because  it  is  mathematically  demonstrable  that  the  longer  line 
ought  then  to  be  for  the  joint  advantage  of  the  community  and  the  rail- 
way (see  Chap  XXI.)- 

2.  Even  if  the  gain  be  considerably  less  than  this,  the  deviation  may 
easily  be  (and  probably  is)  for  the  interest  of  the  railway,  although  not 
in  that  case  expedient  in  itself,  as  a  question  of  public  policy. 

238.  All  the  preceding  conclusions  as  to  the  comparatively 
slight  importance  of  distance  (and  the  same  is  true  of  all  the 
minor  details  of  alignment)  may  well  lead  to  ruinous  conse- 
quences if  they  are  stretched  until  they  crack  to  support  some 
extended  and  radical  change  materially  modifying  the  cost  and 
convenience  of  transportation,  and  so  discouraging  traffic  ;  for 
it  must  never  be  lost  sight  of,  that  anything  which  tends  to  per- 
manently increase  by  ever  so  little  the  cost  to  the  public  of  any 
given  service  is  disadvantageous  to  all  parties,  although  its  dis- 
advantages may  be  more  than  made  up  to  one  party  by  the  gains; 
and  if  the  difference  be  extreme,  the  danger  of  permanent  dis- 
aster to  the  property  is  great.  The  point  which  it  has  been 
sought  to  bring  out  is,  that  even  in  extreme  cases  there  always  is 


CHAP.    VII.— DISTANCE— MORAL  EFFECT.  239 

a  credit  side  of  considerable  importance  to  increase  of  distance 
— contrary  to  the  idea  which  prevails  to  an  unfortunate  extent, 
that  a  short  and  direct  line  is  the  first  desideratum,  to  which 
almost  everything  else  must  bend.  On  the  contrary,  it  would 
be  hard  to  put  the  general  rule  which  should  govern  action 
about  obtaining  a  short  line  in  a  simpler  and  safer  form  than  to 
say  that  it  is  the  one  desideratum  about  a  railway  which  it  is  a 
good  thing  to  have  if  it  costs  nothing,  but  which  must  give  way 
to  other  considerations  in  case  of  conflict,  and  is  not  worth  spend- 
ing much  money  for. 

There  are  cases — as  for  instance  a  line  between  New  York 
and  Philadelphia — where  it  is  of  great  importance;  but  the  excep- 
tional position  of  distance  as  the  one  element  of  cost  of  trans- 
portation which  is  used  as  a  basis  for  collecting  revenue  makes 
such  exceptions  rare.  If  the  conditions  were  different — if,  for  ex- 
ample, we  could  charge  the  passengers  we  did  get  more,  because 
we  had  sacrificed  the  chance  of  getting  some  others  in  order  to 
carry  them  more  quickly — all  this  special  pleading  would  fall  to 
the  ground,  and  distance  would  take  its  true  relative  position 
with  the  other  elements  of  the  cost  of  transportation  on  the  basis 
of  cost  alone.  But  the  very  fact  that  this  is  not  the  case  seems 
to  have  had  the  effect  of  reversing  a  reasonable  deduction  from 
the  premises,  in  the  minds  of  the  more  ignorant  and  thoughtless, 
by  leading  to  some  such  hazy  chain  of  reasoning  as  we  noted  in 
the  beginning  of  this  chapter. 

239.  There  is  another  argument,  of  much  the  same  vague 
kind  as  that  last  referred  to,  but  of  a  more  reasonable  and  tan- 
gible character,  which  is  sometimes  brought  up  as  a  reason  for 
saving  distance,  viz.,  the  ''moral  effect"  of  a  short  line  in 
helping  to  secure  traffic.  Nor  is  this  argument  wholly  unjusti- 
fied, for  there  are  numerous  lines  throughout  the  country  which 
do  apparently  suffer  simply  from  the  length  of  their  line  fright- 
ening away  passengers  and  fast-freight  traffic.  We  may  see 
that  this  effect  is  feared  by  the  current  fashion  of  misrepresent- 
ing geography  in  railway  advertising  circulars. 

240.  Many  lines  which  are  not  particularly  direct,  however, 


240  CHAP.    VII.— DISTANCE— MORAL   EFFECT. 

do  not  do  this,  and  the  prosperit}^  of  a  single  conspicuous  line, 
the  New  York  Central  &  Hudson  River  Railroad,  will  show  that 
there  is  nothing  in  distance  pure  and  simple  to  deter  travel  until^ 
as  in  the  case  of  the  Grand  Trunk  Railwa}^  in  competing  for 
American  business,  the  difference  of  distance  becomes  so  great 
as  Lo  seriously  lengthen  the  total  time  of  the  trip — a  result 
not  commonly  to  be  feared  from  probable  engineering  modifica- 
tions of  any  given  line.  The  enormous  proportion  of  the  New 
York-Chicago  travel  which  the  New  York  Central  secures  in 
spite  of  being  the  longest  of  three  prominent  lines  (970  miles 
against  961  by  the  Erie  and  912  by  the  Pennsylvania),  and  in 
spite  of  taking  passengers  150  miles  north  before  they  begin  to 
go  toward  their  destination  at  all,  is  sufficient  proof  that,  if  a 
line  be  equally  comfortable  and  well  managed,  and  makes 
equally  good  through  time  (as  all  lines  do,  for  the  most  part, 
by  general  agreement,  which  ticket  through  at  the  same  price, 
and  as  any  line  can  successfully  insist  on  doing  when  its  length 
is  not  in  excess  over  10  or  15  per  cent),  it  will  not  suffer  to  any 
material  extent  from  tliis  cause  alone.  That  the  New  York  Cen- 
tral is  no  very  great  sufferer  hardly  needs  further  demonstration 
than  may  be  found  in  various  tables  by  referring  to  the  Index. 

241.  The  difficulty  is  (par.  51)  that  the  lines  least  favored  as  to 
distance  are  generally  less  desirable  in  other  respects.  There 
are  more  connections  to  make,  less  favorable  through-car  arrange- 
ments, a  less  number  of  and  slower  trains,  etc.,  etc.  At  the  very 
worst,  moreover,  this  objection  only  applies  to  a  very  small  por- 
tion, and  that  the  least  profitable  portion,  of  the  traffic  of  a  road; 
and  it  does  not  apply  at  all  to  those  small  changes,  of  a  few  miles 
more  or  less,  which  the  engineer  is  most  frequently  called  upon 
to  consider,  and  to  which  this  chapter  has  mainly  referred. 

242.  The  conclusions  reached  in  this  chapter  have  rarely  been  recog- 
nized in  the  practice  of  engineers,  but  instances  are  not  wanting  where 
they  have  been  clear  enough  to  operating  officers.  As  one  instance  of 
the  latter,  on  the  "  Pan  Handle"  road  (Pittsburg,  Cincinnati  &  St.  Louis) 
a  tunnel  near  Steubenville,  O.,  saving  two  miles  of  distance  and  much 
curvature,  but  costing  $300,000,  was  avoided  by  a  temporary  line.  When 
at  last  means  became  sufficient  to  construct  it,  the  general  manager  of 


CHAP.    VIL— DISTANCE— MORAL  EFFECT.  24 1 

the  line  objected  to  its  construction  on  the  ground  that,  even  though  the 
greater  part  of  their  traffic  was  local  to  the  vast  Pennsylvania  system,  the 
loss  from  revenue  on  the  two  miles  saved  would  far  more  than  counter- 
balance the  saving  in  operating  expenses ;  and  proved  it  so  conclusively 
that  the  construction  was  for  some  years  postponed.  Subsequently,  on 
account  of  the  exceptionally  commanding  position  of  the  Pennsylvania 
roads,  it  was  believed  that  the  old  distance  could  be  considered  as  con- 
structively still  existing  so  that  this  loss  would  not  arise,  and  the  tunnel 
was  built.  Whether  or  not  this  expectation  has  been  maintained  the 
writer  cannot  state,  nor  does  it  affect  the  force  of  the  example. 
16 


CHAPTER  VIII. 


CURVATURE. 


243.    It  is   the 

peculiarity  of  cur- 
vature that  all  its 
disadvantages  lie 
upon  the  surface, 
visible  to  every 
eye  and  compre- 
hensible by  every 
mind.  A  heavy 
grade  is  very  un- 
obtrusive. The 
most  skilful  and 
observant  eye  can- 
not  detect   differ- 

* — Illustrating  THAT  ECONO-  ences     of     grade 

which  decrease  by 
large  percent- 
age the  operating 
value  of  the  line. 
But  curves  attract  instant  attention,  and  their  disadvantages  ap- 
peal even  more  strongly  to  the  imagination  of  the  inexpert  than 
to  the  instructed  judgment  of  the  engineer.     A  visible  defect  or 


MY     OF    CONSTRUCTION,    AVOIDANCE 
OF   CURVATURE   AND    THE    SECURING 
OF  WAV   TRAFFIC  ARE  NOT  NECESSA-    Q, 
RILV       IN      ANTAGONISM      TO      EACH 
OTHER. 


*  This  illustration  the  writer  borrows  from  the  heading  to  a  chapter  on  "  Railway 
Construction"  of  an  English  eng:ineering  work.  Whether  or  not  it  is  a  mere  fancy  sketch 
he  cannot  say  ;  but  it  at  least  has  no  little  verisimilitude  to  not  a  few  actual  works.  The 
question  naturally  arises,  what  the  curve  in  the  foreground  is  for,  especially  if  the  steeple 
in  the  middle  distance  is  a  hint  of  a  town,  or,  if  a  curve  was  deemed  necessarj^,  why  it 
was  not  made  a  little  longer.  There  may  likewise  be  found  in  the  picture  a  hint  as  to 
the  extent  to  which  a  larger  expenditure  for  construction  necessarily  implies  a  better  line. 
The  further  moral  which  the  picture  is  calculated  to  teach  may  be  left  to  the  ingenuity  of 
the  reader. 


CHAP.   VIII.— CURVATURE.  243 

danger  is  always  more  keenly  appreciated  and  dreaded  than  one 
which  it  requires  special  training  to  detect;  and  since  there  is 
always  a  natural  tendency  to  correct  the  faults  which  every  one 
sees  and  to  forget  the  faults  which  no  one  thinks  of,  it  is  evi- 
dent that  this  simple  fact  must  always  have  a  powerful  if  unde- 
tected influence  while  human  nature  remains  what  it  is. 

244.  And  when  we  come  to  consider  what  are  the  more  solid 
objections  to  curvature,  we  find  at  once  that  a  formidable  and 
undeniably  true  list  of  objections  to  it  may  be  made,  consisting 
of  many  counts  ;  as  thus  : 

1.  It  causes  a  cotisidcrable  loss  of  pome?'  and  considerably  more 
wear  and  tear  of  rolling-stock  and  road-bed,  thus  increasing 
expenses. 

2.  //  does  or  may  limit  the  length  of  trains^  and  thus  still  more 
increase  expenses. 

3.  It  causes  a  considerable  expense  for  extra  watchfulness  and  track- 
walking,  and  thus  indirectly  still  more  increases  expenses. 

These  three  are  what  may  be  called  the  definite  and  positive 
objections  to  curvature.  We  can  estimate  them  with  some  de- 
gree of  certainty  and  exactness.  But  there  are  still  others  which 
are  essentially  indeterminate,  and  which  for  that  very  reason  it 
behooves  us  to  examine  into  the  more  closely,  lest  the  haze  of 
doubt  which  unavoidably  surrounds  them  should  on  the  one 
hand  unduly  obscure  them,  or,  on  the  other,  have  a  mirage-like 
effect,  magnifying  them  into  undue  proportions.  Among  these 
causes  are  : 

4.  The  dafiger  of  derailmeiit  is  increased^  and  the  consequences 
of  such  derailment  when  it  occurs  are  more  likely  to  be  seri- 
ous. 

5.  The  danger  of  collision  is  increased  by  the  obstruction  of  the 
view. 

6.  There  is  more  difficulty  in  making  time,  and  thus  passenger 
travel  is  likely  to  be  affected. 

7.  //  injuriously  affects  the  smooth  riding  of  cars,  and  thus  deters 
travel. 

8.  //  impresses  the  imagiiiation  of  travellers  with  a  feeling  of  danger 


244  CHAP.    VIII.— CURVATURE. 

even  if  none  exists,  and  thus  in  a  third  way  affects  travel  unfavor« 
ably;  and,  finally, 

9.  //  is  more  or  less  an  obstacle  to  the  use  of  the  heaviest  and  most 
poiverful  types  of  engines. 

This  is  a  formidable  indictment,  indeed,  and  when  it  is  ex- 
tended from  curvature  in  the  abstract  to  sharp  curvature  as 
against  easy  curvature  it  becomes  still  more  so  ;  for  there  is 
then  more  wear  and  tear,  more  danger  of  limiting  trains  and 
more  injurious  effect  upon  the  safety  and  speed  of  trains,  the 
comfort  of  travellers  and  the  reputation  of  the  line. 

245.  It  is  therefore  not  unnatural  that  a  very  general  course 
of  reasoning  on  the  question  should  be  :  "  Each  one  of  these  ob- 
jections to  curvature  amounts  to  something  ;  plainly,  therefore, 
in  the  aggregate  they  must  amount  to  a  great  deal,  although 
no  one  can  ever  determine  exactly  how  much.  If  the  curvature 
be  sharp  they  will  be  several  times  more  serious,  and  in  fact  will 
then  become  entirely  inadmissible  for  such  a  line  as  ours." 
Thence  may  follow,  perhaps  too  quickly,  a  conclusion  in  the  form 
of  an  order  to  the  engineers  who  are  to  examine  the  country,  ta 
the  effect  that  "the  minimum  radius  of  curvature  permitted  on 
this  line  will  be,"  etc. — an  order  from  which  thereafter  there  will 
be  no  retreat. 

246.  Notwithstanding  this  plausible  reasoning  and  formidable 
indictment,  it  may  be  said  at  once  that  investigation  seems  to 
indicate  that  the  prevailing  error  in  respect  to  curvature  among 
engineers  is  too  great  dislike  of  curvature,  and  especially  of 
sharp  curvature,  and  too  great  readiness  to  spend  money  to  avoid, 
it,  although  a  few  go  to  great  extremes  in  the  other  direction. 
This  conclusion  seems  to  necessarily  result  from  analysis  in 
detail  of  the  weight  to  which  each  of  the  above  objections  is- 
entitled  ;  but  without  presupposing  this,  and  abandoning  all 
prepossessions  in  either  direction,  we  will  consider  each  objection 
to  curvature  as  impartially  as  possible,  beginning  with  what  may 
be  called  the  indeterminate  or  imaginative  (but  not  therefore- 
imaginary)  objections,  4  to  9,  which  cannot  be  reduced  to  a  valu- 
ation in  dollars  and  cents. 


CHAP.    VIII,— CURVATURE— ACCIDENTS  FROM.  245 

THE    DANGER    OF    ACCIDENT    FROM    CURVATURE. 

247.  Railway  accidents  come  from  a  great  variety  of  causes, 
of  which  curvature  is  one.  How  great  a  cause  it  may  be  is  made 
difficult  to  determine  by  the  fact  that  accidents  are  rarely  re- 
ported as  directly  chargeable  to  curvature,  its  effect  being  rather 
to  aggravate  them,  or  to  prevent  timely  discovery  that  there  is 
danger  of  accidents  from  other  causes,  than  to  cause  them  itself. 

Nevertheless  we  can  determine  certain  maximum  and  mini- 
mum limits  for  its  possible  effect  as  a  contributing  or  aggravat- 
ing cause  of  accidents.  The  total  number  of  accidents  to  trains 
per  year,  of  sufficient  seriousness  to  get  into  the  newspapers,  as 
shown  by  the  best  available  statistics  (which  are  very  imperfect), 
is  given  in  Table  99  for  some  thirteen  years  past,  with  some  fur- 
ther details  as  to  accidents  in  Table  100;  and  by  comparison  of 
these  statistics  for  the  eight  years  ending  with  1880,  accidents 
appear  to  have  occurred  very  nearly  at  the  following  rate,  for 
the  railway  system  existing  in  1880: 

Collisions, 400,  causing  120  deaths  and  430  injuries. 

Derailments,  ....  800  "         150      "  "     530        " 

Other  train  accidents,     80         "  30      "  *'       40        " 


1,280  300  1,000 

Of  the  collisions,  about  5  per  cent  are  crossing  collisions,  not 
likely  to  be  affected  by  curvature.  It  is  possible  to  conceive, 
however,  that  any  one  of  the  400  collisions  might  be  injuriously 
affected,  if  not  caused,  thereby. 

Of  the  derailments,  about 

25  per  cent  come  from  broken  or  loose  rails, 

8         "  "  "  cattle  on  track, 

"  washouts, 

"  accidental  and  malicious  obstruction, 

"  misplaced  switches,  and 

"  other  miscellaneous  causes  not  likely  to 

be  affected  in  any  way  by  curvature. 

100  per  cent  in  all. 


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246 


CHAP.   VIII.— CURVATURE— ACCIDENTS  FROM. 


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CHAP.    VIIL— CURVATURE— ACCIDENTS  FROM. 


247 


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248 


CHAP.    VIII.— CURVATURE— ACCIDENTS  FROM. 


Table  100. 

Casualties  Caused  by  the  Different  Classes  of  Accidents  for  Seven 

Years. 

Killed. 


In  Collisions. 

In  Derailments. 

In  Other  Ace. 

Total. 

i88^ 

158 
172 
227 

177 
209 

156 
94 

141 

192 
229 
200 
190 

143 
97 

8 
25 
17 

3 
15 
16 

4 

307 

1884 

389 

188^ 

473 

1882 

380 

1881 

414 

1S80 

315 

1870 

195 

Average 

170 

170 

13 

353 

Injured. 


1881; 

547 
624 
716 
578 
565 
412 
286 

963 
1,062 
1,145 
975 
995 
714 
389 

20 
74 
49 
35 
37 
46 

34 

I,=i30 

1884 

1,760 
1,910 

1,588 

1.597 

1,172 

709 

1883 

1882 

I88I 

1880 

1870 

Average 

533 

892 

42 

i,j67 

Of  the  1,217  accidents  reported  in  1885,  193  caused  the  death  of  one  or  more  persons 
each,  while  282  caused  injury  to  persons  but  not  death  ;  a  total  of  475  accidents,  leaving 
742,  or  61  per  cent  of  the  whole  number,  in  which  there  was  no  injury  to  persons  con- 
sidered serious  enough  for  record. 

The  accidents  recorded  in  1886  were  about  three  for  every  1,000,000  train  miles,  and 
were  divided,  according:  to  their  nature  and  the  classes  of  trains,  as  follows  : 


Accidents. 

Collisions. 

Derailments. 

Other. 

Total. 

47 
102 

315 

247 
434 

51 
21 

345 
102 
770 

To  a  passenger  and  a  freight 

Total 

464 

681 

72 

1,217 

Allowing  two  trains  in  each  collision,  this  shows  accidents  to  a  total  of  1,681  trains, 
of  which  494,  or  29  per  cent,  were  passenger  trains,  and  1,187,  or  71  per  cent,  were  freight 


CHAP.    VIII.— CURVATURE— ACCIDENTS  FROM. 


249 


trains.  This  is  very  materially  less  than  the  true  proportion  of  freight-train  accidents,  if 
accidents  of  all  kinds  were  included,  but  it  includes  a  large  proportion  of  those  involving 
loss  of  hfe  or  very  serious  damage. 

Classified  by  months,  the  aggregates  of  the  reported  train  accidents  of  the  six  years 
1880-18S5  (7,949  in  all)  were  : 


Winter  Months. 

Spring  Months. 

Summer  Months. 

Fall  Months. 

Dec.     687 

Jan.      882 

'      Feb.     812 

Total 2,381 

Per  cent.  .     30.0 

March,  620 
April,    490 
May,     4S3 

1.593 
20.0 

June,    438 

July,    556 
Aug.     705 

1,699 
21.3 

Sept.      770 
Oct.        789 
Nov.      717 

2,276 

28.7 

248.  There  were  in  the  United  States  in  the  year  1880  about 
90,000  miles  of  railroad  in  operation,  employing  about  450,000 
men,  and  over  which  some  5,000,000,000  passenger-miles  were 
run  each  year  and  perhaps  2,000,000,000  or  more  employe  or 
free-pass  miles,  counting  both  passenger  and  freight  service,  the 
number  of  freight  trains  being  at  least  three  times  greater  than 
passenger  trains. 

The  number  of  curves  will  average  considerably  over  one 
per  mile,  as  shown  in  the  following  Tables  loi  to  104  (see  es- 
pecially summary  to  Table  102,  page  263),  or  say  at  least  128,000 
for  the  whole  United  States.  This  is  almost  certainly  not  an 
over-estimate. 

249.  Performing,  then,  the  simple  arithmetical  operation  of 
dividing  128,000  curves  by  1280  annual  accidents  and  by  the 
given  number  of  deaths  and  injuries,  we  find  that  if  all  train  ac- 
cidents which  are  serious  enough  to  get  into  the  newspapers 
were  justly  chargeable  to  curvature  and  to  nothing  else,  there 
would  be  on  an  average  one  such  accident  per  year  for  every  100 
curves,  one  death  for  every  427  curves,  and  one  injury  for  every 
128  curves.  To  present  the  meaning  of  these  figures  in  a  clear 
way:  If  all  train  accidents  were  caused  by  curvature  alone,  there 
would  on  any  one  given  curve  be  an  accident  of  some  kind  worth 
notice  in  the  public  press  once  in  100  years,  a  passenger  or  em- 
ploye killed  once  in  427  years,  and  a  passenger  or  employe  in- 
jured once  in  128  years. 


250  CHAP.    VIII.— CURVATURE— ACCIDENTS  FROM, 

250.  Such  an  exaggeration  of  the  effects  of  curvature,  how- 
ever, is  of  course  wholly  beyond  reason.  It  does  not  appear 
probable  from  the  record  of  Tables  99  and  100  that  more  than 
half  the  individual  accidents  are  of  such  a  nature  as  to  have 
been  at  all  modified  or  affected  by  curvature,  and  of  those  which 
are  likely  to  be  at  times  so  affected — such  as  collisions,  broken 
rails,  cattle  on  track,  washouts,  landslides,  breaking  in  two  of 
trains,  etc.,  etc. — a  large  percentage  are  well  known  to  arise 
from  causes  which  the  alignment  would  not  greatly  affect,  such 
as  frogs,  misplaced  switches,  accidents  to  running  gear,  etc.,  and 
others  are  only  likely  to  be  aggravated  by  curvature.  It  is  ex- 
tremely doubtful,  therefore,  if  more  than  30  or  40  per  cent  of 
train  accidents  are  in  any  measurable  degree  modified  or  af- 
fected by  curvature  ;  and  in  many  of  these  the  effect  is  so  slight 
or  so  doubtful,  tha't  if  we  were  to  assume  that  from  15  to  20  per 
cent  of  all  accidents  are  wholly  caused  by  curvature,  it  w^ould 
probably  be  giving  it  its  full  weight.  It  will  be  safer,  however^ 
especially  as  our  record  is  not  entirely  satisfactory,  to  assume  as 
a  mean  of  possible  extremes  that  25  per  cent  of  the  accidents 
are  caused  by  curvature,  and  curvature  alone. 

251.  In  that  case  we  shall  have  on  any  one  particular  curve, 
and  caused  by  that  curve — 

A  train  accident  serious  enough  to  be  mentioned  in  the 
newspapers  once  in  400  years: 

A  passenger  or  employe  killed  once  in  1708  years; 

A  passenger  or  employe  seriously  injured  once  in  512  years. 

If  we  make,  now,  some  simple  computations  in  compound 
interest  (Table  17,  p.  80)  we  reach  some  rather  surprising  results: 

We  find  that  if  we  were  to  invest  one  dollar  at  4  per  cent 
compound  interest  at  the  time  of  construction  we  should  have 
$6,506,088  to  repair  the  damage  arising  from  the  first  serious 
accident  occurring  on  any  given  curve,  and  caused  by  the  fact 
that  it  was  a  curve  instead  of  a  straight  line  ;  $526,201,500  with 
which  to  heal  the  wounds  of  the  first  man  injured  ;  and  a  sum 
an  innumerable  number  of  million  times  greater  than  the  last 
again  (being  what  it  would  amount  to  at  compound  interest  in 


CHAP.    VIII.— CURVATURE— ACCIDENTS  FROM.  2$  I 

1 196   years)  as  a    fund  wherewith  to    assuage  the   grief    of  the 
dependent  survivors  of  the  first  man  killed. 

Change  these  figures  as  we  will,  and  keep  within  the  bounds 
of  reason,  and  we  shall  yet  find  the  result  substantially  the  same. 

252.  Nevertheless,  an  accident  of  the  most  terrible  descrip- 
tion may  happen  within  a  week  on  any  curve,  and  be  directly 
caused  thereby.  On  some  one  of  the  128,000  curves  in  the 
United  States  it  probably  will.  Accidents  of  some  gravity  are 
continually  reported  which  appear  to  have  been  due  to  or  to 
have  been  aggravated  by  curvature,  and  more  than  one  such  per 
day  must  happen  in  the  United  States  by  our  assumptions.  It 
is  also  undeniable  that  all  curves  are  not  by  any  means  equally 
dangerous.  When  very  sharp  and  on  heavy  grades  they  are 
materially  more  dangerous  than  elsev/here.  But  on  the  whole, 
and  within  the  limits  of  ordinary  and  reasonable  practice,  it 
would  almost  appear,  as  if,  even  it  the  question  were  simply 
curvature  or  no  curvature,  the  only  proper  conclusion  would  be 
that  the  question  of  safety  w^as  not  entitled  to  any  weight  what- 
ever in  deciding  on  the  line  to  be  adopted  or  the  expenditure  to 
be  incurred.  Only  when  all  other  considerations  were  equally 
balanced  should  it  be  made  the  ground  of  a  decision. 

253.  But  the  bald  question,  curvature  or  no  curvature,  never 
is  the  question  before  the  engineer.  The  general  character  of 
the  line  is  irrevocably  fixed  by  the  topographical  conditions. 
He  is  not  called  upon  to  decide  between  the  crooked  solid  line 
and  the  straight  dotted  line  in  Fig.  15,  but  between  a  little  more 


/| 

-T  '  ^'^  —  V<9 

/—  ^  ^  -^—  —  _  _   ^"^^     ' 

"""^'^^Si:^-  --^r^ 

'      « 

^*<i— ^ 

•«                                        * 

Fig.  is. 


and  a  little  less  curvature  as  indicated  by  the  solid  and   nearly 
parallel  dotted  line. 

If  we  could  eliminate  all  curvature  from  railways  we  might 
perhaps  decrease  by  25  or   50  per  cent  the  danger  to  life  and 


252  CHAP.    VIII.— CURVATURE— ACCIDENTS  FROM. 

property.  But  this  is  practically  impossible;  and  as  between 
the  common  case — such  alternate  lines  as  are  shown  in  Fig.  15, 
— let  the  reader  pause  for  a  moment  and  intelligently  consider, 
firsts  what  the  probabilities  are  of  an  accident  on  either  line  due 
to  all  its  curvature,  and,  secondly^  what  the  danger  amounts  to 
of  an  accident  on  the  one  line  due  to  the  difference  in  its  curva- 
ture from  the  other?  For  example,  we  have  in  Fig.  16  a  view 
of  one  of  the  famous  accidents  of  1885  (the  Monte  Carlo  dis- 
aster), which  may  be  said  to  have  been  entirely  chargeable  to 
curvature  in  one  sense,  because  the  crookedness  of  the  line  pre- 
vented the  two  approaching  trains  from  seeing  each  other,  and 
this  on  a  line  where  enormous  sums  were  spent  to  avoid  curva- 
ture or  to  increase  its  radius,  and  on  the  very  top  of  one  of  the 
most  costly  works  for  that  purpose — the  immense  retaining-wall 
shown  in  that  view.  How  much  was  the  danger  of  accident 
diminished  by  these  works  below  what  would  have  existed  had 
the  line  been  more  closely  fitted  to  the  contour  by  throwing  it 
back  on  to  the  solid  in  the  view,  at  the  necessary  cost  of  some- 
what more  and  somewhat  sharper  curvature  ? 

254.  This  question  is  so  important  that  it  seemed  essential 
to  make  the  facts  entirely  clear.  A  natural  and  commendable 
aversion  to  anything  which  seems  to  imperil  life  and  limb  may 
lead  to  a  dissent  from  the  above  conclusions  on  general  prin- 
ciples, as  somewhere  involving  a  fallacy,  but  that  they  are 
practically  true  seems  to  be  proved  positively  in  another  wa}^ — 
by  the  immunity  from  accident  which  many  very  crooked  lines 
enjoy  in  common  with  more  fortunate  rivals,  and  by  the  fact 
that  the  number  of  accidents  is  certainly  no  greater  (in  fact  it 
appears  from  the  last  (1880)  census  to  be  some  18  times  less)  in 
the  States  east  of  Ohio  which  have  two  or  three  curves  to  the 
mile,  than  in  the  States  west  of  Ohio  which  have  a  curve  only 
every  two  or  three  miles,  as  an  average. 

255.  Unfortunately,  from  the  very  fact  that  curvature  plays 
so  small  a  part  as  a  cause  of  accident,  no  general  statistics  can 
be  given  as  to  the  number  of  cases  in  which  it  does  have  an  in- 
fluence;  but  a  very  interesting  little  volume  by  Charles  Francis 


CHAP.    VIII.— CURVATURE— ACCIDENTS  FROM.  253 


254  CHAP.    VIIL— CURVATURE— ACCIDENTS  FROM, 

Adams,  Jr.,  on  "  Railroad  Accidents"  supplies  this  defect  in  a 
measure,  Mr.  Adams  gives  the  details  of  many  of  the  more 
notable,  or  rather  typical,  accidents  which  have  occurred  in  the 
history  of  railways, — some  42  in  all, — and  apparently  by  mere 
accident  specifies  the  character  of  the  alignment  in  almost  every 
case.     Out  of  these  there  were 

8  accidents  on  curves,  killing  253,  injuring  497;   total,  750 
24  "  "    tangents,"        604,        "       1103;        "     1707 

10  *'  unspecified. 

Deaths.  Injuries. 

Average  per  accident  on  curves,  31.6  62.2 

'*  "  "  "    tangents,  25.2  46.0 

This  is  mere  chance  collection,  and  proves  nothing  definite, 
especially  as  a  number  of  bridge  and  other  accidents  are  in- 
cluded, with  which  curvature  or  the  lack  of  it  had  nothing  what- 
ever to  do.  It  is  perhaps  noteworthy,  however,  that  the  propor- 
tion of  accidents  occurring  on  curves  (about  one  fourth)  is  hardly 
so  great  as  might  be  expected  if  it  were  a  pure  matter  of  chance 
whether  accidents  occurred  on  tangents  or  curves.  Several  ter- 
rible collisions  occurred  'Svhen  rounding  curves:"  but  fog  seems 
to  be  a  still  more  fruitful  cause,  as  at  Revere,  Mass.;  and  not  a 
few  are  due  to  pure  and  utter  carelessness,  as  in  the  frightful 
accident  on  the  Richelieu  River  in  Canada,  one  of  the  most  de- 
structive on  record,  about  one  hundred  having  been  killed  out- 
right and  several  hundred  injured.  In  this  case  the  engineman 
ran  into  an  open  drawbridge  on  a  long  straight  line  (as  seems 
clear  from  the  text)  past  a  danger  signal  in  full  view  1600  feet 
from  the  bridge. 

256.  Still,  we  have  fog  and  carelessness  always  with  us,  of 
course,  whether  on  curves  or  tangents,  and  such  risk  as  there 
may  be  from  curvature  is  in  addition  thereto,  so  that  these 
instances  of  terrible  catastrophes  on  tangents  do  not  even  tend 
to  prove  directly  that  curvature  is  a  trifling  cause  of  accident; 
but  what  they  do  prove  is  that  the  unfamiliar  and  occasional  is 
the  most  fruitful  source  of  accident.     The  drawbridge  signal  in 


CHAP.    VIII.— CURVATURE— ACCIDENTS  FROM.  255 

the  last  accident  recorded  was  not  looked  for,  because  the  draw 
was  rarely  open;  and  in  the  same  way  it  is  probable  that  the 
greater  feeling  of  danger  and  more  constant  caution  which 
springs  from  the  existence  of  curvature,  and  more  especially  of 
much  curvature,  makes  it  in  some  measure  a  safeguard  against 
accidents  as  well  as  a  cause  thereof.  Only  in  this  way  can  be 
explained  the  undeniable  safety  with  which,  as  a  matter  of  fact, 
numerous  very  crooked  roads  are  operated. 

257.  To  illustrate  this  possible  danger  from  carelessness: 
There  are  several  hundred  miles  of  the  Union  Pacific  Railroad 
on  which  there  is  practically  no  break  of  either  line  or  grade, 
but  trains  rise  into  view  on  the  horizon  as  at  sea.  As  a  very 
natural  consequence,  it  was  at  one  time,  and  perhaps  in  less 
degree  is  yet,  the  custom  to  operate  the  road  with  almost  entire 
indifference  to  time-tables  or  train-orders.  When  an  opposing 
train  ''hove  in  sight"  both  made  for  the  passing  point  which  hap- 
pened to  be  nearest  between  them,  and  if  their  idea  as  to  where 
this  point  was  happened  to  be  different,  one  or  the  other  would 
"back  out."  Such  conditions  as  these  seem  to  afford  the  ue plus 
ultra  of  safety,  yet  if  it  prevailed  on  all  railways  it  may  be 
gravely  questioned  whether  it  would  on  the  whole  add  much,  if 
anything,  to  the  average  safety  of  railway  travelling;  for  the 
feeling  of  security  and  habit  of  carelessness  which  would  thus  be 
engendered  in  employes  of  every  grade  would  be  apt  to  lead  in 
emergencies  to  the  most  terrible  consequences.  Such  contin- 
gencies, for  instance,  as  dense  fogs  or  sudden  snow-storms  or  a 
cinder  in  the  engineman's  eye,  or  a  dozen  other  possibilities, 
would  be  almost  certain  to  bring  about  occasional  accidents 
which,  under  conditions  exacting  greater  habitual  vigilance, 
would  not  have  occurred. 

258.  Even  in  the  cases  of  derailment  mentioned  in  Mr. 
Adams'  book  it  is  difficult  to  detect  much  effect  from  curvature. 
The  disastrous  derailment  from  a  broken  rail  at  Carr's  Rock,  on 
the  Erie  Railway,  occurred  indeed  on  a  sharp  curve  on  the  edge 
of  a  precipice  (on  a  division  where  nearly  the  whole  line  is  of 
this  description);   but  another  one,  precisely  like  it,  occurred  in 


256  CHAP,    VIII.— CURVATURE— ACCIDENTS  FROM. 

the  immediate  vicinity,  ten  years  before,  on  a  perfectly  straight 
piece  of  track,  which  is  something  pretty  hard  to  find  in  that 
locality.  These  are  the  two  most  serious  accidents  which  have 
ever  (1882)  occurred  from  this  cause  on  that  section  of  the  road. 
In  the  first  instance,  on  a  curve,  24  were  killed  and  80  injured;  in 
the  second  instance,  on  a  tangent,  onh^  6  killed  and  50  injured; 
but  the  difference  is  due,  not  to  the  alignment,  but  to  the  differ- 
ence in  the  height  of  the  precipice — 30  feet  in  one  case  and  Zo 
feet  in  the  other. 

259.  A  very  common  error  with  regard  to  broken-rail  accidents  re- 
quires correction  here.  There  is  not  a  particle  of  evidence — or  certainly 
none  of  much  moment  or  weight — tending  to  show  that  curvature  notice- 
ably increases  the  liability  of  breakage  or  even  the  consequences  thereof. 
As  respects  the  former,  it  is  almost  purel}/  a  matter  of  the  condition 
of  road-bed  and  of  chance  defects.  Thus  the  records  kept  by  the  Rail- 
road Gazette  show  that  such  accidents  are  nearly  nine  times  as  numerous 
in  the  winter  months  as  in  the  siimmer,  there  having  been  of  noticeable 
accidents  caused  by  broken  rails  during  the  eight  years  1873-80:  In 
January,  February,  and  March,  268  ;  in  July,  August,  and  September,  32. 
The  consequences  of  a  rough  road-bed  or  of  the  temperature  of  the 
metal,  or  both,  being  so  very  noticeable,  it  is  clearly  indicated  that  it  is 

the  hammer-like  effect  of  the  locomotive, 
Tj/  /  rather  than  any  direct  pressure,  which 

causes  the  breakage ;  and  this  is  not  in- 

^^^  creased   by  curvature  :   it   is   rather  de- 

'*''*"'*^^^    creased.     On  a  tangent  a  train  impinges 

— ..-^.^^ against  the  rails  with  a  great  deal  of  force 

from  one  side  to  the  other  alternately. 
\|  \  On  a  curve  every  truck  in  the  train  tends 

\A  \  rather  to  hug  the  outside  rail  with  the 

*'  front  outer  wheel — in  a  manner  shown  in 

^"^-  ^7-  Fig.   17,   of  which  we  shall   speak  more 

fully  shortly — both  the  inner  wheels  standing  clear  of  the  rail ;  while  the 
driving  wheel-base  is  preserved  by  the  truck  from  impinging  against 
either  rail  with  anything  like  its  natural  force.  For  these  same  reasons 
a  broken  rail  on  the  inside  of  a  curve  is  noticeably  less  likely  to  cause 
a  derailment  than  if  on  a  tangent;  while  a  broken  rail  on  the  outside, 
although  it  is  of  course  greatly  more  dangerous  than  on  a  tangent,  is 
not  so  much  so  as  might  seem — for  the  reason  that,  even  on  a  tangent,. 


i 


CHAP.    VIII.— CURVATURE— ACCIDENTS  FROM.  257 

some  one  truck  in  the  train  is  likely  to  impinge  at  just  the  right  spot  to 
cause  derailment,  and  one  truck  off  is  nearly  as  effectual  as  a  dozen  to 
cause  a  catastrophe. 

But  if  derailment  does  occur  there  is  certainly  more  danger  on  a 
curve  than  on  a  tangent,  and  in  numerous  other  ways,  which  appeal  very 
strongly  both  to  the  imagination  and  the  judgment,  curvature  is  a  real 
source  of  danger ;  and  of  course  the  sharper  it  is,  and  the  more  of  it 
there  is,  the  more  danger  there  is.  Those  who  maintain  that  it  should 
therefore  constitute  a  serious  element  in  the  problem  of  laying  out  a  road 
have  the  best  of  the  argument  so  long  as  it  is  confined  to  generalities. 
Their  case  only  becomes  weak  when  we  consider  its  force  in  detail. 

260.  The  truth  is  that  nothing  but  a  standing  miracle  keeps 
either  curvature  or  any  other  of  a  dozen  causes  of  accident  from 
being  a  fruitful  source  of  disaster.  The  marvellous  safety  of 
railway  travel  in  the  face  of  such  numberless  chances  for  disas- 
ter is  one  of  the  most  impressive  triumphs  of  human  care  and 
skill,  and  it  is  this  fact  alone  vt'hich  gives  our  argument  any 
force  whatever.  No  one  could  have  foreseen  it,  and  hardly  any 
one  can  fully  realize  it;  but  the  fact  being  as  it  is,  true  wisdom 
requires  that  we  should  recognize  its  consequences,  and  not 
insist  on  trusting  to  the  imagination  for  arguments  in  a  purely 
practical  question. 

Mr.  Adams  has  very  effectively  expressed  this  marvellous 
safety  in  a  pithy  sentence,  by  saying,  that  *' the  chances  of  acci- 
dent in  railroad  travelling  are  so  small  that  they  are  not  materi- 
ally increased  by  any  amount  of  travelling  which  can  be  accom- 
plished within  the  limits  of  a  human  life."  He  proceeds  with 
the  following  interesting  comparative  statistics: 

260(2.  "During  the  four  years  1875-8  only  i  passenger  was  killed 
from  causes  beyond  his  own  control  in  Massachusetts,  and  only  20  in- 
jured. Yet  during  the  year  1878  alone,  excluding  all  cases  of  mere 
injury,  of  which  no  account  was  made,  no  less  than  53  persons  came  to 
their  death  in  Boston  alone  from  falling  down-stairs  and  37  more  from 
falling  out  of  windows;  7  were  scalded  to  death.  In  the  5^ear  1874,  17 
were  killed  by  being  run  over  by  teams,  and  the  pastime  of  coasting  was 
carried  on  at  the  cost  of  10  lives  more.  During  the  five  years  1874-8 
there  were  more  persons  murdered  in  the  city  of  Boston  alone  than  lost 
their  lives  as  passengers  through  the  negligence  of  all  the  railroad  cor- 
17 


258       CHAP.    VIII.— CURVATURE— ''  DEGREE   OF  CURVES^ 

porations  in  the  whole  State  of  Massachusetts  during  the  nine  years 
1 87 1-8,  which  included  the  Revere  and  Wollaston  disasters,  in  which  50 
people  lost  their  lives.  Neither  are  the  comparative  results  here  stated 
in  any  respect  novel,  or  peculiar  to  Massachusetts  :  years  ago  it  was  offi- 
cially announced  in  France  that  people  were  less  safe  in  their  own  homes 
than  when  travelling  on  railroads  ;  and,  in  support  of  this  somewhat 
startling  proposition,  statistics  were  produced  showing  14  cases  of  death 
of  persons  remaining  at  home  and  there  falling  over  carpets,  or  in  the 
case  of  females  having  their  garments  catch  fire,  to  10  deaths  on  the 
rail.     Even  the  game  of  cricket  counted  8  victims  to  the  railways'  10." 

260/^.  All  these  facts  agree  in  indicating  the  conclusion  that 
although  curvature  is  a  considerable  source  of  danger,  yet  it  is 
even  then  so  little  dangerous  to  life  and  property  that  we  are 
not  justified  in  giving  any  financial  weight  whatever  to  this 
argument  against  it,  unless  under  peculiar  circumstances,  or  as 
a  makeweight  when  all  other  considerations  are  exactly  bal- 
anced. The  case  is  entirely  different,  for  reasons  we  cannot  take 
space  to  discuss  at  length,  from  the  defects  in  operating  details 
which  people  rightly  insist  should  be  corrected  even  at  a  large 
immediate  expenditure. 

Before  proceeding  further  with  the  discussion  of  the  question  of  curvature 
it  may  be  well  to  explain  just  what  is  meant  by  the  term  "the  degree  of  a 
curve,"  which  we  shall  have  frequent  occasion  to  use,  for  the  benefit  of  foreign 
readers  if  for  no  others. 

261.  Meaning  of  the  Term  "  Degree  of  Curve." — The  universal  method 
in  America  of  expressing  the  sharpness  of  curvature  is  not  by  giving  the  radius, 
but  by  the  "degree  of  the  curve"  or  number  of  degrees  of  central  angle,  sub- 
t'^nded  by  a  chord  of  100  ft. ;  i.e.,  by  the  angular  change  in  direction  of  the  curve 
in  the  distance  subtended  by  a  chord  of  100  ft.  If  the  central  angle  be  1°,  the 
radius  is  readily  computed  as  5729.65  ft.,  which  is  the  radius  of  a  one-degree 
CURVE,  taken  in  practical  work  as  5730  ft. 

Except  as  the  length  of  the  arc  bears  a  varying  ratio  to  the  length  of  the 
subtending  chord  in  curves  of  different  radii,  it  is  readily  shown  geometrically 
that  the  radius  is  inversely  proportional  to  the  degree  of  curvature;  and  this  is 
so  nearly  true  in  fact  up  to  the  limit  of  an  8°  curve  (within  a  small  fraction  of  a 
foot)  that  it  is  almost  universally  customary  in  the  best  practice  to  record  the 
radius  of  a  1°  curve  as  5730  ft.,  and  to  determine  the  radius  of  curves  of  other 
"degrees"  by  the  approximate  formula, 

7?-  5730 

(To  p.  266.) 


CHAP,    VIII  — CURVATURE— AMOUNT  OF. 


259 


Table  101. 

Statistics  of  Grades  and  Curvature  on  the  Railways  of  the  North- 
eastern United  States. 

[Computed  from  the  Census  Statistics  of  1880.    See  note.] 
New  England. 


Miles 

of 
Road. 

Curvature. 

Gr.\des. 

Name  of  Road. 

Curves 
Per 

Mile. 

1 

Curved.^    Mile. 

i 

P.  C. 

Level. 

Rise 
Per 

Mile.* 

Rise 

and 

Fall 

Per 

Mile.* 

Ruling 
Grades. 

42.0 
33-3 
35-0 

49.6°   i 
38.7° 

0.0 
1-3 

18.7 
24.6 
19-5 

12.2 
15-6 
10.5 

19  "        Conn. to  Nor. 

20  "        Nor.  to  Sum. 

750 
982 

X.89 
.1.67 

Total,  57  roads 

1.859 

1.76 

36.8     1     46.6°   i 

1-7 

30-9 

12.8 

Single  Roads. 

Boston  &  Worcester. . . 

Boston  &  Albany 

B.  &  N.  Y.  Air-line.... 

Concord  &  Porlsm 

Central  Vermont 

44 

202 

51 
40 
120 

1.68 

1.62 
1. 41 
1. 17 

40.5 
56.0 
34-0 
37-2 
37-8 

25.0° 
72-5° 
76.o»   i 
93.0°   ^ 
34-5°   ! 

2.8 
0.0 
6.1 
3-8 
0.9 

10.4 
9-3 
13-5 
19.0 
15-7 

2.8 
13-7 
17-3 
15-3 

8.4 

1: 

50 
80 

42 

457 

1.48 

41. 1 

60.2°  : 

1 

3-1 

13.6 

II. 5 

New  York. 


Alb.  &Susq 

BuflE.,N.  Y.  &Phila... 
N.  Y.  &Can 

*42.5 
120.5 
112. 9 
143.8 
296.6 
102.6 

2.36 
1.14 

0.78 

O.QS 

36.2 
24.8 
34-6 
32-2 
19.8 
34-5 

54.2° 
28.6° 
64.7° 
28.5° 
15.1° 
25.0° 

21.3 

32.2 

75-8 

34-8 

6  8 

5 
3 
0 
0 

I 
0 

9 
8 
0 
0 
8 
9 

13.2 
9.0 

1.6 
3-8 
9.0 

78-56 

39-  43 
24-  34 
21-  33+ 

40-  56 

N.Y.  Central 

"     (Syr.  to  Roch). .. 

Totals  and  av 

918.9 

1-58 

30-3 

36.0° 

34.1 

2 

I 

7-4 

N.  Y.  &  Harlem....... 

Eiie^  E.  Div 

127.0 
87  0 
103.9 
139 -9 
129.2 
79.1 
107.7 

I. 17 
1.67 

3-73 
1.44 
1.25 
1-37 
1.09 

26.7 
29-3 

29.6 
28.4 
25-5 
25-5 

46.5° 
88.0° 

?:? 

28  4° 
31-5° 

II. 4 
9-7 
39-7 
31.0 
12.8 
25-3 
16.8 

3 
17 

I 
I 
5 
7 

1 

s 

8.4 
II. 8 
4-5 
1-7 
10.5 
7-1 
9-3 

40-  42 

Z  X 

12-    18  — 

52-  47 
53 
71-  53 

Del.  Div 

Susq.  "    

W.       "    

Rens.  &  Saratoga 

Roch.  &  State  Line..    . 

Totals  and  av 

773-8 

1.67 

31-3 

41.4° 

21.0 

4 

7.6 

R  ,  W.  &  0 

148.0 
81.0 
57-8 
73-2 
86.8 
71.0 

0.63 
1.60 
1.26 
3.00 
1. 14 
1-51 

17.4 
33-8 
24.1 

41.0 
26.6 
12.5 

17.0° 
31.6° 

V< 
80.5" 

24.0° 

21.7° 

29.4 
24.8 
17-5 
13.6 

31-3 
7.0 

0 

24 
0 

3 

9 

I 

I 
8 

2 

6.8 

si 

II. 6 
12.3 
II. 0 

40-  53 
52 
37-  74 

160-142 
66 
85-127 

Svr.,  Bin-   &  N.Y... . 

Syr.,  Gen.  &  C 

Ulster  &  Del 

Utica  &  B.  River  

U.  Ith.  &  Elm 

Totals  and  av 

517-8 

I    52 

25-9 

33-7° 

20.6 

•7 

r> 

9-5 

*  The  column  "  Rise  Per  Mile"  gives  the  average  excess  of  rise  over  the  fall  in  one  mile. 
The  next  column  gives  the  feet  of  rise  and  fall.  Thus,  if  a  road  rose  500  ft.  and  fell  200  in  100 
miles,  it  would  be  given  above  as  "Rise  Per  Mile,  3.0."  "Rise  and  Fall,  2.0."  The  first 
quantity  is  an  unavoidable  necessity,  due  to  difference  of  level  of  the  termini. 


26o 


CHAP.    VIII.— CURVATURE— AMOUNT  OF. 


Table  101. — Continued., 
New  Jersey, 


Miles 

of 
Road. 

Curvature. 

Grades. 

Name  of  Road. 

Curves 
Per 

Mile. 

P.  C. 

Curved. 

Deg. 
Per 

Mile. 

P.O. 

Level. 

1 

Rise 
Per 

Mile.* 

Rise 

and 
Fall 
Per 
Mile.* 

Ruling 
Grades. 

Morris  &  Essex 

Phila.  &  Atl.  City 

83-7 

54-5 

1. 16 
0.42 

34-0 
10.5 

44-4° 
6.3° 

17.8 
24.8 

2.6 
0.0 

16.4 
10.7 

5°        + 
52.8 

Totals  and  av 

138.2 

0.79 

22.2 

25.3° 

.21.3 

1-3 

13-5 



Pennsylvania. 


Cumb.  Valley 

82.2 
T15.0 

lOI.O 

43-4 
27.2 
I37-I 

0.88 
2.40 
2.60 
1-39 
6.35 
2.42 

173 
39-2 
50.0 
26.0 
49.0 
45-5 

16.6° 

14.4 

20.8 

3-9 

30-3 

0.7 
4.9 
3.2 
5-0 
38.4 
3-3 

12.2 
18.8 
12.2 
14-5 

6.5 

49-  58 

Del.,  Lack.  &  W 

Lehigh  Valley 

Lew.  &  Tyrone 

Montrose 

84.00 
100.0° 

45.3° 
241.0° 

61.6° 

16-    20-|* 
71-48 
95-    74 

No.  Cent 

21-    26-I- 

Totals  and  av 

705-9 

2.67 

37-8     1     91-4° 

14-5 

9.2 

12.3 

Penna.,  Mid.  Div 

W.  Div  

P.  &N.  Y.  Canal 

X30.8 

116. 7 
94-7 
38.6 

287.5 
34-2 

146.5 
21.0 
63.5 
69.9 

1.92 
2.04 
1.76 
2.18 
1.62 
2.52 
2.81 
3.10 

2-93 

3.86 

34-3 
45-0 
56.0 
45-0 

50.6 
46.0 

43-4 
45-3 

46.8° 
72-5° 
54 -0° 

106.0° 
50.3° 
91.0° 

104.3° 
72.8° 

162.0° 

17.2 
17.4 
41.7 
II. 0 
21.7 
1-3 
31-5 
37-4 
47-5 
22.0 

2.0 
3.6 
0.3 
7-5 
0.6 
9.6 
0.2 

0-3 
4.2 

3-4 

4.6 
15-7 
2.6 
8.6 
8.7 
9.4 
II. 0 

";i 

9.1 

29-    19 

45-  52+- 
20-  38 
4=;-  43 

Phiia.  &  Erie 

"      (Su  limit  Section) 

Pitts.  «&  Connell 

W^estern  Pa 

21-  24-I- 
53-105  . 

32-    204- 

52.8 
57-  53 

Wilm.&NoV. ■.■.'.  .*.';;■.". 

Totals  and  av 

1,001.4 

2.47 

45-3 

8.-4° 

24.9 

3-2 

8.7 

Summary  of  North-Eastern  States. 


No  of 
Roads 


Divs. 


State. 


New  England. 
New  York 

New  Jersey... 
Pennsylvania., 

Totals  and  av 


Miles 

of 
Road. 


1,859 
457 
918 
773 
517 
138 
705 

1,001 


Curvature, 


Curves 
Per 

Mile. 


1.76 
1.48 
1.58 
1.67 
1.52 
0.79 
2.67 
2.47 


P.  C. 

Curved. 


37-8 
45-3 


Deg, 

Per 

Mile. 


46.6° 
60.2° 
36.0° 
41.4° 
33-7° 
25-3° 
91.4° 
81.4° 


55-9" 


Grades. 


P.  C. 

Level. 


30-9 
13.6 
34-1 
21.0 
20.6 
21.3 
14-5 
24.9 

22.8 


Rise 

Per 

Mile,* 


1-7 
3-1 
2.1 
9.8 
7,2 
1-3 
9.2 
3-2 


Rise 
and 
Fall 
Per 

Mile.* 


50  9 
13.6 
7-4 
8.3 
9-5 
13-5 
"•3 
8.7 


Compare  Summary  of  Table  102,  with  note. 


CHAP.   VIII,— CURVATURE— AMOUNT  OF. 


261 


The  statistics  which  appear  in  this  and  the  following  Tables  102,  103,  104  were  com- 
puted by  the  writer  from  time  to  time  from  the  statistics  which  were  gathered  for  a  large 
part  of  the  mileage  of  the  United  States  by  the  Census  of  1880,  and  thrown  into  the  cen- 
sus reports  in  an  utterly  valueless  condition,  without  even  being  totaled.  Not  much  can 
be  done  with  them  at  best,  as  the  blank  was  not  properly  prepared  ;  but  as  they  are  a 
record  which  exists  nowhere  else,  and  is  very  useful  in  a  certain  way,  they  have  been  in 
part  here  given.  The  reported  "  maximum  grades"  must  be  received  with  a  great  deal 
of  suspicion,  as  some  of  them'  are  pusher  grades  and  some  of  them  only  a  few  hundred 
feet  long.  The  striking  excess  of  average  grade  in  the  prairie  States  over  what  exists 
in  the  East  is  clear  enough,  and  an  undoubted  fact. 


Table  102. 

Statistics  of  Grades  and  Curvature  on  the  Railways  of  the  North 

Central  States. 

[Computed  from  the  Census  Statistics  of  1880.    See  note  to  Table  loi.] 
Ohio  and  Indiana. 


Miles 

of 
Road. 

Curvature. 

Grades. 

Name  of  Road. 

Curves 
Per 
Mile. 

p.  c. 

Curved 

Deg. 
Per 

Mile. 

P.  C. 

Level. 

Rise 
Per 

Mile.* 

Rise 

and 

Fall 

Per 

Mile.* 

Ruling- 
Grades. 

Cin.,Wab.  &Mich.... 

C.,C.,C.  &I.  (N.  End). 

no. 7 
138.0 
203.1 

98.9 
98.0 

143-9 
158.7 
139.8 
109.0 
104.2 

0.56 
0.23 
0.36 
0.65 
1.90 
1.29 
2.03 
0.42 
0.60 
0.28 

9.0 
14.3 
34-7 
28.5 

31-5 
7.0 

15. 1 
5-4 

1.2° 

6.7° 
8.9° 
14.6° 
5-2° 

4-6° 

27.4 
8.0 
8.3 
13.0 
48.6 
I5-I 
20.5 

I.O 

19.8 
15.3 

0.7 
0.9 
2.4 
I.I 
3-2 
1-3 
0.7 

1-3 
0.0 

9-7 

7-8 

11 

13-7 
7-3 
9-5 
6.6 
3-8 

10.3 
6.8 

52.8    + 

"           "    (Ind.  End) 

C.,H.&Ind 

Cld.  &Mar 

C,  Mt.  V.  &Del 

C,  Tusc.V.  &W 

Dayton  &  Mich 

Evansv.  &  T.  H 

Ft.  W.,  M.  &Cinc.... 

38-  39 
65-65 
79-  67 
66-  66 
60-  47 
31-  25 
43-  42 
45-  50 

Totals  and  av 

1,304-5 

0.83 

16.3 

16.1° 

1      ^7-7 

1.2 

7.8 

Ind..  D.  &S 

J.,  Mad.  &  Ind.CS.  End) 
L.  Erie  &  W  .   

152.0 

IIO.O 

353-0 
540-5 
130.8 
387-9 
103.7 
338.0 
192.8 
40.0 

0.32 

0.54 
0.19 
0.41 

O.IO 

0.74 
0.33 

■■2:58" 

1.02 

7.0 
10.4 

6.6 
12.0 

4-9 
23.7 
10.6 
21.7 
33-7 
19.4 

5-9°    1 
9-5° 

li 

21-5° 

5-2°   1 

28.3° 

46.0° 

24.0° 

33-5 
23-7 
15.4 
18.0 
ig.o 
18.6 
II. 7 

"16.5" 
43.2 

1-5 
2-3 
0-5 
0.1 
I.I 
1.6 
4.4 
0.2 
0.1 
0  fi 

6-9 
5-4 
7-1 

5-2 

4.2 
11.4 
5-8 
8.8 
10.8 
10  0 

40- 
37-37 
52.8 
53-  46- 
21-27 
53-  60 
53-  57 

L.  S.  &M.  S 

"         "     (Air-Line) 

N.Y.,Pa.&0 

"      (W.  Div.  only) 
0.  &Miss 

P.,  C.  &St.  L 

T.  H.  &S.  E 

52.8 
52.8 

Totals  and  av 

2,348.7 

0.70 

15.0 

15-9° 

7-5 

See  note  to  Table  loi. 


262 


CHAP.    VIII.— CURVATURE— AMOUNT  OF. 


Table  102. — Continued. 
Michigan. 


Miles 

of 
Road. 

Curvature. 

Grades. 

Name  of  Road. 

Curves 
Per 

Mile. 

P.  c. 

Curved- 

Deg. 
Per 

Mile. 

P.  C. 

Level. 

Rise 
Per 

Mile.* 

Rise 

and 

Fall 

Per 

Mile.* 

Ruling 
Grades. 

Chicago  &G.  Trunk... 

Det.,  G.  H.  &Mil 

J     L  &  Sag 

330-5 
189.0 
236.0 

63.1 
103.6 
270.0 

61. 1 

0-34 

0.62 
2.14 

T.OI 
0.61 
I. 16 

^7 
18.0 
II. 0 
43-4 
II-3 
26.8 
24.0 

i^:^2: 

11.0° 

18.8° 
19-5° 

23s 
19.0 
19.9 
25-8 
27-5 
21.0 

30-3 

0.3         :            7-2 

0.0                    7.8 

1.9     1       6.8 
0.0          23.0 
2-5     :       7-3 
0.0            6.5 
4-3            8.1 

54-  SI 

42 

52        + 

Marq.,  H.  &  Ont 

Mich.  Air-Line 

Mich   C   

200. 
39-  45 
49-  38 

No.  C.  Mich 

52.8 

Totals  and  av 

1,253-3 

0.91 

20.2 

17.4° 

23-9 

1-3     1       9-5 

Illinois. 


Am.  Cent 

Belleville  &  Eld. 
C.  &  Alton , 


C,  B.  &Q 


C.  &E.  Ill  .-.. 
C,  M.  &  St.  P. 


Totals  and  av. 


Ch.  &  Spr 

Danv.  &S.  W 

O.  &  Miss 

111.  Central 

(N.  End  only) 
"        Branches. . 


Totals  and  av. 


50.6 
49-7 

243-5 
27.8 
79-8 
38-1 

203.3 
99-7 

107.5 


III. 5 
100. 1 
228. o 

364-7 

(252.1) 

340 


145 -I 


0.30 
0.98 
0.27 
0.79 
0.40 
1.08 
0.38 
0.78 
0-39 
0.36 


0.30 
0.38 


(0.06) 


II. a 
15-4 

2.7 
25-3 

8.0 
23.0 
10.8 
14.4 
10.7 

9.0 


5-1 

7-4 
14.9 

9.0 
(3-27) 
12.0 


9-7 


10. o 

7.0 

22.0 

27.8 

6.6 

30-7 
21.3 
19.0 
14.0 
35-3 


19-4 


42.0 
(45.7) 
30.0 


29.7 


5-5 
1.8 
0.9 
0.4 
0.2 
5-2 
0.2 
3-1 
0.1 
0.2 


0-5 

2.6 
0.2 

0.9 

(0.5) 


5-3 
14.6 
6.3 


7-» 
6.7 
7-5 
6-3 
4-9 


6.4 


9.1 
8.9 
9.1 
5-8 
(49) 
9.6 


i-5 


37-  52 
100-119 

43-  80 
26-  35 
45-  61 
64-  64 

38-  55 
37-  49 
60-  33 
32-  26 


57-  66 

58-  58 


63-  45 
(39-  33) 
77-86 


Iowa. 


Burl.,  C.  R.  &N... 

Burl.,  &S.  W 

"       (Mo.) 

Cent.  la 

C.  B.  C.&W 

C,  B.  &Q 

C,  M.  &St.  P 

Dub.  &S.  C  .■'.'.'.'! 
Totals  and  av 


252.7 
59-6 
82.7 
189.0 
35-7 
280.3 
331-7 
150.6 
142.7 


1,525-0 


0.70 
1.90 
1.70 
0.94 
3-40 
0.84 
0.51 
1-53 


.36 


22.6 
36.0 
38.0 
20.2 
38.5 
32-7 
14.4 
23-7 
20.1 


27-3 


17-5" 

57-3= 
55-3= 
15-6= 


10.6° 
36-5° 
24.8° 


36.4= 


13.0 
12.0 


10.7 
13-6 


2.7 
5-6 
2.3 
1.4 
5-5 
1-7 
0.8 
4.2 
3-7 


C4-9 


66.0 
68.6 
68.6 

76-  73 
175-160 
70-  70 
58-  74 
63-  58 
80-  81 


*  See  note  to  Table  loi. 


CHAP.   VIII.— CURVATURE— AMOUNT  OF. 


263 


Table  102. — Continued. 
Wisconsin,  Minnesota,  and  Dakota. 


Miles 

of 
Road. 

Curvature. 

Grades. 

Name  of  Road. 

Mile.    Curved. 

Deg. 
Per 

Mile. 

P.  C. 

Level. 

Rise 

Per 

Mile.* 

Rise 
and 
Fall 
Per 

Mile.* 

Ruling 
Grades. 

C,  M.  &St.  P 

194.4 
196.4 
192.0 
202.1 
215-4 

0.58 
0.58 
0.54 
0.70 
1. 00 

20.0 
I5-I 
12.0 
14.8 
23-7 

14.9° 

12.8° 
13.4° 
30.2° 

36.0 
17.6 
20.0 
23.0 
21.0 

0.1 
0.4 
0.0 
6.5 
0.9 

S-4 
9.0 

10.5 
8.3 

II. 4 

35-  36 
50-  53 
69-  53 
74-  63 
63-  52.8 

t(             ii 

«(             (( 

"     

Totals  and  av 

1,000.3 

0.68 

17. 1 

16.9° 

24.7 

1.6 

8.9 

Summary  of  the  Western  States. 


Statb. 

Miles 

of 
Road. 

Curvature. 

Grades. 

No.  of 
Roads 

or 
Divs. 

Curves 
Per 

Mile. 

P.  C. 

Curved. 

Deg. 
Per 

Mile. 

P.  C. 

Level. 

Rise 

Per 

Mile.* 

Rise 
and 
Fall 
Per 
Mile.* 

10 
10 

7 

Ohio  and  Indiana 

Michigan 

Illinois        ....       

1,304  s 
2,348.7 

1,253-3 

0.83 
0.70 
0.91 

16.3 
15.0 
20.2 
13. 1 

9-7 
27-3 

16.1° 

6.9° 
9.0° 
36.4° 

17.7 
22.2 
23-9 
19.4 
29.7 
15-3 

21.4 

1.2 
1.2 
1-3 

1.8 
0.9 
3-1 

1.6 

7.8 
7-5 
9-5 
6-4 
8-5 
14.9 

5 

7 

Iowa 

1,145.1,     0.32 
1,525.0      1.36 

49 

Totals  and  av 

8,558.8 

o.,8 

16.9 

16.9° 

9.1 

99 

Ditto,  Eastern  States, 
from  Table  loi .    . . 

5,372-0 

1.88 

35-5 

55-9° 

22.8 
22.0 

4-7 
1.9 

13.0 

17 

Ditto,  South'n  States, 
from  Table  103 

3,511.2 

1. 10 

27.6 

31-5° 

12.4 

*  See  note  to  Table  loi. 


The  most  important  moral  to  be  drawn  from  comparison  of  this  with  the  preceding 
table  is  in  the  last  column  of  the  table,  which  it  seemed  impossible  to  average,  viz.,  in 
the  excessive  ruling  grades  throughout  the  West,  which  are  considerably  heavier  than 
in  the  East,  in  spite  of  the  very  much  easier  alignment  and  less  rise  and  fall.  In  lo- 
calities it  was  impossible  or  very  difficult  to  avoid  this,  owing  to  a  succession  of  long  low- 
ridges  extending  for  great  distances  in  each  direction;  but  for  the  most  part  it  is  due  to 
bad  judgment  in  location,  in  avoiding  curvature  and  loss  of  distance  at  any  sacrifice  of 
grade,  whereas  the  reverse  should  be  the  rule.     See  Chapter  XX. 


264 


CHAP.    VIII.— CURVATURE— AMOUNT  OF. 


Table  103. 

Statistics  of  Grades  and  Curvature  on  the  Railways  of  the  South- 

ERN  States  and  Missouri. 


[Computed  from  the  Census  Statistics  of  ig 
Virginia. 


See  Note  to  Table  loi.] 


Miles 

of 
Road. 

Curvature.              1 

Grades. 

Name  of  Road. 

Curves 
Per 

Mile. 

P.  c. 

Curved. 

Deg. 
Per 

Mile. 

P.  C. 

Level. 

Rise 
Per 

Mile.* 

Rise 

and 

Fall  Per 

Mile.* 

Ruling 
Grades. 

Atl  ,  M.  &  0     

408.6 

419.6 

140.6 

81.7 

1.6 
2.4 

I.O 

36.3 
47.0 
33-8 
27.0 

38.0° 
30.0° 

15-5 
13-5 

2.7 

4.1 
1.2 
2.7 
I.I 

13-9 
13-5 
12.4 
10.2 

80-70  — 

Ches  &  0 

Rich.  &  Dan   

R.,F.  &  Potomac 

116-55 

Totals  and  av....... 

1,050.5 

1-7 

36.0 

46.9° 

10.6 

2-3 

12.5 

North  and  South  Carolina  and  Georgia. 


C,  Col.  &  Aug 

Ga.RR.&B 

Macon  &  B 

191. 0 
171. 0 
188.0 

1.05 
0.8s 
0.33 

40.6 
33-5 
16.0 

36.0° 
31-3° 
9.6° 

9.9 
41.0 

1.8 
5-3 
2.0 

22.9 
10. 5 
5-4 

60-67 
39-6 

75 

Totals  and  av 

550.0 

0.78 

30.0 

25.6° 

25-4 

3-0 

12.9 

Kentucky  and  Tennessee. 


Cin.So 

Eliz.,  Lex.  &  B.  S 

L.  &N 

335-9 
102.0 
113-5 
71-3 
272.0 
472.0 
135-2 

1.92 

1-93 
0.81 
0.48 
0.66 
0.80 
0.88 

35-2 
29-5 
19.4 
14.0 
17.0 

31-3 
20.0 

55 

13 
16 
20 
22 

4° 
9° 
9° 

2° 
9° 

13-4 
15-4 
29.0 
22.0 
15.2 
25-5 
12.5 

0.6 
2.8 
0.3 
0.8 
0.8 
0.6 
0.2 

15-6 
15-3 
II. I 
16.7 
12.9 

7-2 

17-5 

60  - 
60-66 
70-53 
70-70 

Memph  &  C           

52.8 

Mobile&O  

St.  L.&S.E 

40-30 
216-90 

Totals  and  av 

1,501.9 

1.07 

23.8 

28.4° 

19.0 

0.9 

13-8 

Missouri. 


Bruns.  &  Chill.. 
Burl.  &S.  W..., 
Cape  G.  &  St.  L 
H.  &St.  Jo 

Totals  and  av. 


79-7 
82.7 
40.0 
206.4 

0.76 
1.70 
0.20 
0.76 

14.7 

38.0 

4-5 

25-0 

22.7° 

55-3° 

17.8° 

46.0 
12.0 
51-6 
20.0 

1-3 
2.3 
0.0 
1-7 

5-6 
17-3 

1-7 
16.9 

408.8 

0.85 

20.5 

25.1° 

32.4 

1-3 

10.4 

52. » 

68.6 
1 6-1 1 
80-80 


CHAP.  VIII,— CURVATURE— AMOUNT  OF. 


265 


Table  103. — Continued. 


Summary  of  Southern  States. 


No.  of 
Roads 

or 
Divs. 

State. 

Miles 

of 
Road. 

Curvature. 

Grades, 

Curves 
Per 

Mile. 

P.  C. 

Curved. 

Deg. 
Per 

Mile. 

P.  C. 

Level. 

Rise 
Per 

Mile.* 

Rise 

and 
Fall  Per 

Mile.* 

4 
3 
6 

Virginia 

N.  and  S.  C.  and  Ga 

Ky  and  Tenn 

1,050.5 
550.0 

1,501.9 
408.8 

X.70 
0.78 
1.07 
0.85 

36.0 
30.0 
23.8 
20.5 

46.9° 

.   25.6° 

28.4° 

25-1° 

10.6 
25-4 
19.0 
32.4 

2.3 
3-0 
0.9 
1-3 

12.5 
12.9 
13.8 
10.4 

4 

Missouri 

17 

3,511-2 

1. 10 

27.6 

3..5°  j 

22.0 

1.9 

12.4 

*  See  Note  to  Table  loi  and  Summary  to  Table  102. 

In  Holland,  which  has  the  levellest  railways  in  Europe,  62  per  cent  is  level,  and  only 
27  miles  out  of  945  on  grades  between  0.5  and  1.5  per  cent. 

In  Germany  25  per  cent  of  the  mileage  is  between  0.5  and  1.5  per  cent,  and  a  little 
over  25  per  cent  curved. 

In  Norway  a  little  more  than  50  per  cent  is  curved,  and  37^^  per  cent  has  grades  be- 
tween 0.5  and  1.5  per  cent. 


Table  104. 


Curvature  Per  Mile  on  Various  Railways  in  the  Rocky  Mountain 
Region  which  have  a  Great  Amount  of  Curvature. 

[Computed  from  Census  Statistics  of  1880.] 


Road. 

Miles. 

Av.  Deg. 
Per  Mile. 

Road. 

Miles. 

Av.  Deg. 
Per  Mile. 

134 
los 
83 
13s 
121 
116 
178 

32  o" 
151.0° 
93.0° 
16.0° 
39-5° 
48.5° 
27-3° 

Colo.  Cent     

34 
II 
22 
100 
105 
6s 
31 
143 
142 

420.0° 
327.0° 
278.0° 

30-5° 
20.9° 

59-2° 
43.0° 

Virg.  &  Truckee 

Cent.  Pac - 

Utah&  No 

(from  San  Francisco 
west.) 

Union  Pac 

"    West  End... 

Texas  Cent.. 

So.  Pacific 

Average 

872 

52-0° 

24.7° 

63.6° 

266  CH.  VIII.— CURVATURE— MEANING  OF  DEGREE  OF  CURVE. 

More  commonly  yet,  the  radius  is  taken  direct  from  a  table,  but  nothing  is 
ever  done  with  it  in  practical  field-work,  and  it  is  only  of  importance  for 
recording  on  maps  or  for  use  in  solving  problems. 

262i  Among  English  engineers  curves  are  usually  defined  as  of  so  many 

chains  (66  ft.)  radius.     The  radius  of  a  i°  curve  in  chains  is  — -^  =  86.813 

chains,  so  that  the  one  method  of  designation  may  be  converted  into  the  other 
by  the  formulae, 

r,   .  ,        .  86.813  .  r.  86.813 

R  m  chams  =  — -: — ,     and     D  = 


D  R  \n  chains 

263.  Continental  engineers  designate  curves  by  the  radius  in  metres.     The 

radius  in  metres  of  a  1°  curve  being ^ —  =  1746.4  metres,  we  have,  forcon- 

3.2804 

verting  the  one  method  of  designation  into  the  other,  the  similar  formulae, 

1746.4  ,      ^  1746.4 

R  in  metres  =  -^-,     and     D  —         '^    ^ 


R  in  metres 


264i  American  engineers,  and  those  adopting  American  practice,  when 
working  with  the  metric  system,  use,  as  the  unit  chord,  a  chain  of  20  metres 
(65.61  ft.)  divided  into  100  links  of  2  decimetres  (.656  ft.)  each.  The  radius  of 
a  curve  having  1°  of  central  angle  for  a  chord  of  100  of  any  unit  is  5730  (5729.65) 
of  that  unit,  so  that  the  radius  in  metres  of  a  1°  metric  curve  is  5729.65  X  0.2  = 
1145.93  (1146)  metres,  or  one  fifth  as  many  metres  as  there  are  feet  in  the  radius 
of  a  1°  foot  curve — as  is  natural  from  the  fact  that  there  are  only  one  fifth  as 
many  units  in  the  chord. 

265.  In  stationing  under  the  metric  system,  however,  the  best  practice  is  to 
use  lo-metre  stations,  setting  stakes  at  every  other  station  only  (or  i  chain 
apart)  on  tangents  and  easy  curves,  and  at  every  station  (or  half-chain)  on  sharp 
curves.     In  practice  this  produces  little  inconvenience. 

266.  The  radius  in  feet  of  a  1°  metric  curve  is  — '- —  of  the  radius  of  a  1° 

100 

•'  foot"  curve,  or  a  little  {i\  per  cent)  less  than  f  (.667)  and  a  little  (4.6  per  cent) 
more  than  f  (62.5),  either  of  which  vulgar  fractions  may  be  used  for  approximate 
inter  conversions. 

267.  Whether  with  English  or  metric  measures,  on  sharper  curves  than  8°  or 
10°,  the  chord  becomes  so  much  shorter  than  the  subtended  arc  that  it  becomes 

inaccurate  to  assume  the  radius  as  — — -.     To  obviate  this  difficulty,  it  is  now 

becoming  usual  in  the  best  practice  to  run  in  curves  sharper  than  8°  with  half 
the  usual  unit  chord,  or  50  ft.,  and  to  run  in  curves  sharper  than  16°  with  one 
FOURTH  the  usual  unit  chord.     It  then  becomes  literally  true,  to  the  nearest  even 


CH.    VIII.— CUR  VA  TURK— MEANING  OF  DEGREE  OF  CUR  VE  267 


foot,  that  the  radius  of  all  curves,  of  whatever  degree,  is  given  by  the  formula 

It  is  expedient  for  practical  reasons  to  set  stakes  thus  frequently  on  sharp 
curves,  so  that  this  practice  involves  no  inconvenience. 

It  is  rarely  necessary  or  expedient,  in  practical  location,  to  use  other  than 
even  degrees  (or,  at  most,  even  half-degrees)  of  curvature,  except  in  "  closing 
curves,"  to  connect  with  other  lines,  and  except  that  certain  degrees  which  con- 
tain an  even  number  of  minutes  (as  50',  1°  40'  (100'),  3°  20'  (200')  curves)  are, 
for  practical  convenience  in  the  transit  work,  sometimes  preferred. 

Table  105  gives  the  radii  in  feet,  chains,  and  metres  of  all  the  curves  below 
30°  which  are  much  used  for  either  metric  or  English  measures.  We  now  re- 
sume consideration  of  the  various  objections  to  curvature. 


Table  105. 
Radii  of  Curves  of  Various  Degrees  in  Feet,  Chains,  and  Metres. 


Degree 

of 
Curve. 

Curves  run  by  English  Measures. 

Curves  Run  by  Metric  Meas- 
ures (20  M.  Chain). 

Radius  in 
Feet. 

Radius  in 
Ciiains. 

Radius  in 
Metres. 

Radius  in 
Metres. 

Radius  in 
Feet. 

0°   30' 
0°   50' 

\°  40'   8 

^I    ,  T 
2  30  -o 

I   1 

7° 
8° 

11,460 
6,876 
5,730 
3-438 
2,865 
2,292 
1,910 
1,719 
1,433 
1,146 

955 
819 

717 

173.626 
100.408 
86.813 
52.089 
43-406 
34-726 
28.938 
26 . 044 
21.704 

17-363 
14.469 
12.402 
10.852 

3,492  8 

2,095.7 

1,746.4 

1,047.8 

873.2 

698.6 

582.1 

523-9 
436.6 

349-3 
291. 1 
278.1 
218.3 

2,291.86 
1,375-12 
1,145-93 
687-56 
572.96 
458.28 
381.98 
343.78 
286.48 
229.19 
190.99 
163.70 
143-24 

7,519-2 

4,511-5 

3,759-6 

2,255.8 

1.879-8 

1,503-8 

1,253-2 

1,127.9 

939-9 

751-9 

626.6 

537-1 
470.0 

S   1 

12°  go- 

14°       u 

16° 

637 
573 
521 

478 
409 
358 

9.646 
8.681 
7.892 
7-236 
6.201 

5.426 

194.0 
174.6 

158.8 

145.5 
124.7 
109. 1 

127-33 

114-59 

104.18 

95-50 

81.85 
71.62 

417-7 

376.0 

341.8  ' 

313-3 

268.5 

235-0 

18°      1 
20°  -s  "S  lA 
24:  dJ" 
30°     u 

318 
286 

239 
191 

4-823 
4-340 
3-618 
2.894 

97.0 

87-3 
72.8 
58.2 

63.66 
57-30 
47-75 
38.20 

208.9 
188.0 
156.6 
125-3 

268  CHAP.   VIII.— CURVATURE— MAKING   TIME. 


DIFFICULTY   IN    MAKING    TIME. 

268.  It  is  beyond  dispute  that  the  addition  of  a  sufficiently 
great  amount  of  sufficiently  unfavorable  curvature  will  seriously 
cripple  any  line.  The  curvature  is  objectionable  not  alone  for 
fast  passenger  trains  but  for  freight  trains  also,  for  it  is  fully  as 
difficult  and  as  dangerous  to  run  freight  trains  over  sharp  curves 
at  25  or  30  miles  per  hour  as  passenger  trains  at  60  miles  per 
hour,  owing  to  the  difference  in  their  mechanical  construction, 
and  yet  with  each  alike  such  speeds  are  often  necessary. 

Here,  as  elsewhere,  however,  the  true  question  before  us  is 
not  "  Does  the  difficulty  exist  ?"  but  "  How  great  is  the  difficulty, 
and  what  are  its  limits  ?"  Considering  the  question  in  this  light, 
and  remembering  that  we  are  not  now  speaking  of  nor  consider- 
ing cost,  but  only  physical  possibilities,  experience  seems  to  in- 
dicate that,  up  to  reasonable  amounts  of  8°  or  even  10°  maximum 
curvature  (717  to  573  feet  radius)  this  difficulty  is  not  one  which 
results  in  very  serious  consequences;  for  lines  which  are  little 
less  than  a  succession  of  such  curves  have  as  fast  schedules  and 
make  as  good  time  and  connections  as  more  favored  lines.  On 
curvature  of  shorter  radius  the  centrifugal  force  become  so 
great  that  either  the  speed  must  be  checked,  or  the  additional 
pressure  against  the  outside  rail  becomes  objectionable. 

269.  In  the  days  of  hand-brakes  and  iron  rails  this  necessity 
of  checking  speed  on  sharp  curves  was  (or  would  have  been)  a 
serious  obstacle  to  habitual  fast  running,  but  since  the  introduc- 
tion of  air-brakes  and  steel  rails  a  train  can  be  checked  up 
slightly  with  such  a  very  trifling  loss  of  time — and  if  it  should 
chance  to  be  omitted,  the  consequences  are  so  much  less  likely  to 
be  disastrous — that,  within  the  limits  of  choice  which  are  ordi- 
narily open  to  the  engineer,  this  question  of  making  time  is  much 
less  likely  than  heretofore  to  be  seriously  affected  by  either  the 
amount  or  the  radius  of  curvature.  Since  the  introduction  of 
steel  rails,  the  question  now  chiefly  concerns  passenger  traffic, 
any  curve   of  less  than   20°  laid  with  steel   (and,  in   fact,  with 


CHAP.    VIII.— CURVATURE— MAKING   TIME.  269 

properly  designed  engines,  much  sharper  curves)  being  safe  (we 
are  now  considering  nothing  else)  at  ordinary  freight-train 
speed. 

270.  For  any  ordinary  differences  of  radii  the  reduction  of 
speed  necessary  to  eliminate  the  additional  centrifugal  force 
due  to  a  shorter  radius  is  not  great.  Much  misapprehension  in 
this  respect  exists,  owing  to  forgetfulness  or  ignorance  of  the 
fact  that  centrifugal  force  increases  only  as  the  degree  of  curva- 
ture, but  as  the  square  of  the  speed,  so  that  comparatively  trifling 
decrease  of  speed  will  place  very  material  differences  of  radius 
on  an  equality  in  this  respect.  Thus,  to  obviate  the  effect 
of  sharpening  a  curve  from  a  5°  to  a  10°  we  do  not  need  to 
halve  the  speed,  but  only  to  reduce  it  in  the  proportion  of  i  :  1^2, 
so  that  if  a  speed  of  60  miles  per  hour  be  safe  on  a  5°  curve 
a  speed  of  42.43  miles  per  hour  (  V'-^/)  is  equally  safe  on  a  10° 
curve ;  and  if  we  again  double  the  degree  of  the  curve  to  20°, 
we  only  reduce  the  admissible  speed  of  equal  safety  by  12.43 
miles  per  hour,  or  to  30  miles  per  hour. 

This  statement  neglects  the  fact  that  the  same  excess  of  centrifugal  force  is 
more  dangerous  on  a  sharp  curve  than  on  an  easy  one;  but  the  difference  in 
that  respect,  while  it  exists,  is  small,  because  the  lateral  flange  pressure  is 
(contrary  to  a  common  misapprehension)  unaffected  by  the  degree  of  curvature. 

271.  The  precise  effect  of  curvature  on  the  admissible  speed  may  be 
determined  as  follows : 

The  centrifugal  force  C  of  any  body  of  weight  W  moving  at  v  ft. 
per  second  in  a  circle  of  r  ft.  radius  is,  in  the  latitude  of  New  York, 

C  =^^  (log  32.16,  1.50731) .     (I) 

To  determine  the  centrifugal  force  of  a  body  moving  at  V  miles  per 

hour  on  a  Z?"  curve,  we  have  7/  =  -^ — -—  =  1.467  V,  and  r  =  ^~--.    Sub- 

60  X  60  D 

stitutiiig  these  values,  we  obtain 

C:=  .00001167  (log  5.06722)  VD  y.  IV,  .    .     (2) 


270 


CHAP.   VIIL— CURVATURE— MAKING   TIME, 


Or,  for  the  centrifugal  force  in  lbs.  per  ton,  multiplying  the  second 
member  of  the  above  equation  by  2000,  we  obtain 


C=  .023:48  VD  (log  8.36825). 


(3) 


From  this  formula  Table  106  is  calculated,  giving  the  centrifugal  force 
in  lbs.  per  ton  of  2000  lbs.  on  any  curve  at  any  speed. 


Table  106. 

Centrifugal  Force  in  Pounds  Per  Ton  of  2000  lbs.  on  Various  Curves 
AT  Various  Speeds. 

[Computed  by  Eq.  (3),  par.  271.] 


Speed 

Miles  Per 

Hour. 

Degree  of  Curve. 

1° 

5° 

10° 

15° 

20° 

10 
20 
30 

2.33 

9-34 

21.01 

37.36 

58.37 

84-05 

114.40 

149-43 
189.12 
233-48 

11.67 

46.70 

105.07 

186.78 

291.85 
420.26 

572.03 

747-14 

945  -  59 

1,167.40 

23-35 

93-39 

210.13 

373-57 

35-02 
140.09 
315-20 

560.35 

875-55 
1,260.79 

1,706.08 
2,241.41 
2,836.78 
3,502.20 

46.70 
186.78 
420.26 

40 

747.14 

50 
60 

70 

80 

90 

100 

583-70 
840.53 
1,144.05 
1,494.27 
1,891.19 
2,334-80 

1,167.40 
1,681.06 

2,288.10 
2,988.54 
3,782.38 
4,669. 5o 

The  centrifugal  force  on  any  other  curve  is  directly  as  the  degree  of  curvature. 
The  heavy  division  hnes  mark  the  assumed  maximum  limit  of  speed  for  safety; 
the  centrifugal  force  is  14  W. 


-when 


272.  For  the  train  to  be  overturned  it  is  essential  that  the  resultant 
of  the  centrifugal  force  and  gravity  shall  fall  without  the  base,  which  is 
upon  the  point  of  occurring,  on  a  level  track,  as  will  be  clear  from  Figs. 
18  and  19,  when 

W       cent.  grav.  above  track 
"C   ~  half-gauge 


CHAP.     VIII.— CURVATURE— MAKING    TIME. 


71 


The  height  of  the  centre  of  gravity  varies  in  different  cars  and  loco- 
motives from  as  little  as  \\ 
to  5  ft.,  in  heavily  loaded  flat 
cars,  to  as  much  as  7  ft.  in 
some  types  of  locomotives. 
Assuming  it  at  6  ft.,  as  in  Fig. 
18,  makes  some  allowance  for 
the  beneficial  effect  of  super- 
elevation ;  which  moreover,  in 
the  extreme  case  of  danger  of 
overturning,  does  not  have 
its  full  effect,  because,  long 
before  the  point  where  it  is 
imminent,  centrifugal  force 
will  so  act  upon  the  springs  as 
to  throw  the  centre  of  gravity 
into     nearly    the    position    it 


Fig. 


Fig.  18. 

would  occupy  if  the  cars  were  a  rigid  body  and  there  were  no  super- 
elevation. 

The  maximum  superelevation  is  about  one  seventh  the  gauge,  or 
about  eight  inches.  This  may  be  considered  as  reducing  the  centrifugal 
force  by  one  seventh  of  the  weight  of  the  body,  or  286  lbs.  per  ton,  barring 
the  action  of  the  springs. 

273.  We  have,  then,  assuming  the  centre  of  gravity  to  be  6  ft.  above 
the  rails,  and  half  the  gauge  (between  centres  of  rails)  to  be  2.4  +  ft.. 


C 


6.0 
2.4 


(4) 


whence  C  =  0.4  ^  when  the  train  is  upon  the  point  of  overturning. 
But  [eq.  (2)]  we  have  also 

C  =  . 00001167  V'DW, (2) 

and  from  eqs.  (2)  and  (4)  we  readily  obtain 


F=|/- 


0.4 


185.1 


.000011672^ 


(5) 


this   being  the   equation   of  the  maximum  velocity  in  miles  per  hour 
which  a  train  can  have  without  leaving  the  rails  by  overturning. 

274.  Long  before  this  comes  the  point  of  danger,  and  long  before  that 


272  CHAP.    VIII.— CURVATURE— MAKING    TIME. 

again  comes  the  point  of  more  or  less  serious  impacts,  oscillation,  and  ap- 
prehension of  danger.  The  minimum  limit  of  objectionable  speed,  below 
which  there  may  be  said  to  be  not  only  no  sensible  danger,  but  no  possibil- 
ity of  annoyance  or  apprehension  of  danger,  does  not  from  its  nature  admit 
of  exact  determination  ;  but  we  shall  obtain  a  result  corresponding  closely 
with  what  have  in  fact  proved  wholly  unobjectionable  velocities  on  various 
curves  if  we  assume  this  minimum  limit  to  be  when  the  action  of  the 
centrifugal  force  upon  the  car-body  does  not  more  than  suffice,  on  easy 
curves  having  the  usual  (but,  as  we  shall  shortly  see,  probably  too  small) 
superelevation  of  about  \  in.  per  degree,  to  throw  it  over  so  as  to 
maintain  it  level  despite  the  superelevation.  The  point  at  which  this 
occurs  may  be  determined  as  follows  : 

The  springs  of  an  easy-riding  passenger  car  have  been  compressed 
through  perhaps  6  in.  by  the  weight  of  the  car-body  from  their  unloaded 
dimensions.  An  addition  of  -^  of  the  weight  resting  on  a  spring,  con- 
sequently, will  compress  it  through  an  additional  \  in.,  and  an  addition 
of  ^  of  the  weight  resting  on  it  will  compress  it  through  \  in.  The 
shifting  of  this  much  of  the  weight  to  the  outer  springs  involves  a  cor- 
responding decrease  of  the  compression  in  the  inner  springs  ;  so  that,  as- 
suming the  leverage  of  the  centre  of  gravity  of  the  car-body  only  to  be 
equal  to  that  of  the  resisting  moment  of  the  springs,  as  it  approximately 
is  (see  Fig.  18),  a  centrifugal  force  of  -g^,  or  say  0.04  W,  will  suffice  to 
preserve  the  car-body  level.  Substituting  this  coefficient,  0.04  for  0.4  in 
eq.  (5),  we  obtain 


.=/ 


0.04  _   58.536.  ^^y 


.00001  i6jD       ^/j) 


this  being  the  equation  of  the  inferior  limit  of  the  dangerous  velocities ; 
i.e.,  that  at  which  the  car-body  of  the  easiest-riding  coaches  will  at  the 
most  remain  level,  and  not  have  a  cant  toward  the  outside  of  the  rail,  with 
the  smallest  usual  superelevation. 

275.  As  both  the  possible  compression  of  the  springs  and  the  amount 
of  superelevation  soon  reach  a  maximum  limit,  this  particular  criterion 
for  determining  what  is  the  inferior  limit  of  obnoxious  velocities  does 
not  hold  precisely  and  theoretically  true  when  extended  to  the  sharper 
curves,  since  it  would  require,  for  instance,  on  a  20°  curve,  10  in.  of 
superelevation  and  5  in.  compression  of  the  springs,  neither  of  which 
are  admissible  ;  but  it  has,  nevertheless,  the  advantage  before  mentioned 
(par.  274)  of  corresponding  tolerably  closely  with  what  have  in  fact  proved 
wholly  unobjectionable  velocities  on  such  curves,  as  it  plainly  should  if  cor- 


CHAP.    VIII.— CURVATURE— MAKING   TIME. 


273 


rect  for  the  lower  curves.  This  appears  in  the  tabulation  of  eqs.  (5)  and 
(6)  given  in  Table  107,  for  curves  of  different  radii  up  to  a  60°  curve  (95 
ft.  radius),  the  latter  being  somewhat  easier  than  the  curve  of  90  feet 
radius  on  the  New  York  elevated  railways,  and  hence  to  be  regarded  as 
about  the  maximum.  The  trains  pass  around  these  curves  at  6  to  10 
miles  per  hour  without  any  disagreeable  centrifugal  force. 
(See  also  par.  865  et  seq.) 


Table  107. 
Giving  for  Various  Curves  the  Inferior  and  Superior  Limits  of  Speed 

WITHIN    WHICH    THE    CENTRIFUGAL     FORCE   IS    MORE    OR    LeSS    OBJECTION- 
ABLE AND  Dangerous. 

[Computed  by  Eqs.  (5)  and  (6),  par.  273.] 


Curve. 

Maximum  and  Minimum  Limits  of  Speed.    Miles  Per  Hour. 

Degree. 

Radius. 
Feet. 

Minimum.    Having  no 
Disagreeable  Effect, 

Maximum.     On  the  Point  of 
Overturning  the  Vehicles. 

2° 

4° 
6° 
8° 

2,865 

1,433 

955 

717 

41.39  Miles  per  hour. 

29.27 

23.90 

20.70         "          " 

130.89  Miles  per  hour. 
92.55 

75-57 
65.44         " 

10° 

573 

18.51  Miles  per  hour. 

58.54  Miles  per  hour. 

12° 

14° 
16° 

18° 

478 
410 
358 
319 

16.90  Miles  per  hour. 

15.64         " 

14-63 

13-78 

53.43  Miles  per  hour. 

49.47 

46.28 

43.58 

20° 

286 

13.09  Miles  per  hour. 

41.39  Miles  per  hour. 

22° 
24° 
26° 

28° 

261 

239 
221 

205 

12.48  Miles  per  hour. 

11-95 

II. 61         "          " 

11.06 

39.46  Miles  per  hour. 

37.78 
36.72 
34.98 

30° 

191 

10.69  Miles  per  hour. 

33.80  Miles  per  hour. 

40° 
50° 

143-3 
114. 6 

9.25   Miles  per  hour. 
8.28 

29.27  Miles  per  hour. 
26.18 

60° 

95.5 

7.56   Miles  per  hour. 

23.90  Miles  per  hour. 

The  speeds  in  the  last  two  columns  are  all  speeds  of  equal  safety,  those  in  the  last 
column  being  equal  to  those  in  the  preceding  column  ~-  Vio  or  3.16.     Multiplying:  or 
dividing  either  column  by  2,  3,  or  any  other  factor  whatever,  will  give  a  new  column  of 
speeds  of  equal  safe  ty. 
18 


2/4  CHAP.    VIII.— CURVATURE— MAKING    TIME. 

276.  These  maximum  and  minimum  limits  correspond  to  a  difference 
in  centrifugal  force  of  i  to  lo ;  yet  it  will  be  seen  that  the  resulting  veloci- 
ties differ  only  as  i  to  I^To  or  i  to  3.16,  as  they  should.  It  will  also  be 
seen  that  the  permissible  speed,  by  whatever  standard,  does  not  vary 
directly  as  the  radius  or  inversely  as  the  degree,  as  may  be  over-hastily 
assumed,  but  as  the  square-root  of  the  radius  or  degree.  That  is  to  say, 
on  any  three  curves  having  radii  as 

I,     2,     3, 

the  centrifugal  force  at  any  given  velocity,  it  is  true,  is  as 

3,    2,     i; 

but  the  coefficient  of  safety  against  overturning  or  of  disagreeable  or 
obnoxious  effect  of  any  kind  admissible  under  any  circumstances  on  a 
road  operated  by  steam,  is  as 

vj    4/^    vi; 

eras  1.73'    I4i.    i.oo- 

277.  We  may  also  note  that  the  maximum  necessary  loss  of  time  from 
a  dead  stop,  in  passenger  service,  under  any  ordinary  circumstances,  is 
only  about  three  minutes,  and  the  loss  of  time  from  slowing  up  for  a  quarter 
of  a  mile  or  so,  under  the  quick  command  of  the  train  given  by  the  air, 
is  very  much  less  than  this,  while  the  steel  rail  has  materially  reduced  the 
difnculty  in  and  objection  to  making  up  for  such  delays  by  higher  speed 
at  other  points.     This  is  shown  more  fully  in  Chap.  XIX. 

For  freight  service  alternations  of  speed  by  the  use  of  brakes  are  still 
very  objectionable,  and  perhaps  will  long  continue  to  be  ;  but  ordinary  cur- 
vature does  not  require  this. 

278.  We  may,  therefore,  conclude  (in  part  on  the  author- 
ity of  the  matter  referred  to  above,  which  it  seemed  more  appro- 
priate to  postpone  to  Chap.  XIX.)  that  any  difference  within  the 
power  of  the  engineer  to  effect  is  not  likely  to  materially  affect 
the  ability  to  make  ordinary  express-train  time.  If  it  were  a 
question  between  2°  curves  or  20°,  or  between  no  curvature 
and  a  great  deal,  it  might  well  make  a  serious  difference  ;  but 
under  ordinary  circumstances  the  question  is  rather  between 
say,  6°  and  10°  curves,  or  between,  say,  10  per  cent  more  and  10 


CHAP,    VIII.— CURVATURE— SMOOTH  RIDING   OF  CARS.    2/5 

per  cent  less  curvature.  In  such  cases,  on  other  than  trunk 
lines  running  fast  expresses,  the  importance  of  this  particular 
question  is  not  simply  diminished  pro  rata,  but  entirely  van- 
ishes. 

279.  The  effect  of  curvature  on  the  smooth  riding  of 
CARS  is  a  matter  of  more  serious  moment  in  not  a  few  cases  of 
lines  with  a  large  through-passenger  traffic. 

For  day  travel  it  matters  less;  but  there  is  no  doubt  that 
since  the  general  introduction  of  sleeping-cars  not  a  little  travel 
has  been  kept  off  the  New  York,  Lake  Erie  &  Western  Railroad, 
for  example,  as  v/ell  as  other  crooked  railways,  for  this  reason 
alone,  when  a  straighter  competing  line  existed.  On  the  other 
hand,  the  number  of  lines  to  which,  on  account  of  the  competi- 
tion of  other  and  straighter  lines,  this  is  as  an  important  consid- 
eration is  not  very  great ;  and  even  when  it  is  or  may  be,  this  also 
is  peculiarly  one  of  those  cases  in  which,  although  a  perfect  cure 
would  be  exceedingly  important  and  valuable,  the  partial  cure 
from  the  slight  modifications  which  are  alone  within  the  power  of 
the  engineer,  without  very  great  expenditure,  will  in  most  cases 
have  little  value.  It  is  also  to  be  remembered  that  if  a  curve  is  in 
thoroughly  good  shape  the  motion  of  a  car  is,  after  it  has  once 
entered  the  curve,  almost  as  steady  as  on  a  tangent.  If  the 
centrifugal  force  and  superelevation  could  be  exactly  balanced, 
the  body  of  a  traveller  either  in  a  sleeping-car  or  day-coach 
would  be  unaffected  by  either.  Unfortunately  this  is  out  of  the 
question;  but  the  worst  effect  usually  comes  from  entering  and 
leaving  a  curve,  and  this  again  chiefly  results  from  the  fact  that, 
as  roads  are  ordinarily  located,  the  line  instantly  changes  from 
a  tangent  to  a  sharp  curve.  The  consequence  is,  inevitably,  a 
disagreeable  lurch  and  "thud;"  which  would  be  much  worse 
than  it  is  except  that  the  trackman  with  his  bar  corrects  the 
errors  of  the  engineer  with  his  transit  by  "easing  off"  the  curve 
at  the  ends,  extending  it  a  hundred  feet  or  more  on  to  the  tangent, 
but  of  course  necessarily  sharpening  the  curve  not  a  little  for  a 
short  distance  beyond  the  technical  "  P.  C."  The  latter  is  un- 
fortunate; but  it  is  far  better  than  to  leave  the  curve  as  the  en- 


276   CHAP.    VIII,— CURVATURE— SAIOOTH  RIDING   OF  CARS. 

gineer  stakes  it  out,  and  it  never  is  so  left  on  old  and  good  track, 
so  far  as  the  writer  has  observed,  but  invariably  flattened  off  at 
the  ends  by  the  trackmen. 

280.  The  "  easing  off"  should,  it  need  hardly  be  said,  be  rather  done  by 
the  engineer  in  proper  form  in  the  first  place,  in  such  manner  as  to  avoid  also 
the  lesser  evil  of  a  kind  in  the  body  of  the  curve.  A  simple  and  praciical 
method  for  putting  in  such  transition  curves  involving  hardly  any  extra  work 
for  this  purpose  (in  fact  rather  facilitating  the  field-work)  is  given  in  the  field- 
book  which  succeeds  this  volume.     See  also  close  of  Chap.  XIX. 

281.  It  may  be  added  that,  as  more  fully  pointed  out  in  the  field-book  re- 
ferred to,  the  use  of  the  parabolas  instead  of  circular  curves  for  railways,  pro- 
posed in  the  early  days  of  railway  construction  and  in  a  few  cases  used,  would 
have  no  important  effect  in  reducing  the  evil  described.  What  is  wanted  is  (i), 
to  ease  off  the  curve  by  a  rapidly  changing  radius  for  a  short  distance  at  the 
ends — a  transition  curve  ;  and  (2),  to  leave  the  great  body  of  the  curve  of 
uniform  radius.     This  the  parabola  does  not  accomplish. 

282.  The  moral  effect  of  excessive  curvature  to  deter 
TRAVEL — or  rather,  the  moral  effect  of  knovirn  excellence  in  that 
as  in  every  other  detail  to  encourage  travel,  is  in  not  a  few  cases, 
— as  for  instance  the  Pennsylvania  Railroad — a  consideration  of 
more  importance  than  appears.  Advertising  is  generally  re- 
garded by  all  business  men  as  a  profitable  outlay,  even  when  it 
is  all  outlay.  When  the  advertising  is  of  such  a  nature  as  to  in 
part  pay  for  itself  by  saving  expenses,  even  if  only  to  a  limited 
extent,  it  becomes  of  course  still  more  desirable,  and  in  the  case 
of  railways  has  the  peculiar  advantage  noted  in  Chap.  III.,  that 
any  additional  sales  they  may  thus  make  cost  almost  literally 
nothing. 

In  the  case  of  some  few  roads  which  have  an  immense,  an 
almost  unlimited,  traffic  to  contend  for,  this  consideration  alone 
may  become  of  such  great  importance  as  to  justify  very  heavy 
expenditure.  Thus,  the  policy  which  the  Pennsylvania  Railroad 
has  adopted  of  polishing  and  perfecting  their  line  in  this  and  in 
various  other  almost  fanciful  ways  will  doubtless  prove  a  money- 
making  operation,  and  largely  on  this  account;  for  even  with 
their  great  traffic,  which  will  justify  almost  any  expenditure  to 
effect  a  perceptible  improvement,  it  might  perhaps  be  difficult 


CHAP,    VIII.— CURVATURE— SMOOTH  RIDING   OF  CARS.    2JJ 

to  justify  the  expenditures  which  they  have  made  to  take  out 
some  of  their  curvature  by  any  correct  estimate  of  the  direct 
saving  in  operating  expenses.  One  of  the  "almost  fanciful  "  ex- 
penditures referred  to  is  to  secure  absolute  perfection  of  appear- 
ance, as  well  as  real  excellence,  in  the  track  and  right  of  way  by 
dressing  the  edges  of  the  slopes  of  the  broken  stone  ballast  to 
an  exact  line,  stone  by  stone,  and  by  elaborately  neat  and  taste- 
ful road  crossings.  Another,  and  the  one  more  particularly  re- 
ferred to,  is  the  expenditure  of  occasional  large  sumiS  in  bold 
lines  to  eliminate  curvature  and  trifling  amounts  of  distance. 

283.  Between  Harrisburg  and  Philadelphia  the  line  of  the  Pennsylvania 
Railroad  is  one  of  the  most  instructive  practical  lessons  on  the  subject  of 
curvature,  perhaps,  which  exists  in  the  world.  The  old  and  very  crooked  line 
built  by  the  State  nearly  fifty  years  ago  is  crossed  almost  every  half-mile  for 
long  stretches  by  the  newer  line,  which  has  been  constructed  piece  by  piece,  and 
which  has  hardly  one  tenth  the  curvature,  while  at  no  point  more  than  a  few 
hundred  feet  from  the  old  line.  Comparison  of  the  two  is  instructive  in  three 
ways: 

First,  and  chiefly,  the  old  line  is  an  example  of  how  immense  amounts  of 
curvature  may  be  introduced  merely  from  ignorance,  carelessness,  or  inexperi- 
ence, without  the  slightest  real  necessity.  At  very  many  points  the  new  line 
was  no  more  expensive  than  the  old,  while  materially  better. 

Secondly,  it  is  at  many  points  an  example  of  judicious  construction,  both  on 
the  new  line  and  the  old  :  the  old  line  being,  very  cheap,  and  answering  a  very 
good  purpose  while  capital  was  scarce  and  traffic  light,  and  involving  little  loss 
to  throw  away  when  these  conditions  had  changed  so  as  to  justify  the  new  line. 
Thus,  while  it  was  wise  to  throw  away  the  work  in  the  end,  it  was  also  wise  to 
build  it  in  the  beginning. 

Thirdly,  there  are  various  points  where  the  new  line,  however  more  pleas- 
ing to  the  eye,  may  be  seen  to  be  far  more  expensive  than  any  ordinarv  traffic 
would  justify  in  proportion  to  the  end  attained.  The  Pennsylvania  Raiiioad, 
however,  has  not  an  ordinary  traffic. 

284.  But,  after  all,  the  lines  are  few  which  have  so  large  a 
competitive  traffic  to  lose  or  gain  as  to  make  the  advertising  value 
of  a  better  line  a  consideration  of  much  moment,  and  then  it  only 
becomes  such  when  it  is  only  one  form  of  a  general  and  notori- 
ous policy.  With  the  Pennsylvania  it  is  so.  Its  track  is  well 
known  among  well-informed  railroad  men,  the  world  over,  to  be 
distinctly  superior  in  its  finish,  if  not  in  its  real  excellence,  to 


278      CHAP.    VIII— CURVATURE  AND  HEAVY  ENGINES. 

anything  which  exists  in  any  part  of  the  world,  and  the  same 
spirit  pervades  most  of  the  details  of  its  management,  but  only 
when  the  competition  is  very  close,  the  traffic  very  heavy,  and 
the  amount  of  avoidable  sharp  curvature  in  question  very  large,, 
could  it  do  so.  In  a  new  and  direct  trunk  line  between  Phila-^ 
delphia  or  Chicago  and  New  York,  for  example,  it  would  be  a 
very  important  consideration. 

285.  So  far,  the  miscellaneous  and  indeterminate  objections  to 
curvature  discussed  apply  chiefly  to  passenger  travel.  Another 
of  great  importance  applies  only  to  freight  traffic,  viz.:  The  ef- 
fect OF  CURVATURE,  and  especially  sharp  curvature,  as  an  ob- 
stacle TO  THE  USE  OF  HEAVY  AND  POWERFUL  TYPES  OF  LOCO- 
MOTIVES. Without  attempting  to  summarize  now  the  mechanical 
reasons  for  the  conclusion,  which  are  given  later  (Chap.  XL),  it 
is  a  fact  that,  in  spite  of  occasional  obstinate  opposition  to  cer- 
tain types  of  engines  being  used  "  on  our  curves"  by  men  who 
ought  to  be  good  judges,  there  is  not  the  slighest  evidence  to 
show  that  all  the  types  now  in  use  are  not  mechanically  very 
nearly  on  a  par  as  respects  the  physical  possibility  of  being  ad- 
vantageously operated  over  any  ordinary  and  reasonable  curva- 
ture. The  wear  and  tear  is  a  little  greater  with  heavy  engines,, 
as  we  shall  see;  but  that  is  not  now  the  question  before  us. 

Certainly  up  to  the  limit  of  10°  curves  (573  feet  radius)  this 
objection  is  wholly  unfounded.  The  New  York,  Lake  Erie  & 
Western,  Baltimore  &  Ohio,  and  numerous  other  lines  (see  Table 
116)  have  curves  of  that  radius  exposed  to  the  heaviest  and  fast- 
est traffic,  over  which  Consolidation  engines  run  without  the 
slightest  evidence  of  peculiar  difficulty,  danger,  or  wear  and  tear. 
In  the  coal  regions  of  Pennsylvania  14°  and  16°  curves  are  not 
at  all  uncommon  on  branch  lines,  and  for  operating  such  lines 
the  Consolidation  engine  was  first  designed  and  had  its  first 
success. 

286.  The  Consolidation  engine  was  designed  by  Mr.  A.  Mitchell,  then 
Master  Mechanic  of  the  Lehigh  Valley  Railroad,  in  1872.  The  type  was 
so  novel  that  the  Baldwin  Locomotive  Works  were  reluctant  to  under- 
take its  construction.      The  Atchison,  Topeka  &  Santa  Fe  Railroad  in 


CHAP.    VIII.— CURVATURE  AND  HEAVY  ENGINES.      2'jg 

1881  operated  16°  curves  with  a  60-ton  Consolidation  locomotive  (see 
Trans.  Am.  Soc.  C.  E.,  1880,  Paper  No.  CLXXX),  with  the  result  that"  it 
is  believed  that  the  Consolidation  engine  travels  the  16°  curves  with  as 
much  ease  as  the  ordinary  '  American  '  engine,  and  causes  less  wear  of 
track  and  permanent  way." 

287.  In  the  "  Seventh  Annual  Report  of  the  American  Railway  Master 
Mechanics' Association"  (1876,  p.  13)  a  committee  of  five  prominent  master 
mechanics  and  mechanical  engineers  report  as  follows  : 

"  With  reference  to  the  loads  hauled  by  these  heavy  engines,  it  maybe 
well  to  say  that  no  practical  difficulties  are  experienced  on  the  Pennsyl- 
vania and  Northern  Central  railroads'  level  divisions  in  hauling  trains 
of  80  or  90  loaded  cars  at  15  miles  per  hour.  These  long  trains  are  hauled 
around  sharp  curves,  of  which  the  radii  range  from  650  feet  (8°  50')  up- 
ward. In  exceptional  cases  very  much  sharper  curves  are  passed.  Thus 
on  the  Baltimore  &  Ohio  Railroad  there  is  a  Y  with  curves  of  136  feet 
radius  (42°  curves),  and  Consolidation  engines  are  run  around  these  curves 
without  trouble.  In  fact  no  difficulty  has  been  reported  in  using  them  in 
all  cases  like  ordinary  freight  engines." 

288.  In  the  same  report  (p.  123)  we  have  a  report  of  experiments  at 
Renovo,  on  the  Philadelphia  &  Erie  Railroad,  to  determine  the  relative 

Table  108, 
Comparative  Resistance  on  Curves  of  Various  Types  of  Locomotives. 

According  to  experiments  on  the  Philadelphia  &  Erie  Railroad. 
[The  precise  results  of  this  table  cannot  be  accepted  as  accurate,  but  they  are  of  value 
as  indicating  that  there  is  at  least  no  great  difference  against  the  heavier  types.] 


Weight. 

Diam.  of 

Kind  of  Engine. 

Drivers. 

Truck. 

Tender. 

Total. 

Drivers. 

American 

lbs. 
48,000 
52,800 
78,500 

lbs. 

20,500 

22,600 

9,700 

lbs. 
32,600 
47,700 
47,700 

lbs. 
101,100 
123,100 
135,900 

ins. 
60 

55 
49 

Ten- wheel 

Consolidation 

Kind  of  Engine. 

Length  of  Wheel-base. 

Resistance 

on  4°  Curve  at  io  Miles 
Per  Hour. 

Rigid. 

Total. 

Total. 

Lbs.  Per  Ton 

Lbs.P'rDeg. 

American 

ft.      in. 

7     6 

12      5 

14     6i 

ft.      in. 
21    lOf 
23     8 
21     I 

lbs. 
1,963 
1,750 
1,850 

lbs. 

39 

28.4 

20.0 

lbs. 
9-75 
7.1 
5.0 

Ten-wheel 

Consolidation 

280      CHAP.    VIII,— CURVATURE  AND  HEAVY  ENGINES. 

curve  resistance  of  various  engines,  which  indicate,  so  far  as  they  go, 
that  if  we  may  estimate  relative  adaptability  to  and  danger  on  various 
curves  by  the  relative  resistance,  the  heaviest  class  of  engines  are  at 
least  as  well  adapted  to,  and  as  safe  on,  sharp  curves  as  any  other  class  of 
engines.  Table  io8  gives  a  summary  of  these  experiments,  which  v/ere 
made  by  Mr.  Isaac  Dripps,  General  Master  Mechanic  of  the  Philadelphia 
&  Erie  Railroad,  with  a  recording  dynamometer  car  which  he  guarantees 
to  have  been  correct ;  but  notwithstanding  this  guarantee,  it  seems  almost 
certain  that  there  must  have  been  some  defect  of  apparatus  which  par- 
tially vitiates  the  results,  as  they  seem  unduly  favorable  to  the  Consoli- 
dation type.  The  tests  may  be  accepted,  however,  as  indicating  quite 
strongly  that  the  difference  is  not  great  against  them.  The  speed  was 
kept  as  near  lo  miles  per  hour  as  possible,  and  the  effect  of  varying 
velocity  estimated  from  the  diagram. 
289.  Mr.  Dripps  says  : 

"  The  locomotives  were  in  good  working  order,  and  were  generally 
taken  for  the  experiments  as  soon  as  detached  from  their  trains,  the  only 
preparation  necessary  being  to  disconnect  the  piston-rods  from  the  cross- 
heads  so  as  not  to  have  the  friction  of  the  piston  in  the  cylinders.  All 
the  other  connections  were  left  precisely  as  if  running  by  steam,  so  that 
the  friction  due  to  all  the  working  parts  of  the  locomotive,  except  the  fric- 
tion of  the  piston  within  the  cylinders,  would  be  indicated.  The  loco- 
motives experimented  with  were  pulled  by  another  locomotive  and  the 
dynamometer  car.  They  would  have  been  pushed  except  for  the  danger 
of  snow  blowing  on  the  track. 

"These  experiments  prove  conclusively,  that  heavy  locomotives  prop- 
erly designed,  with  a  short-wheel  base,  and  with  as  many  bearing  points 
on  the  rails  within  such  base  as  possible, — thus  reducing  the  weight  on 
each  bearing  point, — will  pass  around  curves  with  less  friction,  and  be  less 
destructive  to  the  track,  than  the  ordinary  passenger  locomotive  of  much 
less  weight.  Of  course  these  heavy  locomotives  are  best  adapted  for 
slov/  speeds,  and  will  show  the  greatest  economy,  and  will  work  to  the 
best  advantage  on  railroads  having  double  track,  heavy  grades,  and  a 
heavy  freight  traffic. 

"  The  effective  power  of  Consolidation  locomotives  is  50  per  cent  more 
than  the  ordinary  six-wheel  connected  freight  locomotive  ;  and  from 
actual  service  I  find  that  the  locomotives  of  this  class  work  up  to  their 
power  fully  as  v/ell  as,  in  fact  better  than,  the  six-wheel  connected  locomo- 
tive.    Two  locomotives  of  the  Consolidation  class  will  do  the  same  work 

haul  as  many  cars — as  three  of  the  six-wheel  connected  class;  and  as 

three  of  the  latter  will  cost  $10,000  more  than  two  of  the  former,  there  is 
thus  a  saving  of  $10,000  in  the  original  outlay,  and  the  saving  of  wages  of 
the  crew  of  one  locomotive  (and  train)  daily;  and  with  a  properly  con- 
structed locomotive  of  the  Consolidation  class  the  running  repairs  for 
tonnage  hauled  will  be  less  than  any  other  class  of  locomotives  now  in 


CHAP.   VIII.— MECHANICS  OF  CURVE  RESISTANCE.      28 1 

use.  On  the  narrow-gauge  Denver  &  Rio  Grande  Railway,  which  has 
many  24°  and  30°  curves,  the  Consolidation  type  is  almost  exclusively 
used  for  freight  service,  the  wheel-base  being  only  a  little  shorter  than  is 
usual  for  standard  gauge,  or  in  the  proportion  of  about  12  to  15  feet." 

290.  The  preceding  facts,  taken  altogether,  seem  conclusive 
that  objections  to  the  use  of  any  reasonable  amount  or  radius  of 
curvature  whatsoever,  on  the  ground  that  it  will  be  peculiarly 
objectionable  for  the  heavier  types  of  locomotives,  finds  but  lit- 
tle warrant  in  fact.  Indeed,  it  is  noticeable  that  it  is  on  roads  of 
much  and  heavy  curvature  that  the  Consolidation  type  has  been 
most  readily  adopted  and  is  most  in  use. 

291.  We  have  now  discussed  all  the  indeterminate  and  imagin- 
ative (but  not  therefore  imaginary)  objections  to  curvature,  and 
found  that  while  all  of  them  have  a  foundation  in  fact,  and  may 
be  at  times  of  great  importance,  yet  that  on  the  contrary  some 
of  them  are  always,  and  all  of  them  are  sometimes,  of  so  little 
moment  that  for  the  most  part  they  should  have  no  appreciable 
effect  on  the  decision  as  to  what  curvature  to  use.  We  will 
therefore  return  to  the  concrete  and  definite  objections  to  curva- 
ture, viz.,  its  direct  effect  upon  operating  expenses  and  on  length 
of  trains  (the  latter  considered  in  Chaps.  XVIII.  and  XIX.).  In 
order  to  discuss  these  intelligently  we  must  first  consider  the 
abstract  question  of  the  mechanical  laws  of  curve  resistance, 
from  mistaken  notions  as  to  which  much  that  is  mistaken  may 
arise  in  practice. 

THE   MECHANICS   OF   CURVE    RESISTANCE. 

292i  Curve  resistance  has  never  yet  been  exhaustively  investigated, 
and  our  knowledge  is  in  several  respects  deficient.  The  more  essential 
facts  are  now  tolerably  well  determined ;  but  simple  as  the  subject  ap- 
pears, the  mechanics  of  a  rollingtruck  on  a  curve  is — to  determine  it  cor- 
rectly— a  very  intricate  problem,  the  solution  of  which  we  must  attempt 
to  make  clear. 

293.  The  forces  arising  from  the  fact  of  curvature  are  of  three 
classes : 

I.  Forces  originating  in  and  confined  in  their  action  to  the  truck  itself, 
causing  the  shippage  of  the  wheel  on  the  rail  which  is  the  ultimate  source 


282      CHAP,   VIII.— MECHANICS  OF   CURVE  RESISTANCE. 

of  all  curve  resistance.  The  following  two  classes  of  forces  can  only  act 
by  augmenting  or  diminishing  the  former : 

2.  Centrifugal  and  centripetal  force :  acting  upon  the  car  as  a  whole^ 
and  communicated  to  the  truck  through  the  centre-pin  and  side-bearings. 

3.  A  force  due  to  obliquity  of  traction  originating  within  the  train  as  a 
whole  and  communicated  to  the  car-body,  and  thence  to  the  truck. 

We  will  consider  the  nature  and  action  of  these  forces  in  their  order  r 

294.  The  position  assumed  by  any  rectangular  flanged  wheel-base  in 

passing  around  a  curve  is  shown  by  ob- 
servation and  experiment  to  be  that 
shown  in  Fig.  20,*  The  front  outer 
wheel  crowds  hard  against  the  rail,  and 

^"'**«»^^      the    rear  axle    then    assumes   a   radial 

——...„.....      position,  neither  wheel  touching  the  rail 

unless  the  gauge  is  so  tight  or  the  wheel- 

\  j  \  base  so  long  as  to  bring  the  inner  rail 

VA  \  up  to  the  flange  rather  than  the  flange 

^  ^  to  the  rail.     Fig.  20  shows  the  position 

^^G.  20.  Qf    STABLE    EQUILIBRIUM    tO    which,    if 

any  force  disturb  the  position  of  the  wheels  for  a  moment,  they  promptly 
return.  Therefore,  if  any  force  is  to  permanently  change  their  position 
it  must  be  sufficient  to  slide  them  laterally  on  the  track.  Otherwise  it 
will  not  produce  motion  at  all.  To  slide  the  wheels,  as  to  lift  a  weight, 
the  -nnro  of  an  inch  requires  as  great  a  static  force  in  pounds  as  to  slide 
it  a  foot  or  a  mile.  The  power  consumed  varies  with  the  distance 
moved,  but  the  force  required  to  produce  motion  at  all  does  not  vary. 

This  position  is  likewise  shown  by  experiment  to  be  assumed  just  the 
same,  however  great  or  little  the  superelevation.  This  fact  may  be  ob- 
served by  watching  the  motion  of  cars  around  the  first  sharp  curve  in  any 
yard. 

295.  The  writer  constructed  some  heavy  models  with  both  cylindrical  and 
sharply  coned  wheels,  the  wheel-base  being  capable  of  increase  or  decrease  at  plea- 
sure, and  the  gauge  and  radius  being  likewise  adjustable  by  moving  the  rails.  The 
flanges,  however,  were  made  almost  vertical,  and  with  a  sharp  interior  fillet,  in 
order  to  give  an  exact  point  to  measure  from.     He  found  that  coning  did  not 

*  The  writer  believes  he  was  the  first  to  observe  this  fact,  and  determine  it 
experimentally.  The  general  fact  that  the  rear  flanges  stand  away  from  both 
rails  he  has  since  found  had  been  previously  observed  by  a  number  of  individ- 
uals, but  even  that  is  not  generally  known  to  this  day. 


CHAP.    VIIL— MECHANICS  OF  CURVE  RESISTANCE.      283 


Fig. 


exercise  the  slightest  influence  on   the  position  assumed  by  the  wheel-base, 

which   was   invariably  that  stated,    the   front 

outer  wheel  being  always  in  contact  with  the 

rail  at  b,  Figs.   20  to   23,  and   the  rear  outer 

wheel  standing  away  from  the  rail  by  a  distance 

a,  which,  so  far  as  the  writer  could  determine 

it,  was  always  precisely  equal  to  the  versed  sine 

of  a  chord  of  twice  the  length  of  the  whe el-base 

(see    Fig.    20),    indicating   that   the  rear   axle 

was   always   radial.       In    only    one    case   did 

this  fail, — in  that  outlined  in  Figs.  21  to  23, — 

and  then  only  because  it  was  impossible  for 

the  wheels  to  assume  it.     If  the  gauge  was  so 

tight,  the  wheel-base  so  long,  or  the  curve  so 

sharp  (or  any  two  or  three  of  these  together)  that  the  distance  a  by  which  the 

rear  wheels  naturally  tended  to  stand  away  from  the  outside  rail  was  greater 

than  the  play  of  the  gauge,  then  the  rear  axle  simply  moved  over  until  it  pressed 

against  the  inner  rail,  as  shown  in  Fig.  22. 

296.  With  European  rolling-stock,  having  no  truck,  this  condition  usually 
prevails,     so     that 

their  rails  wear 
quite  differently  on 
curves  from  ours, 
both  inner  and  out- 
er rail  being  ground 
by  the  flange.  On 
this  account  it  is  fre- 
quently laid  down 
in  European  text- 
books that  the  posi- 
tion outlined  in  Fig.  22  is  the  normal  one  for  any  wheel-base  in  curves,  but 
this  error  arises  from  insufficient  investigation,  and  is  disproved  by  American 
experience  as  well  as  experiment. 

When  the  inner  rail  was  entirely  removed,  so  that  the  inner  wheels  ran  on 
their  flanges,  the  position  and  path  of  the  wheels  was  in  no  way  affected,  show- 
ing thav  the  inner  rail  performs  no  necessary  function  in  guiding  the  trucks, 
but  merely  supports  the  wheels. 

297.  These  facts  disprove  the  old  hypothesis  that  coning  would  enable 
the  wheels  to  adapt  themselves  to  the  unequal  length  of  inner  and  outer 
rail,  and  maintain  a  radial  position.  They  can  only  do  so  when  the  axles 
individually  are  free  to  assume  a  radial  position.  Moreover,  owing 
partly  to  this  fact,  and  partly  to  the  effect  of  the  ordinary  wear  on  tan- 


284      CHAP.    VIII.— MECHANICS  OF  CURVE  RESISTANCE. 

gents,  the  tread  wears  down  near  the  flange  very  rapidly,  and  such  con- 
ing as  there  may  be  soon  disappears.  We  may  therefore  neglect  it  here- 
after, and  assume  the  wheels  to  be  cylindrical.  The  coning  now  put  in 
wheels  is  chiefly  useful  as  a  prospective  provision  for  wear ;  and  experi- 
ment shows  that  whether  the  wheels  be  coned  or  not,  the  tendency  of 
any  rectangular  wheel-base  is  to  roll  very  nearly  in  a  straight  line. 

298.  As  we  have  seen  that  the  rear  axle  is  always  radial  to  the  curve, 
the  front  axle,  Figs.  20  to  23,  stands  at  an  angle  A,  Fig.  23,  to  the  rail, 
equal  to  the  arc  subtended  by  the  length  of  the  wheel-base,  /.     With 

a  5 -ft.    wheel-base    (the   usual  length  for 
freight  trucks)  this  angle  would  be,  on  a  1° 

curve,  .05°  or  3',  and   proportionately  on 

■ ^^^  other  curves;  with  a  12-ft.  wheel-base  the 

-  angle   is   0.12°  =  7.2'.      The    distance    by 

> — -    which  the  rear  outer  wheel.  Figs.  20  to  23, 

Fig.  23.  stands  at  a  distance  from  the  outer    rail 

\  \  (being  equal  to   the  ver.  sin  of  twice  the 

I  \  arc  subtended  by  /)  is  readily  determined 

V  to  be,  from  what  has  preceded, 

For  a  5-ft.  wheel-base,  .0022  foot  per  degree  of  curvature. 
For  a  12-ft.  wheel-base,  .00127  foot  per  degree  of  curvature. 


299.  The  gauge  of  a  road  is  the  exact  distance  between  inside  of  rails 
and  the  gauge  of  the  wheels  is  usually  set  so  as  to  allow  a  normal  play  of 
from  f  to  f  inch,  averaging  about  \  inch  or  .04  feet.     The  rear  inner 
wheel,  then,  of  a  5-ft.  wheel-base  will  be  close  against  the  inner  rail  on  a 

•"^^    =  17°   curve +,   and   a  12-ft.  wheel-base  on  a  —  3°  curve  +■ 

.0022  .0127 

In  watching  ordinary  cars  pass  around  a  curve,  however,  there  will  be  con- 
siderable fluctuations  in  the  position  of  the  rail  owing  to  irregularities  of 
both  curve  and  truck. 

300.  The  slipping  of  wheel  on  rail  on  a  curve  arises  from  two  causes : 
First.  Longztudmal  slipping,  due  to  the  difference  in  length  of  inner 

and  outer  rail.  This  difference  on  any  given  curve,  or  part  of  a  curve,  is 
equal  to  an  arc  of  a  radius  equal  to  the  gauge,  and  the  same  number  of 

degrees  long;  i.e.,  it  is,  on   any  given  distance  d,        d  x  —,  or,  on  a 


CHAP.   VIII.— MECHANICS  OF  CURVE  RESISTANCE.      285 

I  °  curve  and  standard  gauge,  d  x  -^^  =  .00082^.    On  any  other  D°  curve 

5730 
it  will  be  o.ooo2>2dD. 

Secondly.  Lateral  slipping.    The  front  axle,  as  we  have  seen,  stands 
at  an  angle  A,  Fig.  23  or  a.  Fig.  24,  to  the  rail.    In  rolling  through  an 


Fig.  24. 


infinitesimal  distance  d,  therefore,  the  wheel,  since  it  tends  of  itself  to 
roll  straight  forward  in  the  direction  PA  must  be  slidden  laterally 
through  a  distance  AA'  =  d  sin  a. 

For  a  5-ft.  truck  on  a  1°  curve AA'  =  d  sin  3'  =  .00087^. 

For  a  i2-ft.  truck  on  a  1°  curve AA'  —  d  sin  7.2'  =  .oo2id. 

This  lateral  slipping  takes  place  only  on  the  front  axle,  since  the  rear 
axle,  as  we  have  seen,  is  and  maintains  itself  radial  to  the  curve. 

301.  On  the  front  axle  both  lateral  and  longitudinal  slipping  is  taking 
place  simultaneously  and  continuously,  and  the  question  then  arises  how 
the  longitudinal  slipping  is  divided — whether  the  outer  wheel  slips  for- 
ward or  the  rear  wheel  backward,  or  the  total  amount  is  divided  between 
the  two.  A  single  experiment  as  to  this  point,  as  careful  as  its  delicate 
nature  would  permit  with  ordinary  rolling-stock,  was  once  made  on  the 
"  Horse-shoe  curve"  of  the  Pennsylvania  Railroad,  with  the  conclusion 
that  both  wheels  slipped  ;  but  it  is  impossible  that  this  condition  obtains 
generally  and  continuously,  since  that  wheel  will  slip  which  can  slip 
easiest,  and  the  slightest  variation  in  either  the  load  or  the  coefficient  of 
friction  will  give  one  wheel  or  the  other  an  advantage  in  this  respect. 
Either  the  superelevation  or  the  centrifugal  force  is  alone  competent  to 
produce  enough  inequality  of  load  to  effect  this,  for  one  or  the  other 
must  always  be  in  excess,  unless  by  accident.  And  furthermore,  if  one 
wheel  should  begin  to  slip  first,  it  would  certainly  continue  to  do  so,  for 
the  same  reason  that  when  a  locomotive  driver  begins  to  slip,  its  ratio  of 


286      CHAP.   VIII.— MECHANICS  OF  CURVE  RESISTANCE. 


adhesion  (i.e.,  coefficient  of  friction)  is  heavily  reduced.  It  may  there- 
fore be  considered  as  certain  that  all  longitudinal 
slip  in  every  case,  unless  by  accident,  is  confined 
to  either  the  inner  or  outer  wheel  exclusively ; 
although  it  may  not  be  the  same  wheel  for  any 
two  successive  axles,  nor  for  any  two  consecutive 
moments. 

302.  Admitting  this  to  be  true,  the  truck  in 
rolling  on  a  curve  is  rotating  about  some  one 
wheel,  A,  as  a  centre,  as  shown  in  Fig.  25  ;  and 
we  have  the  following  condition  of  things  in, 
say,  a  5-foot  truck  rolling  around  a  curve  : 
Fig,  25.  (i)  One  rear  wheel,  y^,  is  not  slipping  at  all  in 

either  direction. 

(2)  One  rear  wheel  is  slipping  longitudinally  at  the  rate  of  .ooo%2dD 
(in  a  i2-ft.  truck  also,  .ooZidD). 

(3)  One  front  wheel  is  slipping  laterally  at  the  rate  of  oooSgdB  (12- 
ft.  truck,  .QOiidD). 

(4)  One  front  wheel  is  slipping  both  laterally  and  longitudinally  at 
the  same  rates  as  in  the  above,  giving  a  combined  rate  of 


4/. 00082^  +  00089^  dD. 


Table  109  give  the  summary  of  the  slipping  thus  indicated. 
Table  109. 

Total  Slipping  of  One  Wheel  in  Feet  that  takes   Place  in   passing 
OVER  100  Ft,  of  Various  Curves. 


5-Ft.  Truck 

;  4  Wheels. 

12- Ft. 

Truck;  4  Wheels. 

Formula 

1° 

5° 

10° 

20° 

1° 

5° 

10° 

20° 

.000 
.082 
.089 
.121 

.000 
.410 

.445 

.605 

0.00 
0.82 
0.89 
1.21 

0.00 

1.64 
1.78 
2.42 

.000 
.082 
.210 
.225 

0.00 
0.41 
1.05 
I-I3 

0.00 
0.82 
2.10 
2.26 

0.00 
1.64 
4.20 
4-51 

I  front     " 

.0089^^' 

V.00822+0089VA 
or  for  i2-ft.  truck, 

Total  slip 
wheel  .. 

of 

one 

.292 

1.460 

2.92 

5-84 

•517 

2-59 

5.18 

IO-35 

as  shown  in  Fig, 
27. 

wheel. 

Average  per 

•073 

•365 

0-73 

1.46 

.013 

0.65 

X.30 

2.60 

303.  The  formula  (4)  requires  explanation  :    Since  the  wheel  is  slip- 
ping in  two  directions  at  right  angles  to  each  other,  it  will  at  each  instant 


CHAP.    VIIL— MECHANICS  OF  CURVE  RESISTANCE.      28/ 


of  time,  while  advancing  over  an  infinitesimal  distance,  d.  Fig.  25,  slip 
longitudinally  in  the  direction  a,  and  laterally  in  the  direction  /.  The 
true  direction  and  amount  of  slip- 
ping will  therefore  be — neither  a, 
nor  /,  nor  both  together — but  along 
the  diagonal  d.     Figs.  26  and   27 


represent  to  scale  the  actual  con-   S        ,002.10  q  B''^ooz9    C 

ditions.  Fig.  26.— i2-ft.  truck.       Fig.  27.— s-Ft.  Truck. 

This    is    merelv    foUowinp-    the       Amount  and  constituent  elements  of  the  slip  of 
iniS    IS    merely    loiiowiug    lug  ^.j^^  ^^^^^  ^^  pj^_  ^^^  j^  passing  over  a  distance  I 

fundamental  law  of  the  composi-  on  a  1°  curve. 

tion  of  velocities,  which  is  the  same  in  its  nature  as  the  composition  of 
forces.  It  has  been  carelessly  assumed  at  times  that  a  total  sliding  of 
the  wheels  represented  by  the  sum  of  the  two  sides  a  and  /  rather  than 
by  the  hypothenuse  d,  measures  the  distance  through  which  the  wheel 
slides,  and  the  consequent  loss  of  foot-pounds  of  energy,  but  this  is  palp- 
ably erroneous. 

304.  It  will  be  observed  that  according  to  Table  109  the  wear  due  to 
curvature  on  the  front  wheels  is  more  than  double  (4.20  to  1.64)  that  on 
the  back  axles.  Any  check  upon  this  from  observed  wear  of  car  wheels 
is  in  the  nature  of  things  impossible  from  the  fact  that  the  direction  of 
motion  of  the  car  is  reversed  with  every  trip.  With  engine  and  tender 
trucks,  however,  this  is  not  the  case.  Statistics  of  this  kind  likewise  are 
very  difficult  to  obtain  ;  and'the  following  little  table  (Table  no),  embrac- 
ing observations  on  the  Camden  &  Atlantic  Railroad,  is  all  of  the  kind 
which  the  author  has  ever  been  able  to  discover.  This,  however,  appears 
as  far  as  it  goes  to  strikingly  confirm  the  theory  advanced.  It  is  to  be 
observed  that  the  wear  of  tender-truck  wheels  is  11.2  per  cent  greater  on 
the  front  than  on  the  back  axle,  and  the  wear  of  the  engine  truck-wheels 
37.6  per  cent  greater.  In  considering  these  figures  it  is  to  be  remem- 
bered : 

1.  The  Camden  &  Atlantic  has  very  little  curvature. 

2.  Curvature  is  only  one  cause  for  rail  wear,  the  others  being  use  of 
brakes  and  sand,  original  defects  and  regular  running  wear  on  tangents, 
which  would  be,  if  not  substantially  equal  for  both  axles,  much  more 
nearly  equal  than  that  from  curvature. 

The  average  might  be  and  probably  is  somewhat  affected  by  a  ten- 
dency— especially  on  a  small  road  where  the  engines  were  well  known — to 
condemn  two  wheels  at  once  which  had  been  running  the  same  time,  al- 
though there  might  reaUy  be  not  a  little  difference  in  their  wear.  The 
great  excess  in  the  difference  in  wear  in  the  engine  trucks  is  notable. 


288      CHAP.   VIII.— MECHANICS  OF  CURVE  RESISTANCE. 

Table  110. 

Wear  of   Leading  and   Trailing  Wheels  of   Locomotive  and  Tender 
Trucks  on  the  Camden  &  Atlantic  Railroad. 

[Compiled  from  Report  to  Am.  Ry.  M.  M.  Assoc,  on  Loc.  Wheels  and  Axles  (Rep.  1878,  p.  23), 

by  Rufus  Hill,  M.  M.] 

Engine  Trucks. 


Size. 

No.  of 
Pairs. 

Mileage. 

Relative 

Life  of 

Wheels  on 

Front  Axle. 

Back  Axle 

=   I.O. 

Remarks. 

Lead. 

Trail. 

28  in. 
26   " 

8  each. 

28,998 
15,461 

43,024 

27,008 

.674 

•573 

Av.  all  eng.  wheels, 

28,623. 
Av.  all  tender  wheels, 

26,821. 

Average 

22,230 

35,016 

.6.4 

Tender  Trucks. 


30  in. 
28  in. 


10  each. 


27,897 
29,249 

23,419 
20,365 


25,232 


31.997 
32,736 
23,560 
25,346 


28,410 


.87 
,894 
.994 
.803 


Front  truck. 
Back  truck. 
Front  truck. 
Back  truck. 


The  table  is  stated  to  have  been  made  up  from  records  of  condemned  wheels  only, 
it  does  not  give  a  fair  idea  of  the  average  mileage  of  all  wheels. 


305.  It  does  not  fellow  that  the  total  shippage,  and  hence  total  curve 
resistance,  of  a  six-wheel  truck  would  follow  exactly  the  same  law  as  that 
of  a  four-wheel  truck  of  the  same  length  of  wheel-base  and  carrying  the 
same  load ;  but  it  is  useless  to  consider  that  question  for  lack  of  positive 
knowledge  as  to  the  position  naturally  assumed  by  a  six-wheel  truck.  It 
is  probably  the  same  as  if  the  middle  pair  were  omitted,  but  there  is  no 
evidence  of  that  fact. 

306.  Although  we  have  seen  that  coning,  however  much  or  little 
there  may  be,  has  no  influence  whatever  in  practice  upon  the  position 
assumed  by  the  truck,  yet  if  any  coning  exists  it  will  certainly  modify  the 
AMOUNT  of  slipping,  and  hence  the  resistance.  To  consider  how  much 
it  will  or  may  modify  it,  however,  would  lead  us  into  hopeless  and  profit- 
less intricacy,  because  there  must  be  slippage  under  any  circumstances 
with  a  rectangular  wheel-base,  which  will  speedily  wear  away  the  coning 
on  the  working  part  of  the  tread. 


CHAP.    VIIL— MECHANICS  OF  CURVE  RESISTANCE,      289 


It  is  probable,  however,  that  the  effect  of  the  coning  while  it  exists  is 
either  ;z27  or  positively  injurious,  taking  front  and  rear  axle  together,  for 
the  reason  that  the  position  assumed  by  the  wheels  bears  no  relation  to 
that  required  by  the  coning  and,  especially  on  the  front  outer  wheel,  is 
liable  to  increase  its  diameter  unduly. 

307,  So  far,  there  is  as  little  reason  to  doubt  our  correctness  as  can 
be  expected  in  any  subject  which  has  not  been  exhaustively  and  thor- 
oughly investigated  experimentally;  and  frictional  slippage  which  has 
been  estimated  includes  all  that  takes  place  between  rail  and  wheel  ex- 
cept (i)  that  due  to  flange  friction  and  (2)  the  possible  action  of  other 
forces  communicated  to  the  truck. 

308.  To  determine  the  resistance  arising  from  the  slippage  estimated,, 
the  very  delicate  question  arises  of  what  is  the  coefficient  of  sliding  fric- 
tion under  such  circumstances. 

The  primary  fact  to  be  remembered  in  estimating  this  is  that  the  ve- 
locity of  the  sliding  surface  upon  each  other  is  very  small,  as  shown  more 
fully  in  the  following  Table  iii,  computed  directly  from  the  preceding 

Table  ill. 

Velocity  in  Feet   Per  Second  with  which  the  Wheel  slides  on  the 

Rail  on  Various  Curves. 


Velocity  of 

Sliding 

;    Feet 

Per  Second. 

Velocity  of  Train. 

5-Foot  Truck. 

i2-Foot  Truck. 

1° 

5° 

10° 

20° 

I* 

5* 

10° 

20° 

10  miles  per  hour. .  -j 

.012 

10 
.018 

.06 
to 

.09 

.12 

to 

.18 

•24 
to 
.36   J 

.012 

to 
•034 

.06 

to 

•17 

.12 
to 

•34 

.24 
to 

.68 

30  miles  per  hour..  -| 

.036 

to 
•054 

.18 

to 

.27 

.36 

to 

.72 

.72 
to 

1.44 

.036 
to 

.102 

.18 

to 

•51 

.36 

to 

1.02 

.72 

to 

2.04 

Table  110,  by  assuming  that  10  miles  per  hour  =  15  (instead  of  14.67)  feet 
per  second. 

Our  knowledge  of  the  coefficient  of  sliding  friction  at  these  extremely 
low  velocities  may  be  summarized  as  follows  : 

1.  It  is  materially  greater  than  at  ordinary  and  perceptible  velocities, 

2.  It  is  very  greatly  more  sensitive  to  minute  changes  of  velocity  than 
at  ordinary  and  perceptible  velocities. 

3.  Its  maximum  at  a  velocity  of  0+  is  something  over  \  with   loco- 
motives and  perhaps  \  with  car  wheels  as  ordinarily  loaded. 

19 


290      CHAP.   VIII.—MECHANICS  OF  CURVE  RESISTANCE. 


These  laws  were  most  authoritatively  determined  and  most  com- 
pletely illustrated  by  the  famous  brake  experiments  of  Capt.  Douglas 
Galton  and  Mr.  George  Westinghouse,  the  general  results  of  which  are 
embodied    in  Tables  112  and  113.     We  shall  have  occasion  to  refer  to 

Table  112. 

Coefficients  of  Friction  between   Cast-iron  Brake-shoes  and  Steel- 
tired  Wheels. 

[Determined  by  Experiments  of  Capt.  Douglas  Galton  and  Geo.  Westinghouse,  Jr. 
Trans.  Inst.  M.  E.,  1878.] 


Coefficients  of  Friction. 

Velocity. 

Miles  Per  Hour. 

At  First. 

After  5  Sec. 

After  10  Sec. 

After  15  Sec. 

After  20  Sec. 

0  -j-  to  I  or  2 

.250 

7i 

.242 



I3i 

.213 

•193 



17 

,205 

.157 

.110 

20i 

.182 

.152 

.133 

.116 

.099 

27 

.171 

.130 

.119 

.081 

.072 

30i 

.163 

,107 

.099 

34 

•153 





........ 

37i 

.152 

.096 

.083 

.069 

41 

.144 

•093 

48 

.132 

.080 

.070 



54 

.106 

•045 

60 

.072 

.063 

.058 



While  these  results  are  unquestionably  more  nearly  correct  than  any  other  existing 
evidence,  there  is  considerable  room  for  doubt  as  to  the  exact  values  given. 

Table  113. 
Coefficients  of  Friction  of  Skidded  Wheels. 

[As  determined  in  the  Galton-Westinghouse  Experiments.    See  Table  112.] 


Coefficient 

OF  Friction. 

Velocity. 

Miles  Per  Hour. 

Steel  Tire  on 

Steel  Tire  on 

Steel  Rail. 

Iron  Rail. 

0  + 

.242 

.247 

7 

.088 

.095 

13 

.072 

.073 

27i 

.070 



34 

.065 

.070 

41 

.057 

52 

.040 

.060 

54 

.038 

60 

.027* 

*  Mean  of  three  tests  only. 


CHAP.    VIII.— MECHANICS  OF  CURVE  RESISTANCE.      29I 

these   experiments  frequently.     Many  independent  experiments  confirm 
their  essential  trutn. 

309.  Assuming  \  as  thee  oefficient,  the  resistance  of  the  wheels,  if  slid 
through  all  the  distance  that  they  are  advanced  along  the  track,  would  be 
in  lbs.  per  ton, 

2000  X  i  =  500  lbs. 

As,  however,  on  a  1°  curve,  they  only  slide  through  an  average  of 
.00073  of  that  distance,  the  resistance  arising  from  surface  friction  only 
between  rail  and  wheel  would  be  i?  =  2000  x  ^  x  .00073  =  o-S^S  lb. 

This  is  the  curve  resistance  (except  for  error  in  the  coefficient)  that 
can  be  accounted  for  at  slow  velocities,  excluding  flange  friction  and  the 
effect  of  shocks  and  irregularities.  From  the  general  laws  of  friction 
summarized  above,  it  would  seem  probable  that  both  the  surface  and 
flange  friction  would  decrease  with  either  (i)  increase  of  velocity  or  (2) 
decrease  of  radius,  which  has  the  same  effect  to  increase  the  velocity  of 
sliding,  at  any  given  speed. 

In  Appendix  A  will  be  seen  experimental  evidence  tending  to  support 
the  first  of  these  conclusions,  and  by  inference  the  second  also. 

310.  A  third  theoretical  cause  of  surface  friction  has  been  suggested,  viz. : 
Rotative  friction  of  the  wheel  on  the  rail,  due  to  the  fact 
that  it  not  only  slides  but  revolves,  but  its  existence  can- 
not be  conceded. 

It  is  true,  as  claimed,  that  the  actual  contact  is  by  a 
surface  and  not  a  theoretical  point  or  line ;  but  although  the 
wheel,  in  moving  through  an  infinitesimal  distance  AB, 
Fig.  28.  is  actually  rotated,  yet  as  this  takes  place  simul- 
taneously with  the  other  sHding  its  effect  is  simply  to  de-  Fig.  28. 
crease  the  velocity  on  one  side  of  the  center  of  contact  by  as  much  as  it  in- 
creases it  on  the  other  side. 

311.  Flange  Friction. — We  have  seen  that,  at  each  instant  of  time, 
the  truck  rotates  through  a  minute  angle,  turning  as  it  were  on  one  or 
the  other  of  its  rear  wheels,  A,  Fig.  25,  as  a  pivot ;  the  other  three  wheels 
sliding  on  the  surface  of  the  rail  in  the  direction  indicated  by  the  dotted 
lines.  The  force  which  causes  this  rotation — the  only  force  which  exists 
to  do  so — is  the  reaction  or  pressure  of  the  rail  against  the  flange  of  the 
front  outer  wheel. 

It  necessarily  follows  from  this  fact  that,  assuming  that  the  coefficient 
of  friction  is  not  affected  by  the  velocity  of  sliding,  this  pressure  or  reac- 
tion  is  always  the  same  on  curves.     For,  however  easy   the  curve,  a 


292      CHAP.    VIII.— MECHANICS  OF  CURVE  RESISTANCE. 


minute  sliding  motion  is  continuously  taking  place,  caused  by  the  reac- 
tion of  the  flange  ;  and  the  static  force  or  pressure  required  to  slide  one 
body  on  another  through  an  infinitesimal  distance  is  sufficient,  if  con- 
tinuously applied,  to  slide  it  through  any  distance  whatsoever.  The 
POWER  CONSUMED  varies  with  the  degree  of  curvature,  because  power  or 
energy  of  any  kind  is  measurable  only  by  a  double  unit,  the  force  applied 
X  the  distance  through  which  it  acts.  The  latter  (the  distance),  we  have 
already  seen,  varies  with  the  degree  of  curvature,  and  hence  the  power 
consumed  does  also  ;  but  the  static  force  applied  does  not  vary  with 
the  degree  of  curvature. 

This  very  important  distinction  is  one  which  should 
be  clearly  comprehended  and  kept  in  mind.  A  very  mis- 
taken idea  is  too  prevalent  that  the  flange  pressure  as  well 
as  curve  resistance  increases  with  the  degree  of  curva- 
ture. 

An  apparent  contradiction  to  this   statement  is  the 
well-known  excess  of  flange  wear  on  sharp  curves,  but 
this    is   rather   a    confirmation.      The    greater    distance 
slidden  through  produces  the  greater  wear,  not  greater  pressure. 

312.  The  front  outer  wheel  alone  has  its  flange  normally  in  contact  with 

the  rail.  The  forces  acting  upon 
the  front  outer  wheel  are,  first, 
the  load,  Z,  Fig.  29,  resting  upon 
it,  acting  vertically  downward  ; 
secondly,  a  horizontal  pressure 
against  the  rail  sufficient  to  slide 
three  wheels  (see  Fig.  25,  page 
286),  each  loaded  with  L. 

Assuming  a  coefficient  of 
sliding  friction  of  0.25,  this  late- 
ral force  amounts  to  0.75  L,  and 
the  resultant  in  magnitude  and 
direction  of  these  two  forces  is 
shown  in  Fig.  29. 

313.  The  manner  in  which 
the  various  forces  thus  meas- 
ured will  act  is  not  doubtful 
in  theory,  and  we  have  their  footprints  on  the  rails  themselves  to  assure 
us  that  theory  and  practice  correspond.  Instead  of  the  pressure  on  the 
rail  being  vertical,  as  in  Fig.  30,  we  have  the  conditions  and  the  relative. 


Fig.  30. 


CHAP.    VIIL— MECHANICS  OF  CURVE  RESISTANCE.      293 


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CHAP.    VIII.— MECHANICS  OF  C-URVE  RESISTANCE, 


position  of  rail  and  wheel  shown  in  Fig.  31.  Figs.  32  to  41  give  a  series 
of  rail  section  selected  from  a  great  number  taken  by  the  writer  on  the 
Atlantic  &  Great  Western  (now  New  York,  Pennsylvania  &  Ohio)  Rail- 
road, showing  the  wear  which  actually  results  from  the  conditions 
watched.  They  were  exact  copies  originally,  to  full  scale,  and  are  now 
reduced  one  half. 

Fig.  30  is  a  half-scale  section  of  a  new  flange  and  rail  section  of  ordi- 
nary form  (they  vary  somewhat  in  outline,  but  that  is  unimportant)  in 
their  natural  relative  position  on  a  tangent.  Fig.  31  shows  the  same  new 
U  flange    and    rail  section    in 

.LATERAL  THRUST. !  .  their  uatural  relative  posi- 

:  tion  ON  ANY  CURVE  WHAT- 

\  EVER,  however  sharp  or  flat. 


Fig.  ,31. 


Fig.  42. 


The  tread  stands  entirely  free  of  the  top  of  the  rail,  the  surfaces  in  con- 
tact being  neither  the  horizontal  tread  nor  the  vertical  flange,  but  the 
curved  surfaces  which  are  perpendicular  to  the  resultant  shown  in  Figs. 
29  and  31.  To  understand  this,  let  the  reader  turn  Fig.  31  around  diag- 
onally until  the  diagonal  stands  in  a  vertical  position,  and  let  him  con- 
ceive it  to  represent  the  vertical  force  of  gravity  alone.  He  will  see  that 
the  wheel  would  naturally  take  this  position— as  naturally  as  a  wheel 
shaped  like  Fig.  42  rolls  on  the  central  curved  surface  instead  of  the 
side  surfaces. 

314.  The  consequences  of  this  condition  of  things  are  these: 
First.  The  disproportion  in  the  diameter  of  the  wheels ;  hence  the 
necessary  longitudinal  slipping,  and  hence  the  curve  resistance,  is  materi- 
ally increased.     If  the  increase  of  radius  of  wheel  be  ^V  '"ch,  the  extra 
distance  slipped  through  per  station  of  100  feet  by  one  wheel  will  be  1.16 


CHAP.    VIII.— MECHANICS  OF  CURVE  RESISTANCE.      295 

feet ;  which,  by  referring  to  Table  109  on  page  286,  will  be  seen  to  be  as 
much  as  occurs  on  the  surface  of  the  rail  on  a  4°  curve.  This  increase, 
it  follows  from  what  has  preceded,  is  constant  for  all  curves,  and  thus 
tends  to  disproportionately  increase  the  resistance  of  easy  curves.  But 
precisely  how  much  the  resistance  thus  arising  may  be  with  new  wheels, 
it  is  profitless  to  inquire,  because, 

Seco7tdly,  The  inner  angle  of  the  wheel  and  the  outer  corner  of  the 
rail  is  gradually  worn  away,  the  greatest  wear  being  always  on  the  corner 
of  the  outside  rail  and  in  the  direction  of  the  resultant  (see  Figs.  32  to 
41),  on  curves  of  all  radii. 

The  rapidity  of  wear  depends,  not  upon  the  pressure,  which  is  con- 
stant on. all  curves,  nor  (to  any  marked  extent)  upon  the  angle  of  wheel 
to  rail,  but  upon  the  amount  of  sliding  which  takes  place — or,  in  other 
words,  varies  directly  as  the  degree  of  curvature. 

315.  Finally,  from  the  effect  of  these  causes  we  have  a  still  further 
change  of  conditions,  viz.: 

Thirdly.  As  the  wear  proceeds,  the  surfaces  in  contact  become  larger 
and  larger,  and  this  introduces  a  further  source  of  slippage,  rail  wear  and 
curve  resistance,  the  ultimate  form  of  which  is  shown  in  Fig.  41.  That 
particular  section  was  taken  from  a  16°  curve;  but  the  outer  rail  on  all 
curves,  of  however  long  radius,  tends  to  take  precisely  the  same  form  in 
the  end.  Thus  in  some  similar  sections  to  those  shown  in  Figs.  32  to  41, 
on  the  Pennsylvania  Railroad,  rails  from  4°  curves  after  sustaining  nearly 
four  times  the  tonnage  of  the  rails  showm  in  Fig.  34,  were  in  even  worse 
condition  than  the  rail  from  a  16°  curve  shown  in  Fig.  41. 

In  a  rail  worn  like  Fig.  41.  the  true  bearing  surface  on  which  the 
wheel  rolls  (compare  Fig.  31)  is  directly  on  the  corner,  and  the  rubbing 
surfaces  above  and  below  are  revolving  in  a  circle  of  nearly -^-inch  longer 
radius,  the  average  of  the  whole  surface  being  nearly  if  not  quite  \  inch. 

It  necessarily  results  from  this,  that  while  the  wheel  is  rolling  through 

any  distance  its  surfaces  slip  on  the  rail  through  — —  or  ^  of  that  dis- 
tance ;  =  1.51  feet  in  100. 

316.  The  coefficient  of  friction,  moreover  (as  well  as  rail  wear),  with 
such  large  surfaces  in  contact,  is  probably  considerably  larger  than  when 
the  bearing  is  on  a  mere  point,  as  in  the  unworn  rail,  Fig.  31  ;  for  the 
formerly  accepted  "law"  that  friction  is  independent  of  the  areas  in  con- 
tact has  been  proven  untrue  for  lubricated  and  still  more  for  unlubri- 
cated  surfaces,  as  was  found  out  practically  long  since  with  brake-shoes. 


296      CHAP.    VIII.— MECHANICS  OF  CURVE  RESISTANCE. 


The  information  on  friction  laid  down  in  most  of  the  standard  text-books 
is  very  deceptive. 

317.  This  third  source  of  extra  resistance,  due  to  badly  worn  rails,  is 
reached  in  a  much  shorter  time  on  sharp  curves,  and  as  a  rule  exists  only 
on  them  ;  but  nevertheless,  when  it  exists,  the  amount  of  the  extra  re- 
sistance caused  thereby  is  independent  of  the  radius.  If  rails  be  equally 
worn  it  will  amount  to  substantially  the  same  on  all  curves. 

When  the  wear  has  become  so  great  that  the  rail  has  the  form  of  Fig. 
41,  so  that  the  flange  bears  against  the  rail  almost  down  to  its  point,  the 
wear,  and  resistance  as  well,  is  doubtless  very  much  increased.  In  a  lot 
of  rails  which  have  been  all  exposed  to  substantially  the  same  tonnage, 
like  those  in  Figs.  32  to  41,  this  cojidition  will  be  likely  to  exist  only  on 
the  sharpest  curves,  and  accordingly  the  apparent  indications  of  a  test  of 
such  rails  will  be  that  rail  wear  increases  very  much  more  rapidly  than 
the  degree  of  curvature — in  fact  nearly  as  the  square  of  the  degree  of 
curvature. 

The  writer  himself  reached  this  conclusion,  from  the  only  facts  then 
before  him,  in  his  report  on  these  observations. 

318.  But  if,  on  the  contrary,  we  investigate  the  tonnage  7iecessary  to 
produce  the  same  wear  of  rails  on  different  curves,  we  shall  find  it  to  be 
almost  directly  as  the  degree  of  curvature,  and  this  is  undoubtedly  the 
true  law  of  rail  wear ;  from  which  it  follows  that  the  rate  of  wear  on 
any  one  curve  increases  as  the  rails  become  more  worn,  and  this  pro- 
duces the  deceptive  appearance  of  a  rate  of  wear  varying  as  some  function 
of  the  square  of  the  degree  of  curvature. 

319.  As  to  the  wear  on  the  inner  rail,  it  is  apparent  that  the  effect  of 
the  flange  pressure  (see  Fig.  29,  page  292)  is  to  increase  by  about  one 
third  the  load  resting  on  the  front  outer  wheel.  We  might  accordingly 
expect  that  all  the  longitudinal  slipping  would  be  confined  to  the  inner 
wheel  which  runs  (see  Figs.  20  to  23)  with  its  flange  entirely  clear  of  the 
rail.  From  this  we  might  expect  (i)  that  the  wear  of  the  inner  rail  would 
be  wholly  on  top,  and  (2)  that  it  would  be  more  rapid  than  the  outer  rail. 
This  is  always  found  to  be  the  case,  as  will  be  evident  from  Figs.  32  to  41. 
The  excess  of  top  wear  on  the  inner  rail  would  undoubtedly  be  much 
more  disproportionate  than  it  is  except  for  this  fact : 

The  bulk  of  tonnage  is  slow  traffic,  and  in  such  cases  the  excess  of  the 
superelevation  over  the  very  small  amount  required  to  balance  the 
centrifugal  force  (^  inch  per  degree  at  15  miles  per  hour;  see  page  298) 
produces  a  slight  excess  of  load  on  the  inner  wheels ;  not  sufficient  to 
counterbalance  the  effect  of  the  flange  pressure  on  the  front  axle,  but 


CHAP.    VIII.— MECHANICS  OF  CURVE  RESISTANCE.      297 

amply  sufficient  to  cause  the  rear  axle,  both  flanges  of  which  stand  clear 
of  the  rail,  to  slip  entirely  on  the  outer  rail  on  slow  trains,  as  being  the 
point  of  least  resistance. 

320.  We  thus  have  this  condition  : 

(i)  The  front  outer  wheel  produces  all  the  flange  wear  and  little  or 
none  of  the  top  wear, 

(2)  The  front  inner  wheel  produces  nearly  all  the  wear  on  inner  rail 
— confined  entirely  to  top  of  rail. 

(3)  The  rear  outer  wheel  of  slow  trains  produces  nearly  all  the  top 
wear  on  outer  rail. 

(4)  The  rear  inner  wheel  produces  only  the  normal  tangent  wear. 

321.  As  respects  the  aggregate  amount  of  curve  resistance  :  From  all 
these  data  together  we  may  expect  it  to  be — 

(i)  0.37  lb.  per  ton  per  degree  of  curvature  as  a  minimum,  varying 
directly  with  the  curvature,  plus — 

(2)  Upwards  of  i  lb.  per  ton  as  a  constant  addition  due  to  flange 
friction  on  new  rails  (assuming  the  coefficient  of  friction  to  be  as  low  as 
0.25,  as  it  appears  to  be  with  car  wheels.     With  engine-drivers  it  is  about 

(3)  As  rail  wear  increases  there  will  be  a  very  considerable  further 
addition  to  the  resistance  due  to  the  flange  wear  on  worn  rails.  This 
effect  will  become  visible  very  much  sooner  on  the  sharper  curves,  but 
it  will  occur  sooner  or  later  on  all  curves  when  the  flange  has  cut  into 
the  side  of  the  rail. 

321(3:.  Let  us  compare  these  conclusions  with  experience  : 

1.  Actual  experiment  on  the  63°  curves  (90  feet  radius)  of  the  New 
York  elevated  railroads,  conducted  by  Charles  E.  Emery,  M.  Am.  Soc. 
C.  E.,  shows  the  resistance  to  be  0.43  lb.  per  ton  per  degree  of  curva- 
ture on  new  rails  with  fixed  wheels  in  the  ordinary  mode,  and  0.33  lb. 
per  ton  with  loose  wheels.  (If  the  reader  will  refer  back  to  Table  109 
and  the  accompanying  discussion,  he  will  see  this  to  be  as  nearly  as  may 
be  what  our  theory  would  indicate.) 

2.  The  late  Benj.  H.  Latrobe  experimented  on  14°  curves,  with  new 
rails  also,  and  found  the  resistance  to  be  .40  lb.  per  ton. 

3.  French  experiments  with  about  12-ft.  wheel-bases  on  easy  curves 
show  about  1.25  lbs.  per  ton  resistance. 

4.  The  writer  made,  by  the  aid  of  very  delicate  electrical  apparatus, 
what  he  believes  to  be  the  most  accurate  experiments  on  train  resistance. 
so  far  as  they  went,  which  have  as  yet  been  made  ;  and  his  conclusions, 
so  far  as  relating  to  curve  resistance,  were  that  curve  resistance  is  much 


298      CHAP.    VIII.— MECHANICS  OF  CURVE  RESISTANCE. 


greater  per  degree  on  easy  curves  and  at  slow  speeds,  as  shown  in 
App.  A. 

322,  This  completes  our  analysis  of  the  forces  originating  and  acting 
within  the  truck  itself,  which  are  the  only  ones  of  importance.  Let  us 
see  what,  if  any,  effect  the  forces  acting  upon  the  car  body  and  train  as  a 
whole  have  to  modify  this  result. 

Centrifugal  force  and  superelevation  act  upon  the  car  as  a  whole, 
and  their  effect  is  communicated  to  the  truck  through  the  centre-pin  or 
side-bearings. 

The  centrifugal  force  C  in  lbs.  per  ton  of  any  body  moving  at  V  miles 
per  hour  on  a  D°  curve  we  have  already  found  to  be  (eq.  (3),  par.  271), 

C  =  0.2335  ^'A (I) 

from  which  Table  106,  page  270,  was  computed. 

323.  The  superelevation  of  the  outer 
rail  creates  a  force  tending  to  draw  the 
car  inward  and  to  counteract  the  cen- 
trifugal force.  Its  amount,  by  a  well- 
known  mechanical  law  (Fig.  44),  bears 
the  same  ratio  to  the  weight  as  g.  Fig. 
43,  does  to  the  superelevation  e.  On  a 
4  ft.  8^  in.  gauge  (say  4  ft.  lof  in.  centre 
(J  I     ^*-*»,,,^         to  centre  of  rail)  it  amounts,  therefore. 


in  lbs.  per  ton  per  inch  of  superelevation,  to  ro-z--  x  2000  =  34.04  lbs. 

The  maximum  amount  of  elevation  which  is  ever  to  be  found  on  rail- 
ways is  about  8  inches,  creating  a  force  of  272.32  lbs.  per  ton.  Many 
roads  limit  it  to  6  inches,  or  204.24  lbs.  ;  but  we  may  for  safety  assume 
the  maximum  to  be  10  inches,  or  340.4  lbs.  per  ton. 

Comparing  this  with  Tables  106  and  107,  it  will  be  seen  to  just  about 
balance  the  centrifugal  forces  at  what  is  marked  as  the  maximum  safe 
speed,  according  to  usual  practice,  on  various  curves. 

324.  To  determine  the  effect  of  these  forces  on  curve  resistance,  let 
us   assume  the  extreme  case — that  the  maximum  superelevation  is  en- 


CHAP.    VIII.— MECHANICS  OF  CURVE  RESISTANCE.      299 

tirely  unbalanced  by  centrifugal  force.     This  is  the  utmost  limit  that 

safety  permits. 

The  first  effect,  with  the  centre  of  gravity  in  the  position  shown  in 

39 
Fig.  43,  is,  by  well  understood  mechanical  laws,  to  throw  — r  or  about  70 

per  cent  of  the  load  upon  the  inner  rail,  leaving  only  30  per  cent  on  the 
outer  rail.  This  increase  of  load  will  compress  the  springs  on  the  inside 
and  by  the  further  tipping  of  the  car  body  cause  the  inside  rail  to  carry 
three  fourths  or  more  of  the  total  load. 

The  second  effect  is  to  confine  all  longitudinal  slipping  to  the  outside 
wheels  as  being  the  least  lightly  loaded.  This,  however,  we  have  seen  to 
be  the  case  with  the  front  axle  under  any  ordinary  circumstances.  The 
lateral  slip  of  the  front  axle  is  of  course  not  affected. 

The  third  effect,  resulting  from  the  combination  of  the  above  causes. 


i  ^^^! 


2000 


/00a 


Q^     JtGO 

Fig.  45. — Front  Outer  Wheel. 

(The  higher  rectang-le  shows 
the  conditions  without  supereleva- 
tion; the  smaller  rectang-le,  with 
superelevation.) 


i.<^\ 


2009 


tooo 


— ,3000 


'^A 


Fig.  46. — Rear  Outer  Wheel. 


Fig.    47. — Both 
Inner  Wheels. 


is  to  change  the  magnitude  and  direction  of  the  forces  acting  on  each 
wheel  in  the  manner  shown  in  Figs.  45  to  47,  in  which  the  solid  lines 
show  the  magnitude  and  direction  of  the  forces  already  determined, 
independent  of  the  superelevation. 

Or,  in  other  words,  taking  from  Table  109,  page  286,  the  slippage 
which  regularly  takes  place  in  a  5-foot  wheel-base  on  a  10°  curve,  we 
have — 


Slippage  in  feet 
per  TOO  feet. 

Increase  of  Load. 

New 
Slip. 

Rear  inner  wheel 

"      outer      "     

Front  inner     "      

"      outer     "      

0.00 
0.82 
0.89 
1. 21 

50  per  cent,  increase. 
50    "       "       decrease. 
50    "       "      increase. 
39    "       "      decrease. 

0.00 
0.41 

1-33 
•74. 

Total  amount. 

2.92 

15  per  cent,  decrease. 

2.48 

300      CHAP.    VIII.— MECHANICS  OF  CURVE  RESISTANCE. 

The  further  resistance  from  flange  friction  on  the  front  outer  wheel 
(as  also  flange  rail  wear)  should  also  be  diminished  about  39  per  cent. 

325.  We  thus  see  grounds  for  believing  that  the  general  effect  of  even 
an  extreme  amount  of  unbalanced  superelevation  may  be  to  somewhat 
decrease  the  resistance,  but  not  to  any  important  extent ;  and  with  the 
ordinary  and  proper  limit  of  6  or  7  inches  superelevation,  partially 
balanced,  as  it  always  is  in  practice,  by  centrifugal  force,  the  effect  be- 
comes almost  insignificant  one  way  or  the  other,  although  still  apparently 
to  decrease  the  resistance  so  far  as  it  has  any  effect  at  all.  On  the  other 
hand,  a  similar  computation  to  the  above  as  to  the  effect  of  an  unbalanced 
centrifugal  force  will  indicate  that  it  has  a  very 
similar  and  equally  inconsiderable  effect  to  in- 
crease the  resistance.  Fig.  48  shows  the  most 
objectionable  effect  from  excess  of  centrifugal 
force.     (See  par.  327.) 

326,  Let  us  now  see  what  effect  such  unbal- 
anced forces  do  not  have.  They  do  not  alter  in 
any  manner  whatsoever  the  position  of  any  of  the 
wheels,  nor  can  they  by  any  possibility  do  so,  it 
would  appear,  until  the  centrifugal  or  centripetal 
^^^;LANc7?''''cENT?fFuYrL  forcc  bccomcs  a  force  so  great  that  it  would  slide 
Force  on  Reaction  of   ^j^^  wheels  laterally  on  the  track  if  the  car  were 

Front     Outer     Wheel  -^ 

AGAINST  Rail.  Standing  still  on  the  rails,  which  would  be  when 

(Compare   Fig.  45,  show-  '^  i^^u  jr    jr    •        , 

ing  effect  of  an  equal  the  supcrelcvation  was  equal  to  the  ^^<?^. /r2^.  + 
frTpTaf  forTe^fromlupe?:  gauge,  OX  at.  say,  \  gauge,  or  about  14  inches. 
elevation.)    See  Table  106    p      ^j^g  force  required  to  slide  a  rolling  wheel  on 

for    velocity    necessary    to     -^  ^^  ^  ^ 

produce  this  amount  of  cen-    ^he    rail,    either    laterally    or    longitudinally,    is 
"  neither  greater    nor  less  than  if  the  wheel  were 

standing  still  (unless  there  may  be  some  slight  and  unknown  modifica- 
tion, of  the  coefficient  of  friction) ;  and  so  long  as  the  force  is  not 
FULLY  sufficient  to  do  this,  it  has  no  effect  at  all  to  move  the  body.  All 
it  can  do  is  to  increase  or  decrease  the  pressure  of  the  flange  against 
the  outside  rail,  and  this  (within  the  limits  of  safe  and  customary  prac- 
tice) only  to  a  trifling  extent.  This  results  from  an  elementary  mechani- 
cal law  which  has  been  too  readily  lost  sight  of  by  theorizers  on  this 
subject,  that  a  lifting  force  of  1999  pounds  is  as  incapable  of  lifting  a  ton 
as  a  force  of  one  pound. 

327.  The  real  objections  to  too  much  superelevation,  or  to  too  high  ve- 
locity, is  its  effect  upon  safety.  Throwing  so  much  weight  upon  one  rail 
and  one  set  of  springs,  is,  if  carried  to  excess,  highly  dangerous,  although 


i    %. 

,l7tX  /SV0=.7SL\ 

CHAP.    VIII.— MECHANICS  OF  CURVE  RESISTANCE.      301 

the  resistance  is  not  in  any  case  very  seriously  affected.  An  excess  of 
superelevation  would  appear  to  be  the  least  evil  of  the  two,  however,  in 
all  respects,  for  we  have  seen  (par.  324)  that  it  has  probably  some  slight 
effect  to  decrease  the  resistance  of  the  slowest  freight  train. 

328.  The  contrary  assumption  is  very  general,  but  it  is  absolutely  unsup- 
ported by  experimental  evidence  so  far  as  the  writer  can  discover,  and  it  cer- 
tainly finds  little  defence  in  theory.  The  truth  is,  that  much  of  the  current  and 
almost  endless  discussion  of  this  topic  among  road-masters  and  even  engineers 
has  its  root  in  insufficient  examination  of  the  mechanics  of  the  problem.  It  is 
ASSUMED  that  the  two  obtrusively  evident  forces,  centrifugal  force  and  its  oppo- 
site, are  the  only  ones  to  be  considered,  and  that  the  truck  is  thrown  against  one 
rail  or  the  other  by  these  forces  according  as  either  force  preponderates.  Yet 
one  has  only  to  watch  the  wear  of  rails  and  the  motion  of  a  truck  around  a 
curve  to  find  that  there  is  some  force  independent  of  either  (which  we  have 
analyzed  at  length)  which  presses  the  outer  wheel  against  the  rail  with  tre- 
mendous force,  however  high  the  superelevation  ;  and  from  this  it  follows  that 
it  is  the  effect  of  the  other  two  central  forces  upon  this  force  which  is  the  real 
problem  to  be  considered. 

329.  We  conclude,  therefore,  that  the  centrifugal  and  cen- 
tripetal forces  have  but  a  trifling  effect  on  curve  resistance,  and 
that  the  proper  rule  for  superelevation  is  to  elevate  sufficiently 
to  balance  the  centrifugal  force  of  the  fastest  trains  up  to  a 
maximum  of  six  to  eight  inches.  This  will  slightly  decrease  the 
resistance  and  danger  of  accident  to  freight  trains,  and  greatly 
improve  the  comfortable  riding  of  passenger  coaches,  provided 
always  that  some  uniform  rule  be  followed,  since  almost  any 
rule  is  better  than  none. 

330.  A  third  source  of  possible  curve  resistance,  obliquity  of  trac- 
tion, affects  the  train  as  a  whole.  The  conditions  of  the  problem  are 
presented  in  Fig.  49. 

It  may  now  be  considered  as  established  that,  despite  a  prevalent 
impression  to  the  contra- 
ry (which  many  able  engi-  g.       p A 

neers  have  shared),  no  loss  ^^-'"^  rt- 

of  power  whatever  occurs  ,.^'' 

from  this  cause.     Let  OA,     -"'' 

Fig.  49,  represent  the  trac-  '°"  '*9* 

tive  force  to  be  transmitted  through  the  coupling  O  to  the  car  B.     As 

there  is  a  change  of  direction  in  the  force  at  O,  it  is  sometimes  claimed 


302      CHAP.    VIII.— MECHANICS  OF  CURVE  RESISTANCE. 

that  no  force  OA  can  be  caused  to  act  on  the  following  car  in  the 
changed  direction  OB  without  a  certain  loss  of  tractive  force,  and  hence 
waste  of  energy.  This  position  is  in  both  respects  unsound.  There  is 
no  loss  of  tractive  force  at  each  car  due  to  obliquity  of  traction,  and,  even 
if  there  were,  it  would  not  necessarily  imply  any  waste  of  energy.  It  fol- 
lows that  the  method  of  analyzing  the  strains  by  which  such  position  is 
supported  (which  consists  in  making  the  angle  OCA,  Fig.  49,  a  right 
angle  and  then  taking  the  force  OB  =  AC,  or  less  than  OA)  is  incorrect. 

331.  The  correct  way  of  representing  the  action  of  the  forces  involved 

is  by  the  parallelogram  of  forces  shown 
in  Fig.  49,  which  should  be  constructed 
as  shown,  with  OB  =  OA,  the  force  OA 
being  transmitted  undiminished  through 
O-  as  around  a  pulley ;  the  lateral  stress 
OC  having  no  more  effect  to  reduce  the 
force  OB  than  the  stress  OC,  Fig.  50,  has 
to  make  the  force  OB  less  than  OA.  Both 
in  Figs.  49  and  50,  if  the  stress  OC  is  suf- 
ficient to  produce  lateral  motion  in  the 
direction    OC  by  overcoming  the  static 

resistance,  it  will  or  may  consume  power,  and  the  force  OB  may  be  thf-n 
quite  different  from  AO,  but  otherwise  not. 

In  a  train  of  cars,  the  lateral  component  has  only  the  effect  to  mi- 
nutely increase  the  lateral  resultant  of  the  superelevation,  which  we  have 
just  seen  tends  to  decrease  the  resistance  (if  anything),  but  has  no  effect 
to  change  the  position  of  any  wheel,  or  to  increase  perceptibly  the  pres- 
sure of  the  wheels  against  the  rails. 

Conceive  the  track  to  be  a  complete  circle,  and  the  train  to  com- 
pletely fill  it.  Conceive  the  floor  of  the  cars  to  be  a  rigid  continuous  cir- 
cular platform.  There  would  then  nowhere  be  a  lateral  resultant  of  the 
kind  discussed,  but  no  reason  is  apparent  why  the  curve  resistance  should 
be  either  greater  or  less. 

332.  The  transmission  of  force  from  car  to  car,  through  a  train  on  a 
curve,  is  an  almost  exact  mechanical  parallel  to  the  transmission  of 
power  by  a  rope  or  chain  over  a  pulley ;  the  rope  being  the  string  of  car 
bodies,  and  the  car  wheels  the  pulleys.  The  fact  that  the  pulleys  are 
carried  by  the  rope  itself,  instead  of  in  a  block  exterior  to  it,  i-s  a  mere 
detail  not  affecting  the  mechanical  conditions.  In  either  case  the  loss 
from  such  transmission  is  simply  the  friction  of  the  pulley.  Conceive  a 
chain  made  of  successive  links,  each  carrying  a  pulley  wheel  and  being 


CHAP.    VIII,— MECHANICS  OF  CURVE  RESISTANCE.      303 

dragged  over  a  large  cylinder  or  succession  of  cylinders,  large  or  small. 
Conceive,  further,  the  rope  to  be  so  long  and  the  friction  of  the  pulleys 
so  great  that  the  whole  power  of  the  prime  mover  is  consumed  in  keep- 
ing the  chain  in  motion  at  uniform  speed.  We  have  here  a  perfect 
mechanical  parallel  to  a  train  in  motion  on  a  curve,  except  for  the  one 
minor  fact  that  the  resultant  of  all  the  forces  acting  on  the  wheels  does 
not,  in  case  of  a  railroad  train,  lie  exactly  (although  it  does  nearly)  in  the 
plane  of  the  wheels  themselves,  whereas  in  the  case  of  the  pulley  wheels 
it  does.  But  no  resistance  arises  at  the  coupling-points  from  "  change  of 
direction,"  or  obliquity  of  traction,  or  from  any  other  source  than  the 
friction  of  the  pulleys  proper,  in  either  case.  It  is,  of  course,  true  that 
the  resistance  of  the  rear  pulleys  would  tend  to  press  each  pulley  in  ad- 
vance more  tightly  against  the  surface,  and  so  produce  greater  friction  in 
the  pulley  itself  than  would  otherwise  exist ;  and  similarly  in  the  case  of 
a  railroad  train  it  is  entirely  pertinent  to  prove  that  a  lateral  centripetal 
force  is  produced  by  obliquity  of  traction,  so  that  the  resultant  of  all 
forces  does  not  lie  in  the  plane  of  the  wheel,  and  that  this  fact  produces 
greater  friction.  The  latter,  however,— the  only  possibility  pertinent  to 
discuss,— is  commonly  neglected  in  discussions  which  assume  that  lateral 
resultants  from  obliquity  of  traction  indicate  fro7n  their  mere  existence  a 
loss  of  energy.  FORCE,  i.e.,  static  stress,  is  one  thing,  resistance,  i.e., 
destruction  of  dynamic  energy,  is  another  and  quite  different  thing.  We 
cannot  figure  away  energy  with  a  parallelogram  of  forces,  but  must  prove 
when  and  how,  if  at  all,  it  is  lost  by  additional  friction.  As  a  matter  of 
fact  there  appears  to  be  no  loss,  but  a  trifling  gain,  under  ordinary  con- 
ditions, from  the  fact  that  the  centripetal  tendency  is  increased. 

333.  There  is  so  much  misconception  as   to  this  matter  that  we  may  en- 
deavor to  make  it  still  clearer.     In   Fig.  51  let  the  lines  OOP  represent  the 
axes  of  two  successive  cars  moving  in  either  direction  ;  PP,  the  two  coupling- 
pins;  and  Z,  the  coupling-link.    Let 
the  lines  SS  represent  in    magni-  ^1 

tude  and  direction  the  tensile  force 
acting  upon  the  link  and  tending  to 
rupture  it.  As  a  matter  of  course, 
these    forces    S  must  be  equal  to  ^^^'  5'- 

each  other,  since  action  and  reaction  are  equal,  and  when  resolved  into  forces 
acting  along  the  axes  of  the  cars  this  makes  the  latter  also  equal.  The  losses 
of  tensile  force  from  car  to  car  occur  at  the  centre-pins  O  of  each  car,  and  not 
at  the  coupling-points  P.  The  tension  on  the  front  end  and  back  end  of  the 
draw  gear  of  any  given  car  is  always  different  by  the  amount  of  the  frictional 
resistance  of  that  car  ;  but  the  longitudinal  strains,  parallel  with  the  respective 


304      CHAP.    VIII.— MECHANICS  OF  CURVE  RESISTANCE. 

axes  of  the  cars,  on  the  rear  draw-gear  of  a  forward  car  and  the  front  draw- 
gear  of  a  rear  car,  are  always  equal  to  each  other  in  magnitude,  although  differ- 
ent in  direction  by  the  amount  of  the  angle  between  the  axes.  That  is  to  say, 
the  diminution  of  tensile  force  from  car  to  car  is  internal  to  each  car,  and  not 
at  all  at  the  coupling-point. 

334.  But  the  point  is  not  worth  disputing,  for  the  loss,  if  it  were 
granted  to  exist,  is  very  small.  Assuming  the  car  body  to  be  30  feet 
long,  the  deflection  angle  OAB,  Fig.  49,  will  evidently  be,  on  a  Z>°  curve, 
0.3Z)  or  18'  X  D,  and  of  the  tractive  force  F  {  =  OA,  Fig.  49)  there  will 
be  an  assumed  loss,  which  let  =  L,  at  each  coupling,  from  obliquity  of 
traction : 

Z  =  i^  (I  -  cos  18O  i^  =  0.000016DF. 

The  tractive  force  of  a  Consolidation  engine  is  something  over 
20,000  lbs.  at  the  engine  and  zero  at  the  end  of  the  train,  averaging,  say, 
10,000  lbs.     Then  the  loss  per  car  will  average,  on  a  1°  curve, 

Z  =  0.16  lb.  per  car, 
or,  on  a  10°  curve  with  a  60-car  train, 

L  =  g6  lbs. 
Not  a  very  serious  matter,  certainly. 

335.  We  conclude,  therefore,  as  to  curve  resistance  : 

1.  Obliquity  of  traction  and  the  length  of  the  train  have  no 
appreciable  effect  to  modify  curve  resistance. 

2.  Centrifugal  force  within  the  limits  of  practice  has  but  lit- 
tle effect  on  the  resistance,  but  that  little  is  to  increase  it. 

3.  Centripetal  force  from  superelevation  within  the  limits  of 
safe  practice  has  but  little  effect  on  the  resistance,  but  that  little 
is  to  reduce  it. 

4.  The  best  rule  for  superelevation  is  to  elevate  for  the  fast- 
est regular  speed  up  to  a  maximum  limit  of  6  to  8  inches  in  all. 

5.  Rail  wear  and  curve  resistance  over  rails  in  the  same  con- 
dition are  as  nearly  as  may  be  directly  as  the  degree  of  curva- 
ture, with  some  minor  elements  wliich  are  independent  of  radius. 

6.  Rail  wear  and  curve  resistance  are  appreciably  less  with 
new  rails  than  with  old,  and  become  greater  as  the  outer  rail  is 
worn  away  to  the  shape  of  the  flange. 

7.  The  pressure  of  the  flanges  against  the  rail  is  the  same  on 
all  curves  independent    of    radius,  but   the    wheel   stands  at  a 


CHAP.    VIII.— MECHANICS  OF  CURVE  RESISTANCE.      305 


greater  angle  to  the  rail  as  the  curve  is  sharper,  and  likewise  is 
sliding  faster  on  the  surface  of  the  rail,  increasing  the  danger  of 
derailment  correspondingly,  by  some  unknown  amount,  but  not 
nearly  in  proportion  to  the  degree  of  the  curve. 

8.  The  lowest  probable  limit  of  curve  resistance  at  ordinary 
freight  speeds  and  in  ordinary  curves  is  about  \  lb.  per  ton 
per  degree  of  curve,  with  all  in  perfect  order.  With  w^orn  rails 
and  somewhat  rough  track  it  may  be  as  high  as  f  lb.  per  ton. 

9.  While  so  obscure  a  point  cannot  be  considered  as  estab- 
lished by  the  existing  experimental  evidence,  all  the  more  trust- 
worthy existing  evidence  seems  to  combine  with  theory  to  indi- 
cate that  curve  resistance  per  degree  of  curve  is  very  much 
greater  on  easy  curves  than  on  sharp  curves  ;  so  that  when  the 
resistance  is  i  lb.  per  ton,  for  example,  on  a  1°  curve,  it  may  be 
6  to  8  lbs.  per  ton  on  a  10°  curve,  and  not  more  than  15  to  18 
lbs.  per  ton  on  a  40°  to  50°  curve.      (See  Appendix  A.) 

10.  It  may  be  considered  established  that  curve  resistance  is 
affected  somewhat  by  the  speed,  and  probably  by  a  very  consid- 
able  percentage;  so  that  if  the  curve  resistance  in  motion  be 
\  lb.  per  ton  it  may  be  as  high  as  i  lb.  per  ton  on  worn  rails, 
for  speeds  of  less  than  4  or  5  miles  per  hour,  or  for  the  first 
train   length  or  thereabout   in  getting  under 

way.     As  a  stoppage  on  any  curve  is  always    ^onffHuctmaf Slip. 
a  possibility,  this  contingency  should  not  be 
forgotten  when  reducing  grade  on  curves,  es- 
pecially near  possible  stopping  points. 

11.  The  beneficial  effect  of  the  narrower 
gauge  is  small  with  the  same  length  of  wheel= 
base.  With  a  3-ft.  gauge  as  against  a  4.7-ft. 
gauge,  with  a  wheel-base  of  4- 7  ft.,  it  is  about  fig.  s^.-Effect  of  Dif- 

j^ ^ — j ^  ference    of    Gauge   on 

as    (not   exactly  as)     ^-7  XJiL  _  -L^  —  1.     lengtVof  Whe™S 

y      ^^    _1_     A     ij"^  5*57^  REMAINING  THE  SAME. 

O       \     "^^  I  (The    comparative    slip- 

less,  as  outlined  in  Fipf.  152.    With  a  wheel-base  pI^s'  °^  ^^^  wheels  m  a 

^    ^  Sfiven     distance     is    repre- 

110.72  sented  by  thetwodiag-onals 

of  2g  the  gain  is  onlv —-=  12  per  cent  less,   marked iV.  g.  and  st'd.  g.) 

'    97-36 
If,  however,  the  length  of  wheel-base  decreases  with  the  gauge 


306      CHAP.    VIIL— MECHANICS  OF  CURVE  RESISTANCE. 


the  gain  is  directly  as  the  gauge.     All  the  preceding  refers  only 
to  the  surface  friction  on  the  top  of  rail,  flange  friction  being 

much  less  affected.  Longitudinal  slip 

12.  Increasing  the  length  of  wheel-base, 
say,  from  gauge  to  2  gauge  increases  curve  fric- 
tion  as   outlined  in   Fig.   53,  in   the  ratio   of 

2  2  "^6 

— ^—  z=  c.%  per  cent. 

336.  Perhaps  the  best  existing  experimental  confir- 
mation of  the  eleventh  conclusion  above  is  to  be  found 
in    some    delicate    experiments    on    models    by    Mr.    Reuben 
Wells  (Rept.  Am.   Ry.   M.  M.  Assoc,   1876),  which  have  at- 
tracted  far   less    attention  than  their  merit  deserves.     While 
no  one  test  of  any  kind  can  be  considered  decisive,  the  tests 
do  afford  an  indication  which  is  perhaps  more  delicate  and  re- 
liable as  a  test  of  principle  than  could  easily  be  made  with  the 
actual  rolling-stock.     With  trucks  representing  to  y^   scale  a  p^^  ^^^  _  Effect 
wheel-base  of  4  ft.  10  in.  and  gauges  of  3  ft.  and  4  ft.  8^  in.  on 
a  curve  representing  to  the  same  scale  one  of  300  ft.  radius 
and  273  ft,  long,  gravity  being  the  impelling  force,  Mr.  Wells 
found — 


Speed, 

Miles  Per  Hour. 

5.76 

■      7-59 

10.12 

16.70 


Resistance 
St,  G. 

46,80 
48.96 

45-76 
68.20 


lbs.  per  ton  (actual), 
N.  G.  p.  c.  of  N.  G. 

39,14  83.6 

41.66  85.1 

41.66  9I-0 

64 . 40  96-0 


OF  Difference 
OF  Length  of 
Wheel-base  on 
Curve  Resist- 
ance, Gauge 
remaining  the 
same. 


By  formula  above 

\ gauge- -\-  whedlbase^ 

-   the  per  cent  of  N.  G. 

should  be,  uniformly, 

82.7  p.  c. 


If  we  consider  that  in  these  observed  resistances  the  normal  tangent  roll- 
ing friction  is  included,  whereas  in  the  formula  it  is  not,  the  two  correspond 
wonderfully  closely,  indicating,  however,  that  the  absolute  amount  of  curve 
resistance  decreases  with  the  speed-which  is  probable  from  other  reasons. 
The  tests  were  made  by  raising  the  track  to  a  grade  which  would  give  the  de- 
sired velocity  and  the  resistances  in  lbs.  per  ton  deduced  therefrom.  The  high 
absolute  amount  of  the  latter,  compared  with  normal  rolling-stock  resistance, 
should  not  be  allowed  to  convey  an  impression  that  the  models  were  rough. 
On  the  contrary,  they  show  that  it  was  very  delicately  constructed,  as  the  re- 
sistances per  ton  of  its  actual  weight  are  but  little  more  than  three  times  what 
might  be  expected  with  fully  loaded  cars,  which  is  even  less  than  the  probable 
difference  in  coefficient  of  friction  due  to  the  difference  of  load. 

Mr  Wells's  primary  purpose  in  undertaking  these  tests  was  to  determine 
how  much  there  might  be  in  the  alleged  theoretical  advantages  of  loose  wheels 


CHAF.   VIII.— MECHANICS  OF  CURVE  RESISTANCE.      30/ 

for  passing  curves.  He  found  that  in  no  case  was  much  gained,  while  in  some 
cases  the  loose  wheels  were  a  positive  disadvantage.  The  preceding  theoreti- 
cal discussion  of  the  mechanics  of  curve  resistance  may  be  readily  shown  to 
point  directly  to  the  same  conclusion,  and  almost  to  Mr.  Wells's  identical  fig- 
ures, had  it  appeared  expedient  to  extend  this  discussion  for  that  purpose. 

337i  The  late  Baron  Von  Weber,  whose  great  services  to  the  cause  of 
science  entitle  anything  vouched  for  by  him  to  a  presumption  in  its  favor, 
gave  currency  to  a  very  absurd  formula  in  respect  to  curve  resistance,  which 
has  been  quite  extensively  quoted  as  trustworthy,  as  it  was  alleged  to  rest  on 
some  extensive  and  elaborate  experiments.  This  formula  gave  the  total  resist- 
C 

ance  as  a  function  of ,  R  being  the  radius  in  metres.     This  formula 

-"^  —  55 
gives  resistances  increasing  much  faster  than  the  degree  of  curve,  instead  of 

slower,  as  we  have  found;  the  results  varying  from  a  resistance  of  0.8  lb.  per 
net  ton  per  degree  for  a  curve  of  1000  metres  radius  (3310  ft.,  or  1°  44')  to  a 
resistance  of  1.67  lbs.  per  net  ton  per  degree  for  curves  of  100  metres  radius 
(331  ft.,  or  17°  20').  But  by  extending  the  formula  to  a  little  sharper  curves  its 
untrustworthy  and  absurd  nature  is  at  once  seen.  For  a  curve  of  60  metres 
radius  (197  ft.)  we  obtain  a  resistance  9,45  times  as  much  per  degree  as  on  a 
curve  of  1000  metres  radius,  and  for  a  curve  of  55  metres  radius  or  less  an  in- 
finite resistance.  As  the  curves  of  the  New  York  elevated  railways  are  of  less 
than  30  metres  radius,  and  as  ordinary  American  engines  were  operated  over 
a  curve  of  50  ft.  radius  for  some  time  without  accident  or  delay,  on  the  United 
States  Military  Railroads  in  the  late  war,  this  is  hardly  a  rational  result. 

338.  A  new  and  dangerous  doctrine  has  lately  been  advanced,  in  a  semi- 
official manner  which  has  given  it  wide  currency  as  a  conclusion  of  the 
Master  Car-Builders'  Association,  al- 
though it  was  in  no  sense  such  in  fact, 
viz.,  that  the  corners  of  rails  should 
be  rolled  to  a  larger  radius  (f  inch)  so 
as  to  exactly  fit  the  radius  of  the  fillet 
or  interior  corner  of  the  flange,  instead 
of  the  two  being  of  quite  dissimilar 
radius,  as  in  Fig.  31,  which  shows  the 
more  usual  and  the  only  proper  prac- 
tice. 

These  conclusions  were  expressed 

in  an  otherwise  able  paper,  by  M.  N.  ^'°-  54- 

T7^..„^„     c  *  r  *u      A  •     •  ^^'S"-   54  is  Fig".   19  of  Mr.   Forney's  paper, 

Forney,   Secretary  of  the  Association    "The  Relation  of  Railroad  Wheels  and  Rails 

(Kept.  M.  C.  B.  Assoc,   1885);   and  the    %T^'^f^^''x    ^"f  shows  a  New  York  Central. 
*^  '  o/)  rail-head  and  a  flange  with  a  hllet  of  %  inch 

theory  was  based  upon  the  claim  that  radius.) 

the  usual  form  of  rail  and  flange,  such  as  is  shown  in  Figs,  30  and  31,  causes 

sharp  flanges,  producing  wear  such  as  is  outlined  in  Fig.  54  ;  the  corner  of  the 


308      CHAP.   VIII.— MECHANICS  OF  CURVE  RESISTANCE. 

rail  wearing  to  a  larger  radius,  and  the  fillet  of  the  flange  to  a  smaller  radius, 
thus  producing  sharp  flanges. 
The  facts  are : 

1.  (See  Table  114.)  Only  a  very  small  percentage  of  wheels  ever  get  sharp 
flanges,  and  there  are  never  two  sharp  flanges  on  one  axle;  showing  that  some 
mechanical  defect  of  wheel  or  truck  (usually  the  latter)  is  the  chief  cause  of 
sharp  flanges,  and  not  some  general  cause  acting  upon  all  wheels  alike. 

2.  Except  in  the  one  case  of  the  outside  rail  on  curves,  rails  invariably  wear 
^, to  a  much  smaller  corner  radius,   as  in  Fig.   55,  re- 

''  ""■"^.     produced  from  an  example  of  wear  in  Mr.  Forney's 

^';  paper  (see  also  Figs.  32    to  41),  and    never   in    the 
manner  outlined  in  Fig.  54. 

3.   In  the  one  case  of  the  outside  rail  on  curves 
the  rails  do  finally  wear  away  in  something  like  the 
l^^'G.  55.  manner  outlined  in  Fig.  54,  until  the  side  of  the  rail 

takes  almost  the  exact  form  of  the  flange,  as  in  Fig.  41,  but  there  is  then  much 
more  friction,  more  rapid  wear,  and  more  danger  of  derailment  than  when  the 
rails  are  new,  as  in  Figs.  31  or  54  ;  because,  although  the  bearing  surface  is 
small  in  the  latter  case,  it  is  subjected  to  only  rolling  wear,  whereas  if  the 
flange  fits  all  around  the  rail  corner  the  additional  bearing  surface  is  exposed 
to  rubbing  friction.     (See  par.  313  et  seq.) 

339.  Imagine  a  heavy  sphere  rolling  down  a  plank,  as  in  Fig.  56.     It  has  a 

very  small  bearing  surface,  yet 
any  additional  bearing  surface 
which  might  be  gained  by  turn- 
ing the  plank  into  a  trough 
"exactly  fitting"  the  sphere 
Fig.  56.  would     plainly    produce    more 

friction  and  more  wear,  rather  than  less.  The  same  conditions  obtain  in  Fig. 
54,  where  the  material  outside  the  dotted  lines,  which  it  is  proposed  to  remove 
in  first  manufacture,  is  really  "  precious  metal,"  serving  to  long  postpone  the 
day  when  the  rail  and  flange  fit  as  Fig.  41,  and  a  very  rapid  rate  of  wear  begins. 
The  metal  outside  the  dotted  lines  in  Fig.  54  will  require  at  \gq.sI  fotir  times  as 
great  a  tonnage  to  wear  it  away  as  will  be  required  to  wear  away  an  equal 
weight  of  metal  after  it  is  gone.  Moreover,  the  wear  of  flange  outlined  in  Fig. 
54  never  takes  place  at  all  except  in  a  very  small  percentage  of  the  wheels 
(2  to  6  per  cent),  indicating  that  it  is  not  due,  when  it  does  take  place,  to  the 
form  of  the  rail. 

340i  What  sound  practice  would  seem  to  require,  therefore,  is: 
I.  The  tread  of  the  wheel  should  have  something  the  form  of  Fig.  57,  with 
a  fillet  radius  of  at  least  fin.,  mstead   of  the -J-in.  radius  which  Mr.  Forney 


CHAP.   VIII.— MECHANICS  OF  CURVE  RESISTANCE.      309 


.LATERAL  THRU  ST 


recommended,  and  the  -f-in.  radius  which  the  Master  Car-Builders'  Association 
have  unfortunately  adopted  as  standard. 

2.  The  original  corner  radius  of  the  rail  should  be  little  if  any  greater  than 
i  or  y\  in. 

In  this  way  we  shall  postpone  as  long  as  possible  the  evil  day  when  the  rail 
and  wheel  will  not  simply  roll  upon  but  grind  into  each  other. 

341.  The  deleterious  effect  of  having  the  corner  of  the  rail  of  larger  radius 
than  the  fillet  of  the  flange  is  clearly  visible  in  Fig.  58.  When  any  lateral 
flange  pressure  arises  from  p 
the  passage  of  a  curve  or 
other  cause,  instead  of  the 
bearing  surfaces  being  able 
to  still  maintain  the  merely 
rolling  contact  of  minimum 
wear,  as  outlined  in  Figs.  31 
and  59,  we  have  the  rubbing 
side  contact  shown  in  Fig.  58, 
sure  to  produce  rapid  side 
wear,  in  addition  to  the  usual 
top  sliding  and  wear.  This 
has  actually  resulted  with 
rails  of  such  form.  On  the 
Lehigh  Valley  and  on  the 
parts  of  the  Pennsylvania  laid 
with  its  new  rail  section  of  -§■ 
in.   corner  radius,  both  rails, 

on  both  curves  and  tangents, are  badly  worn  far  down  the  side  of  the  rail,  as  if 
laid  very  tight  of  gauge,  whereas  with  rails  of  the  usual  form  this  never 
results,  however  old  or  worn  the  rails,  except  on  the  outside  rail  of  curves. 

342.  Mr.  M.  N.  Forney,  in  the  paper  above  referred  to  (par.  338),  gives  the 
best  existing  evidence  as  to  the  effect  of  coning  on  the  natural  path  of  trucks 
having  parallel  axles.  He  experimented  with  an  apparatus  s^uch  as  is  shown 
m  Fig.  60.  To  determine  positively  if  these  results  were  correct,  the  writer 
has  smce  constructed  and  tested  a  model  of  quite  different  form  with  closely 
similar  results. 

Mr.  Forney's  model,  compared  with  a  full-sized  truck,  was  made  to  a  scale 
of  i  in.  =  I  foot,  or  ^  of  full  size.  The  wheels  on  each  axle  represented  full- 
sized  wheels  of  34^  and  31^  in.,  or  a  difference  of  3  in.  in  diameter.  The 
radii  of  the  actual  path  of  the  model,  with  wheels  set  at  various  distances  apart, 
are  shown  m  Fig.  61.  Converting  all  the  dimensions  of  the  model  and  the 
results  of  the  experiments  into  the  full  size  which  they  represented,  they  in- 
dicate that  a  single  pair  of  wheels  on  the  same  axle,  with  a  difference  of  3  in.- 


FiG.  59. 


3IO      CHAP.    VIIL— MECHANICS   OF  CURVE  RESISTANCE. 


Fig.  57. 


|€ 4Vi! ^ 

Fig.  58. — Rail  Section  and  Wheel-tread,  Lehigh  Valley  Railroad. 
(Showing  effect  of  having  corner  of  rail  of  larger  radius  than  fillet  of  flange.) 


CHAP.    VIII.— MECHANICS  OF  CURVE  RESISTANCE.      31I 


in  their  diameters,  will  roll  in  a  curve  of  53^  il.  radius.  Two  pairs  of  such 
wheels,  if  the  axles  are  held  parallel,  as  in  the  model,  would  roll  in  the 
following  curves: 

:t  will  roll  in  a  curve  of    67  ft.  radius. 


Axles  3  ft.  apa 

4 

5 

6 

7 

8 

9 
10 


133 

I74i 

251 

337f 

479 

643i 


Fig.  60. — Model  used   by  Mr.  M.  N.  Forney   for   Investigating  the  Effect  of  Coning 
ON  the  Path  of  Rectangular  Wheel-bases. 


With  an  average  coning  of  -^  in.  in  the  length  of  the  tread,  and  an  average 
play  in  the  gauge  of  f  in.,  we  find  about  ^  in.  to  be  the  difference  of  diameter 
which  ordinary  coned  car  wheels   can  have,  assuming  that  both  wheels  stood 


312      CHAP.    VIII.— MECHANICS  OF  CURVE  RESISTANCE. 


close  to  the  outside  rail,  which  they  do  not  (see   Fig.  20  and  par.  294). 
would  correspond  to  results  in  actual  practice  as  follows  : 


This 


i 

\xles  3  ft.  apart  will  roll  in  a  curve 

of 

2.572  ft.  radius. 

"      4 

" 

3,513 

K 

/ 

"      5 

" 

5.107 

/ 

<i     g             «•               <. 

(< 

6,700 

/ 

<<      ^            <(               (( 

•' 

9.638 

J 

f 

<<      0             ((               tt 

<< 

12,969        ** 

/ 

ti     g             (f               « 

«< 

18,393 

h 

y 

««    10             **               " 

«< 

24,700         " 

/ 

' 

/ 

/ 

« 

4 

^ 

■a 

1< 

a 

J(^ 

^. 

c 

y^ 

^ 

'5 

c 

^ 

# 

i 

t 

< 

^ 

'^ 

i 

b — -^ 

M 

% 

> 

S 

W^ 

V 

^IT  * 

c 

ij«* 

2 

L 

3»/2«       4 

7~~ 

ife^ 

; 

4 

Gauge,  2.3s  in. 

Fig.  61. — Radius  of  Path  of  Wheel-base  shown  in  Fig.  60,  with  Wheels  set  at  Various 
Distances  apart,  as  shown  along  the  Base-line. 


These  figures  indicate  that  even  under  the  most  favorable  possible  circum- 
stances coning  can  have  little  effect  to  facilitate  the  passage  of  curves. 

343.  Having  now  investigated  the  nature  of  rail  wear  on 
curves  and  the  causes  of  curve  resistance,  we  are  better  prepared 
to  take  up  and  estimate  at  their  true  worth  the  positive  objec- 
tions to  curvature,  as  summarized  at  the  beginning  of  this  chap- 
ter, which  are  : 

1.  The  direct  cost  of  curvature  of  various  radii;  that  is 
to  say,  the  greater  wear  and  tear  of  road-bed  and  rolling-stock, 
and  the  greater  consumption  of  fuel. 

2.  The  limiting  effect  of  curvature  on  the  weight  and 
length  of  trains. 

A  moment's  consideration  will  show  that  these  two  causes 
of  expense  are  sharply  defined  from  each  other.  For  every 
curve,  whether  sharp  or  fiat,  and  wherever  situated,  must  cause 
a  certain  amount  of  wear  and  tear  and  waste  of  power,  although 


CHAP.   VIII.—CURVATURE— EFFECT  ON  EXPENSES.     313 

it  may  not  cause  an}''  shorter  trains  to  be  hauled,  which  is  its 
DIRECT  effect  on  expenses;  but  if  the  curvature  be  very  sharp  or 
very  unfavorably  situated,  or  if  the  line  be  very  nearly  level,  so 
that  there  are  no  heavy  grades  to  limit  trains  in  advance  of  cur- 
vature, there  will  finally  come  a  point  where  too  much  or  too 
sharp  curvature  will  not  only  cause  wear  and  tear,  but  likewise 
cause  the  length  of  trains  to  be  cut  down.  In  that  case  the  di- 
rect expense  of  the  curvature,  for  wear  and  tear  and  waste  of 
fuel,  will  continue  on  as  before,  but  there  will  now  be  a  new 
source  of  expense  added  to  that  which  exists  on  all  curves  with- 
out distinction. 

We  for  the  present  (until  Chaps,  XVIII.  and  XIX.)  consider 
only  these  direct  sources  of  expense  which  are  common  to  all 
curvature  wherever  situated,  assuming  that  it  does  not  require 
more  trains  to  be  run,  but  simply  makes  it  more  expensive  to 
run  them. 

THE   EFFECT   OF   CURVATURE   ON    OPERATING   EXPENSES. 

344.  Fuel. — We  have  already  seen  (par.  186)  that  about  33  per  cent 
of  the  cost  of  fuel  goes  for  getting  up  steam,  kindling  fires,  running  to 
and  from  trains,  stopping  and  starting  trains,  standing  idle,  etc.,  etc.,  and 
is  hence  a  constant  wastage,  independent  of  the  distance  run.  AH  of 
this  may  be  considered  as  likewise  unaffected  by  curvature,  and  in  addi- 
tion thereto  there  is  another  and  important  source  of  loss,  viz.,  conden- 
sation due  to  radiatipn  of  heat,  which  varies  with  the  time  of  exposure, 
and  hence  with  the  distance  run,  but  is  inappreciably  affected  by  the 
power  developed  per  hour.  Every  part  of  a  locomotive,  even  the  lagging, 
is  hot  enough  to  burn  the  hand  in  the  coldest  weather. 

The  fire-box  is  usually  left  entirely  exposed  (by  a  mistaken  negligence, 
which  is  gradually  being  corrected  in  some  few  instances,  as  on  the  Lake 
Shore  &  Michigan  Southern  Railway,  on  which  all  the  fire-boxes  are 
lagged  *),  and  the  ends  of  the  cylinders  are  protected  only  by  metal 
plates.  As  a  consequence,  the  average  amount  of  fuel  consumed  in 
winter  is  shown  by  abundant  statistics  to  be  very  uniformly  about  20  per 
cent  greater  than  in  summer,  or  about  i  per  cent  for  each  2°  F.  difference 
of  temperature. 

*  It  is  claimed  that  an  economy  of  some  10  per  cent  in  fuel  was  attained  on 
the  Lake  Shore  by  such  lagging  of  the  fire-box.     Am.  Ry,  M.  M.  Rep't,  1885. 


314     CHAP.    VIII.— CURVATURE— EFFECT  ON  EXPENSES. 

345.  To  appreciate  the  full  force  of  this  fact,  we  must  remember  that 
the  hottest  summer  day  is  cold  to  the  cylinders  and  boiler.  The  temper- 
ature within  the  boiler  is  about  350°  F.;  and  hence  whether  the  temper- 
ature outside  be  o"  F.  or  100°  F.  makes  little  proportionate  difference. 

Let  us  suppose  the  average  fuel  consumption  in  July,  with  an  average 
temperature  of  ^']°  F.,  to  be  60  lbs.  per  m.ile.  In  January,  with  an  aver- 
age temperature  of  37"  F.,  experience  shows  that  the  consumption  will 
be  some  20  per  cent  greater.     Then  we  have  : 


Temperature. 


Lbs.  Coal 


Interior.  Exterior,  Difference.    Burned  Per  Mile. 

July,  350°  ^r  27f  60 

January,        350°  37°  313°  72 

Increase  p.  c,  40°  14.6  p.  c.  20  p.  c. 

The  cause  of  this  enormous  effect  of  difference  of  temperature  is  very 
obscure,  and  it  would  lead  us  too  far  to  discuss  it  in  detail.  The  matter 
has  attracted  far  less  attention  than  it  should,  and  even  the  facts  from 
which  any  discussion  of  causes  must  start  are  but  little  known  to  railroad 
men.  It  will  be  seen  that,  superficially  considered,  the  facts  seem  to  in- 
dicate that  a  very  large  proportion  of  the  fuel  consumption  is  due  to  the 
effects  of  exterior  temperature  ;  for  if  a  decrease  of  40°  F.  or  i|-  per  cent 
in  the  difference  between  the  temperature  within  and  without  the  boiler 
saves  20  per  cent  of  the  fuel,  it  would  seem  as  if  we  had  only  to  decrease 
the  difference  a  little  farther  to  save  half  or  three  quarters  of  it. 

This  conclusion  would  be  absurd,  but  all  that  it  is  desired  here  to 
show  is  that  exterior  radiation  is  a  very  serious  matter.  The  chief  causes 
for  the  great  difference  in  winter  and  summer  fuel  consumption  are  prob- 
ably these : 

I.  The  rolling  friction  is  considerably  higher.  Most  of  the  energy 
destroyed  by  friction  must  take  the  form  of  heat,  and  as  the  journals 
speedily  attain  about  the  same  temperature  in  both  winter  and  summer 
(moderately  warm  to  the  touch)  the  difference  in  temperature  of  the 
journals  and  the  external  air  is  much  greater  in  winter,  and  this  means 
so  much  more  journal  friction. 

This  theoretical  deduction  lacks,  as  yet,  direct  experimental  evidence,  pend- 
ing which  it  must  be  regarded  as  doubtful.  By  some  strange  omission,  the 
comparative  winter  and  summer  train  resistance  has  not  been  the  subject  of  di- 
rect investigation,  so  far  as  the  writer  is  aware;  but  that  there  is  considerable 
difference  appears  to  be  indicated  by  the  fact  that  it  is  found  necessary  in  prac- 


CHAP.    VIII.— CURVATURE— EFFECT  ON  EXPENSES.     315 

tical  operation  to  cut  down  trains  in  winter  by  about  10  per  cent  (say  from  20 
cars  to  18,  or  from  40  cars  to  36),  for  which  it  is  difficult  to  imagine  any  other 
rational  explanation.  The  popular  explanations  are  :  (i)  That  the  wind 
travels  more  miles  in  winter  than  in  summer,  which  is  not  true;  and  (2)  that 
the  track  is  in  worse  condition,  which  is  unquestionably  true  to  some  extent ; 
but  there  are  very  few  days  when  snow  and  ice  cause  much  trouble  on  the  sur- 
face of  the  rail,  which  is  for  the  most  part  as  clean  in  winter  as  in  summer, 
and  the  effect  of  heaving  of  the  road-bed  on  train  resistance,  although  impor- 
tant, can  hardly  account  for  the  difference  which  exists. 

346.  Internal  radiation  also,  from  the  hot  steam,  when  first  admitted 
to  the  cylinder,  into  the  interior  walls  thereof, — whence  it  is  almost  in- 
stantly returned  again  into  the  exhaust  steam,  as  the  temperature  falls 
from  reduction  of  pressure,  without  having  done  any  work,— is  admitted 
to  be  a  very  great  source  of  waste,  but  is  entirely  distinct  from  the  exter- 
nal radiation,  for  it  is  not  appreciably  affected  by  the  external  tempera- 
ture, and  does  vary  with  the  power  demanded,  and  inversely  with  the 
speed  ;  in  all  of  which  details  it  differs  from  external  radiation. 

It  is  true  that  a  locomotive  standing  still  and  not  using  steam  loses 
but  a  trifling  amount  from  radiation  (about  30  lbs.  per  hour);  but  the 
conditions  are  vastly  different  when  working  against  a  fierce  wind  with 
every  part  to  be  kept  hot,  and  it  is  difficult  to  resist  the  evidence  that 
at  least  \  of  the  fuel  consumed  goes  to  replace  radiated  heat.  If  so,  as 
33i  psJ"  cent  goes  for  other  causes  of  wastage,  we  have  50  per  cent  of  the 
fuel  left  as  that  portion  which  varies  directly  with  the  power  demanded. 
Possibly  it  is  still  less,  but  it  can  hardly  be  much  more. 

The  correctness  of  this  conclusion  is  indicated,  in  a  measure,  by  the  coal 
burned  by  engines  running  light.  An  engine  which  will  burn  60  to  80  lbs,  per 
mile  with  its  full  train,  will  burn  20  to  30  lbs.  per  mile  only  to  run  itself. 

347.  Assuming  curve  resistance  to  average  about  \  lb.  per  ton,  it  is 
perhaps  as  correct  an  average  as  possible  to  say  that  a  continuous 
11°  20'  curve  causes  an  average  additional  train  resistance  of  about  6  lbs. 
per  ton,  or  about  doubles  the  resistance  of  a  train  on  a  level.  A  mile  in 
length  of  such  a  curve  contains  600°  of  curvature. 

We  may  say,  therefore,  that  600°  of  curvature  will  waste  about  50  per 
cent  as  much  fuel  as  the  average  burned  per  mile  run. 

348.  Repairs  of  Engines. — Referring  to  Table  85,  page  203,  it  will 
be  seen  that  the  proportion  of  this  item  assignable  to  the  average  effect 
of  curvature  and  grades  is  about  19  per  cent,  nearly  all  of  it  arising  from 
wear  of  wheels  and  tires.  Experimental  data  as  to  the  actual  effect  of 
either  grades  or  curvature  on  locomotive  or  car  repairs  are  very  few. 
Statistics  of  actual  expenditures  for  such  purposes  on  lines  differing  con- 


3l6     CHAP.    VIII.— CURVATURE— EFFECT  ON  EXPENSES. 

siderably  in  grades  and  curvature  afford  no  assistance,  except  to  drive 
us  to  the  conclusion  that  curvature  has  little  or  no  effect,  as  we  have  al- 
ready seen  (par.  164). 

349.  We  may  get  at  the  probable  effect  of  curvature  on  engine  re- 
pairs little  more  definitely,  at  least  to  the  extent  of  checking  any  error  of 
consequence,  as  follows  : 

The  ways  in  which  engine  repairs  are  affected  by  curvature  are  two : 

First, — and  more  important, — by  the  additional  wear  of  tires  and 
wheels. 

Secondly,  by  the  effect  on  wear  and  tear  of  the  additional  power  de- 
manded. 

The  last  is  an  inconsiderable  element,  because  the  additional  power 
demanded  by  the  curvature,  even  in  extreme  cases,  is  inconsiderable 
when  measured  in  foot-pounds.  Thus,  if  there  be  300°  in  a  mile, — which 
by  turning  to  Tables  loi  to  104,  page  259,  will  be  seen  to  be  a  very  large 
allowance, — this  amounts  to  less  than  a  continuous  6°  curve,  or  3  lbs.  per 
ton  continuous  addition  to  the  train  resistance.  On  descending  grades 
this  is  rather  a  help,  saving  the  use  of  brakes.  On  ascending  grades  of 
say  I  per  cent  the  normal  train  resistance  is  some  26  lbs.  per  ton,  and  3 
lbs.  per  ton  resistance  adds  but  12  per  cent  to  this.  As,  then,  only  31 
per  cent  of  the  cost  of  engine  repairs  (exclusive  of  running-gear)  varies 
directly  with  the  distance  run  on  tangent,  the  increase,  if  in  direct  pro- 
portion, would  be  only  0.12x0.31  =  3.7  per  cent  for  300°,  or  say  7.5  per 
cent  for  600°  of  curvature,  so  far  as  this  cause  alone  is  concerned. 

The  maintenance  of  running-gear  (including  frames,  which  is  a  very 
small  item)  amounts  to  30  per  cent  of  the  total  cost  of  engine  repairs, 
but  of  this,  only  one  third,  or  10  per  cent,  can  properly  be  assigned  to 
the  effect  of  curvature  and  grades.  We  may  assume  that  two  thirds  of 
this,  or  6.7  per  cent  of  the  total  cost  of  engine  repairs,  is  due  to  curva- 
ture. By  turning  to  Table  104,  we  shall  find  that  the  average  amount 
of  curvature  on  an  average  railway  is  some  30°  per  mile.  On  a  contin- 
uous 11°  20' curve,  containing  600°  per  mile,  the  curvature  is  20  times 
this  amount ;  and  hence  on  such  a  mile  the  extra  cost  due  to  the  curva- 
ture would  be  6  X  20  =  120  per  cent  of  the  average  cost  of  engine  repairs 
per  mile.  This  seems  to  be,  and  is,  a  rude  process  ;  but  it  may  be  further 
checked  as  follows  : 

350.  The  cost  of  maintaining  tires  average  on  trunk  lines,  like  the 
Erie  or  Pennsylvania,  about  i^  cts.  per  mile  run,  with  an  average  cost  of 


CHAP.    VIII.— CURVATURE— EFFECT  ON  EXPENSES. 


317 


engine  repairs  of  some  6  cts.  as  a  minimum.  Their  average  curvature 
per  mile  is  some  50°.  The  above  allowance  (of  120  per  cent  addition  to 
the  total  cost  of  engine  repairs  by  600"  of  curvature)  is  equivalent  to  al- 
lowing that  with  continuous  11°  20'  curves  the  total  cost  of  running-gear 
maintenance  would  be  7.2  cts.  per  train-mile,  or  six  times  greater  than  it 
is  now,  on  an  average,  with  twelve  times  as  much  curvature.  While 
this  may  not  be  much  too  large,  it  is  certainly  ample.  See  also  the  fol- 
lowing data  (Table  114)  as  to  the  wheel  wear  of  cars  and  the  causes 
thereof. 


Table  114. 

Percentages  of  Wheels  removed  in  1884  on  the  New  York,  Lake  Erie 
&  Western  Railroad  for  Various  Causes  of  Each  One  of  Twenty- 
four  Different  Makes. 

(Out  of  a  total  of  some  300,000  wheels  and  18,000  removals.) 

Class  i.— Six  Best  Makers— aggregating  78.2  Per  Cent,  of  All  Wheels  in 

Service. 


Makers. 

Cracked  and  Broken. 

Shelled 
Out. 

Sharp 
Flange. 

Slid 
Flat. 

Worn 

Flat& 

Worn 

Out. 

Total. 

P.  C.  of 

Removals 

Broken. 

Crack'd 

Total. 

to  No.  in 
Service. 

1  

1.2 
2.7 
0.5 

5-3 
2.0 
3-0 

2.0 

14.9 
10. 1 
23.2 
20.8 

12.2 

8.4 
9-5 
15-4 
15-4 
25.2 
23.8 

0.3 

J1 

0.7 
0.6 
0.0 

4.8 
1.9 
1.6 

'A 

1.2 

9.6 
22.9 

25-9 
29.7 
3S.O 
11-3 

76.9 
64.0 
56.6 
49.4 
36.6 
63-7 

100. 
100. 
100. 
100. 
100. 
100. 

3-69 
7.40 
3.00 

2 

3  

4 

5 

6 

8.97 

Average 

14.4 

0.7 

-7 

22.3 

60.1 

100. 

4-39 

Class  2. — Six  Next  Best  Makers — aggregating  17.2  Per  Cent  of  Wheels  in 

Service. 


7 

8 

9 

10 

II 

42    

Average 


2.4 

17.0 

19.4 

0.0 

6.9 

20.8 

52-9 

100. 

2.5 

12.2 

14.7 

0.1 

16. 1 

20.4 

48.7 

100. 

2.8 

30.8 

33-6 

0.1 

6.4 

21.0 

38.9 

100. 

1-5 

27.9 

29.4 

0.1 

2.9 

18.8 

48.8 

100. 

1-3 

9-7 

II. 0 

0.3 

23.2 

33-2 

32.3 

100. 

3-1 

.3.« 

16.9 

0.0 

6.1 

40.1 

36.9 

100. 

2.2 

23-7 

25-9 

0.1 

8.2 

21. 1 

44-7 

100.      1 

1 

8.21 
14-63 

9.26 

10.88 
22.5 
8.23 


TO.  94 


3l8      CHAP.    VIIL— CURVATURE— EFFECT  ON  EXPENSES. 


Table  114. — Continued. 


Class  3.— Twelve  Worst  Makers— aggregating  only  4.6  Per  Cent  of 
Wheels  in  Service. 


13 

14 

**I5 

*i6 

***i7   

**i8 

**i9 

*20 

*2I     .. . .. 

22 

23 

Average 


•9 

71.9 

72.8 

0.0 

0.0 

22.3 

4-9 

100. 

3-4 

59-3 

62.7 

0.0 

0.0 

23.7 

13.6 

100. 

10.4 

19.6 

30.0 

0.3 

14.2 

II. 9 

43-6 

100. 

0.0 

0.0 

0.0 

0.0 

54-6 

45-4 

0.0 

100. 

6.3 

21.9 

28.2 

0.0 

21.8 

9.4 

40.6 

100. 

4-9 

14-5 

19.4 

0.0 

24.1 

17.8 

38.7 

100. 

7-9 

8.6 

16. 5 

0.0 

9-3 

143 

59-9 

100. 

1.6 

22.9 

24-5 

0.0 

4-9 

15-6 

550 

100. 

6.0 

36.2 

42.2 

o-S 

4.6 

17-4 

35-3 

100. 

0.2 

88.8 

90.0 

0.0 

1.6 

7.0 

1-4 

100. 

5-8 

26.4 

32.2 

0.0 

3-3 

49.6 

14.9 

100. 

7-5 

4-5 

12.0 

0.0 

8.9 

44-7 

34-4 

100. 

4.4 

37-2 

41.6 

0.0 

12.4 

20.3 

25-7 

100. 

14.40 

3.76 

90-5 

12.62 

19. 1 

76.9 
14. 1 
28.9 
25.2 

5  00 
2.29 


20.16 


Bold-face  numbers  represent  makers  having  from  20,000  to  50,000  wheels  each  in  service. 
Starred  numbers  indicate  the  smaller  makers,  viz.,  *  Less  than  1000  in  service;  **  less  than 
500  in  service;  ***  less  than  300  in  service. 


Summary. 


Six  Best 
Makers. 

Six  Next 
Best. 

Twelve 
Worst 
Makers. 

Av.  of  all 
on  Road. 

Per  cent  of  whole  number  in  service 

Broken      .     .          

78.2 

2.0 
12.2 

17.2 

2.2 

23-7 

4.6 

4-4 
37-2 

100. 0 
2.4 
19.4 

Cracked 

Broken  and  cracked                  . 

14.2 
0.7 
2.7 
22.3 
60.1 

25-9 
0.1 
8.2 

21. 1 

44-7 

41.6 
0.0 
12.4 
20.3 
25-7 

21  8 

Shelled  out 

0.4 

5-8 

21.7 

50-3 

Sharp  flange 

Slid  flat 

100. 0 
4-39 

100. 0 
10.94 

100. 0 
20.16 

Per  cent  of  number  in  service  removed 

6.21 

percentage  of  total  number  in  service  removed  for  each  cause. 


Six  Best' 
Makers. 

Six  Next 
Best. 

Twelve 

Worst. 

Total. 

Per  cent  of  whole  number  in  service 

78.2 
0.09 
0.54 

17.2 

0.23 
2.60 

4.6 

0.88 
750 

Broken 

Cracked 

0.15 

0.63 
0.03 
0.12 
0.98 
2.63 

2.83 
0  01 
0.89 
2.31 
4.90 

8.38 
0.00 
2.50 
4.10 
5.18 

1-35 

Shelled  out 

Sharp  flange 

0.36 
1-35 
3-13 

Shd  flat 

Total  removed 

4-39 

10.94 

20.16 

6  21 

CHAP.   VIII.— CURVATURE^EFFECT  ON  EXPENSES.      319 

While  the  above  table  gives  valuable  and  trustworthy  indications  of  the  relative  quali- 
ties of  different  makers,  it  gives  an  entirely  false  idea  of  the  absolute  qualities  of 
American  chilled  car  wheels^  unless  a  large  allowance  is  made  for  the  fact  that  it  is 
modified  immensely  by  the  constant  annual  additions  of  new  stock.  This  is  immediately 
evident  in  the  total  number  removed  for  all  causes,  which  is  only  6.21  per  cent  of  those  in 
service,  indicating  on  its  face  an  average  life  of  sixteen  years,  which  is  certainly  more 
than  twice  the  actual  average  life  of  wheels  on  the  road  in  question,  and  would  be  much 
more  than  twice  or  even  three  times  the  average  Hfe  in  years,  except  that  the  average 
mileage  per  car  per  year  has  recently  been  very  low. 

An  average  life  of  eight  years  for  car  wheels  would  require  izj^  per  cent  per  year  aver- 
age renewals,  against  only  6.21  per  cent  actual  renewals — a  discrepancy  of  over  one  half. 
The  constant  additions  of  new  roUing-stock  which  are  known  to  have  been  made  on  the 
road  are  the  only  apparent  cause  for  this  effect.  With  such  an  abnormal  proportion  of 
new  wheels,  the  proportion  of  failures  from  "old  age"  will  be  decreased,  and  hence  that 
the  proportion  of  failures  from  acute  diseases,  such  as  cracked  or  broken,  will  be  abnor- 
mally increased  ;  since  in  a  large  proportion  of  the  wheels  these  are  the  only  failures  which 
are  occurring. 

This  table  sheds  especially  valuable  light  on  the  cause  of  sharp  flanges.  It  will  be 
seen  that  there  is  twenty  times  as  large  a  proportion  of  wheels  removed  because  of  sharp 
flanges  among  bad  wheels  as  good  ones,  and  that  with  good  makers  the  proportion  of 
wheels  removed  for  sharp  flanges  (2.7  per  cent,  and  that  on  a  very  crooked  road)  is  so 
small  as  to  indicate  that  bad  quality  of  the  wheel  itself  is  the  leading  cause  of  sharp  flanges. 

Of  broken  or  cracked  wheels,  only  about  one  quarter  break  in  the  flange  or  tread,  and 
nearly  two  thirds  of  the  fractures  arise  from  the  bursting  strains  produced  by  forcing  the 
wheels  on  the  axles. 


351.  Repairs  of  Cars.— In  Table  86,  page  203,  the  proportion  of  the 
cost  of  this  item  assignable  to  the  effect  of  grades  and  curvature  is  given 
as  some  23  per  cent.  Of  this  at  least  three  fourths  would  ordinarily  be 
assignable  to  the  effect  of  grades  and  only  one  fourth  to  curvature. 
Then,  proceeding  exactly  as  in  the  case  of  engine  repairs,  we  have  6  x  20 
=  120  per  cent  of  the  average  total  cost  of  car  repairs  per  mile  as  the  extra 
cost  due  to  600°  of  curvature.  This  estimate  is  certainly  large  enough, 
and  probably  considerably  too  large. 

An  exact  distribution  of  the  cost  of  rolling-stock  repairs  to  its  various 
causes  is  very  difficult,  because  the  expenses  are  not  ordinarily  kept  by 
items,  but  only  by  aggregates.  Some  recent  statistics  as  to  wheel  wear, 
however  (the  chief  and  almost  the  only  item  of  car  repairs  affected  by 
curvature),  given  in  Table  1 14,  afford  some  valuable  insight  into  the  causes 
which  destroy  them  most,  and  indicate  that  the  wear  from  curvature  is 
a  comparatively  minor  element. 

352.  Wear  of  Rails.— We  may  take  the  wear  of  good  rails  on 
curves,  as  an  average  of  their  whole  life,  at  about  \  lb.  per  10,000,000  tons 


320      CHAP.    VIII.— CURVATURE— EFFECT  ON  EXPENSES. 

per  degree  of  curve,  or  certainly  not  more  than  this.  Observations  by 
the  writer  on  the  railroads  of  the  New  York,  Pennsylvania  &  Ohio  Rail- 
road, and  some  more  elaborate  investigations  on  the  Pennsylvania  Rail- 
road by  Dr.  Charles  B.  Dudley,  agree  in  indicating  this,  when  allowance 
is  made  for  the  fact  that  the  wear  is  not  at  a  uniform  rate  during  the 
whole  life  of  the  rail  (par.  313  et  seq.),  but  is  perhaps,  rudely  speaking, 
only  one  fourth  of  the  total  during  the  first  half  of  its  life  and  three 
fourths  during  the  latter  half.  As  a  consequence,  as  already  pointed  out 
(par.  315),  the  wear  showa  by  an  investigation  of  a  lot  of  rails  of  the 
same  absolute  age  on  different  curves  will  apparently  indicate  a  very  much 
greater  wear  on  sharp  curves ;  but  this  appearance  is  deceptive. 

The  wear  in  tangents,  then,  being  (as  it  is)  about  i  lb.  per  10,000,000 
tons  duty,  the  wear  on  a  continuous  11°  20'  curve  will  be  ^  lb.  x  iii  = 
5f  lbs.  per  degree  of  curve,  or  be  increased  567  per  cent  over  the  tangent 
wear.  But  this  is  assuming  that  the  tangent  rails  are  so  good  that  they 
will  need  renewals  only  from  the  effect  of  abrasion,  in  which  case  rails 
will  cost  only  about  ^ct.  per  train-mile. 

With  inferior  steel  rails,  as  formerly  with  iron  rails,  the  proportionate 
increase  of  wear  is  very  much  less  than  this,  owing  simply  to  the  fact 
that  the  tangent  wear  is  so  very  much  greater.  The  additional  rail 
wear  on  curves  was  estimated  by  the  writer  in  the  first  edition  of  this 
treatise — and,  so  far  as  he  can  now  judge,  with  very  close  correctness — 
at  100  per  cent  increase  over  the  tangent  wear  on  an  11°  20'  curve.  The 
absolute  rate  of  abrasion  is  much  the  same  with  all  rails,  iron  or  steel, 
good  or  bad.  With  rails  that  fail  only  by  abrasion,  therefore,  the  curve 
wear  adds  a  large  percentage  to  a  very  small  total  cost.  With  rails 
that  mash  or  split  in  service,  the  curve  wear  becomes  a  much  smaller 
percentage  of  a  much  larger  total. 

353.  Cross-ties. — The  effect  of  curvature  on  ties  has  been  much  de- 
creased by  the  introduction  of  steel  rails,  and  will  be  still  further  and  very 
largely  decreased  by  the  introduction  of  creosoted  ties.  Still  its  effect 
on  the  life  of  ties  is  considerable,  Several  5''ears  of  the  tie's  life  must  be 
sacrificed  on  sharp  curves  because  the  holding  power  of  the  spike  be- 
comes too  little.  The  so-called  "  cutting"  of  ties  (par.  121)  is  also  greater 
on  curves,  and  mainly  on  the  outside  of  the  rail.  As  the  rail  wears  by 
flange  cutting,  moreover,  it  is  necessary  either  to  renew  the  rails  prema- 
turely or  to  throw  them  in  to  gauge.  The  effect  of  all  these  causes  to- 
gether to  shorten  the  life  of  ties  is  a  pure  matter*of  fact;  and  considerable 
observation  of  and  inquiry  as  to  practice  in  this  respect  indicates  that 
the  following  comes  very  near  to  the  average  life  of  white-oak  ties  on 


CHAP.    VIII.— CURVATURE— EFFECT  ON  EXPENSES.      32 1 

sand   or  gravel   ballast,  imperfectly  drained — the    life  given   on  curves 

being,  if  anything,  too  short : 

On  a  tangent, 9  years. 

On  a  2°  curve,     .<,.,..  8       " 

On  a  6°  curve 7       " 

On  a  10°  curve,  ......  6      " 

On  a  14°  10°  16°  curve,    ...  5       " 

From  this  we  may  conclude  that  the  cost  for  ties  on  an  ll°  20'  curve 
(600°  per  mile)  is  about  50  per  cent  greater  than  on  a  tangent,  and  that 
the  increase  is  directly  as  the  degree  of  curvature  on  any  given  distance; 
or,  in  ortier  words,  is  uniform  per  degree,  whatever  the  radius. 

354.  Track  Labor  is,  as  a  matter  of  fact,  but  little  affected  by 
curvature.  It  is  an  unusual  thing  to  see  sections  made  shorter  than 
others  on  this  account.  If  two  contiguous  sections  are  noticeably  differ- 
ent in  this  respect  it  is  not  unusual  to  take  a  quarter  or  half  a  mile  off 
one  and  add  it  to  the  other,  but  any  greater  difference  than  this  is  un- 
lilcely.  Yet  comparing  the  conditions  which  would  exist  on  a  mile  of 
tangent  and  a  mile  of  11°  20'  curve,  it  might  not  unfairly  be  claimed  that 
there  would  be  a  difference  of  50  per  cent  in  the  cost  of  track  labor ;  and  to 
avoid  that  very  objectionable  result,  an  underestimate  of  the  disadvan- 
tages of  curvature,  we  may  assume  this,  which  will  amply  cover  the  facts. 

355.  Summing  up  the  various  Items  affected  by  Curva- 
ture, we  obtain  the  following  Table  115,  giving  the  assumed 
effect  on  expenses  of  600°  of  curvature. 

The  total  cost  per  year  per  daily  train  of  1°  of  curvature  given 
below,  Table  115  (43.3  cts.),  divided  by  the  rate  of  interest  on 
capital,  will  give  the  justifiable  expenditure  to  save  1°  of  curva- 
ture estimated  per  daily  train,  viz.: 

At    5  per  cent,  .....     ^^~-     =     $S.33' 

At    8  per  cent, -^4P       =        '5.41. 

0.8  ^  ^ 

At  10  per  cent, ^-"^33      _       ^^^ 

And  similarly  for  any  other  rate  of  interest;  this  being  assumed, 
as  heretofore,  not  to  be   a  precisely  accurate  result,  but  one  as 
exact  as  is  either  practicable  or  necessary  to  avoid  serious  errors. 
21 


322      CHAP.   VIII.— CURVATURE— EFFECT  ON  EXPENSES. 


Table  115, 

Estimated  Average  Cost  Per  Train-Mile  of  600°  of  Curvature. 

[Being  equivalent  to  a  continuous  ii°  20'  curve,  one  mile  long,  assumed  to  double  the 
average  train  resistance  in  lbs.  per  tons.] 

(Cost  of  train-mile  assumed  at  $1.00.) 


Item. 
(As  per  Table  80.) 


Averag^e 

Cost  of  Item. 

Cts.  or  Per 

Cent. 


Per  Cent  added  by 

6oo*  of  Curvature, 

as  above. 


Cost  due  to 
Curvature. 


Fuel 

Water 

Oil  and  w^aste 

Repairs,  engines 

Switching-engines  service. 
Train  wages  and  supplies 

Repairs,  cars 

Car  mileage 

Rail  renewals 

Adjusting  track 

Renewing  ties 

Earthwork,  ballast,  etc... 

Yards  and  structures 

Station  and  general 


50  per  cent. 
25     "       " 
25     "       " 
125     "       " 
Unaffected. 

120  per  cent. 
Unaffected. 

300  per  cent. 
50    "       " 
50    "       - 
50    "       " 
Unaffected. 


3.8 
0.1 
0.2 
7.0 


[2.0 


6.0 

1.5 
2.0 


Total  cost  per  train-mile  of  600° 
of  curvature  (cts.  or  per  cent). 


100.  o 


35.6  per  cent. 


35.6 


35.6 
Total  cost  per  train-mile  per  degree,  ~r—  =      .0593  ct. 

Total  cost  of  1°  of  curvature  per  year  per  daily  train  (.0593  ct.  x  365  X  2)  =  43.3      cts. 

356.  The  similar  estimate  which  the  writer  made  in  the  first 
edition  of  this  treatise  gave  a  smaller  estimate  for  the  value  of 
curvature  than  this,  viz.,  22.5  cts.  instead  of  35.6  for  the  cost 
per  train-mile  of  600°  of  curvature — a  difference  of  over  50  per 
cent;  and  this  in  spite  of  the  fact  that  the  former  estimate  was 
for  the  most  part  on  an  iron-rail  basis.  The  only  positive  reason 
for  this  difference  is  that  the  writer  has  seen  reason  to  increase 
the  estimate  of  the  effect  of  curvature  on  rolling-stock  repairs,  al- 
though a  chief  reason  has  been  to  ensure  that  the  estimate  was 
large  enough.  According  to  the  above  estimate,  the  total  cost 
of  a  train-mile  should  be  10  per  cent  greater  on  a  road  having  100° 
more  curvature,  which  is  the  most  that  the  evidence  warrants. 


CHAP,   VIII.— CURVATURE— EFFECT  ON  EXPENSES,      323 

357.  To  illustrate  how  very  little  difference  any  probable  error 
in  the  above  estimate  can  make  in  the  justifiable  expenditure  to 
avoid  curvature:  Assuming  the  case  of  a  road  running  10  daily 
trains  each  way,  the  justifiable  expenditure  to  save  1°  of  curva- 
ture, at  8  per  cent,  is  $54. 10,  and  to  save  20°,  $1082.00;  a  sum  which 
will  warrant  no  very  large  amount  of  work  to  avoid  it.     The 

ANNUAL    LOSS    TO    REVENUE    IF   IT    BE    NOT    AVOIDED  wiU  be 

43.3  cts.  X  10  trains  X  20°  =  $86.60; 

a  sum  sufficient  to  pay  for  perhaps  two  extra  trains  over  the  road 
during  the  year  or  for  running  7302  trains  instead  of  7300.  When 
the  effect  of  the  most  trifling  difference  of  grade  is  compared  with 
this  it  becomes  slight  indeed. 

358.  This  example  is  for  a  considerable  traffic  and  for  a  con- 
siderable amount  of  curvature,  to  save  at  one  point.  As  such 
it  well  illustrates  the  principal  purpose  of  such  estimates  as  we 
have  just  made.  It  is  not  to  avoid  errors  of  10,  20,  or  even  50  or 
100  per  cent  in  the  sums  spent  to  save  curvature;  for  we  cannot 
go  far  wrong  if  we  assume  either  $700  or  $800  or  $1200  or 
$1500  as  our  standard  value  for  such  an  amount  of  curvature, 
instead  of  $1058.  But  its  principal  purpose  is  to  save  us  from  the 
manifold  greater  errors  which  may  so  easily  result  from  follow- 
ing mere  guesswork  and  "judgment:"  from  spending  $5000,  or 
$10,000  to  gain  something  whose  true  value  lies  between  $700 
and  $1500,  as  has  been  done  in  many  cases  on  heavy  work;  or 
from  the  corresponding  error  of  introducing  10°  or  20°  of  curva- 
ture recklessly,  which  might  be  saved  at  trifling  cost,  or  perhaps 
at  no  cost  at  all,  by  a  little  more  care. 

359.  All  the  preceding  estimate  of  the  direct  cost  of  curvature 
has  been  based  upon  the  assumption  that  the  cost  per  degree 
was  for  the  most  part  uniform  for  all  curves,  independent  of 
radius;  i.e.,  that  the  cost  of  the  curvature  in  100  stations  of  1° 
curve  was  essentially  the  same  as  that  in  10  stations  of  10°  curve. 
This  assumption  appears  to  be  unquestionably  justified  by  the 
facts,  but  the  reasons  why  it  is  so  are  considered  later,  in  Chap. 
XIX.,  page  638. 


324      CHAP.    VIII.— CURVATURE— EFFECT  ON  EXPENSES. 

360.  A  particular  form  of  bad  practice  in  respect  to  curva- 
ture, and  one  of  the  most  prevalent  and  indefensible  of  the  minor 
errors  of  location,  is  a  weakness  for  very  long  tangents  and  a 
readiness  to  spend  money  to  secure  them.  A  reasonably  long 
tangent,  say  not  less  than  400  feet,  is  always  very  desirable,  if  not 
absolutely  essential,  in  order  to  taper  out  the  superelevation  and 
afford  room  for  proper  transition  curves;  but  beyond  this  there 
is  no  justification,  theoreLical  or  practical,  for  expending  more 
than  a  very  small  sum  to  avoid  any  number  of  short  and  gentle 
curves.  The  difference  in  distance  resulting  from  even  very  con- 
siderable and  frequent  breaks  in  a  tangent  is  too  trivial  to  be  a 
serious  consideration  on  lines  of  small  traffic  (although  it  may 
look  as  if  it  were  considerable,  especially  on  the  ground;  see 
Chap.  XXVIII.),  and  the  same  is  at  least  equally  true  of  the 
curvature.  Thus  let  us  suppose  that  there  is  a  section  of  a  mile 
and  a  half  out  of  one  of  those  four-  or  five-mile  tangents,  in 
moderately  difficult  country,  for  which  the  following  curved 
alignment  may  be  substituted  with  some  economy  in  first  cost: 


Curves. 

Central 
Angle. 

Total  Length  of 

Tangents  between 

Intersections, 

1°  Z    for  300  ft. 
li"'  R   "     600  '* 
1"  L     "     600  " 
2°  R    "     500  " 
2°  L    "     200  " 

Total 

12° 

10° 

4^ 

2,500  ft. 
2,500   " 
2,000   " 
1,100    " 

38° 

8,100  ft. 

Such  an  alternate  alignment  would  perhaps  have  the  effect  of 
reducing  a  succession  of  considerable  cuts  and  fills  materially. 
How  much  does  it  damage  the  operating  value  of  the  line  ? 

The  difference  in  distance  is  as  nearly  as  may  be  23  feet  in 
about  8350.  The  amount  of  curvature  introduced  is  38°.  Then 
to  an  hypothetical  line  running  10  trains  per  day  each  way  and 


CHAP.    VIII.— CURVATURE— EFFECT  ON  EXPENSES.      325 

paying  8  per  cent  for  capital   the  value  of  the  difference  would 

be— 

23  feet  distance  at  (possibly)  0.30  cts.  X  10,     ^69  00 

38°  curvature  at  $5.41  X  10, 2,055   ^o 

Total, $2,124  80 

Many  a  tangent  has  been  broken  up  improperly  to  effect  less 
saving  than  this;  but,  on  the  other  hand,  a  saving  of  8000  to 
10,000  cubic  yards  of  excavation  is  enough  to  balance  it;  and  if 
we  reduce  the  estimated  traffic  by  two  thirds  or  three  quarters, 
in  all  ordinary  country  the  saving  by  breaking  up  the  tangent 
would  far  more  than  justify  doing  so,  even  in  light  work,  for  the 
above  figures  fully  represent  every  measurable  disadvantage 
from  a  moderately  curved  line  of  that  character. 

Especially  if  the  general  character  of  the  work  is  heavy,  the 
caution  of  par.  14  becomes  of  vital  moment  on  such  alignment 
if  the  most  careful  engineer  would  avoid  error. 

Table  116. 
Sharpest  Curves  in  Regular  Use  on  Standard-Guage  Roads. 

(Chiefly  from  a  list  published  in  the  Railroad  Gazette  of  Oct.  4,  1878.) 


Road. 

Locality. 

Sharpest  Curve. 

Radius. 
Ft. 

Degree. 

N.  Y.,  New  Haven  &  Hartford 

Springfield,  Mass 

410 

383 

320 

310 

400 

375 

300 

136 

395 

300 

238 

300 

246 

175 

55  to  125 

90,  100,  103.5, 

125,  150 

50 

14° 
15° 
18" 

Lehigh  &  Susquehanna 

Stony  Creek 

»s                              u 

18°  32' 
14°  22' 
15°  20' 
19°  10' 
43' 

14°  32' 
19°  10' 
24°  15' 
19°  10' 
23°  30' 
33°  15' 

Baltimore  &  Ohio 

Harper's  Ferry,  Md.  side 

u                                 »( 

Harper's  Ferry,  Va.  side 

Y  for  Consolidation  Engines. . . 
In  Peru             

Oroya  Railroad 

Virginia  Central  

Over  Rockfish  Gap  Tunnel. ..  . 

t(           ((           ((         11 

Centennial  Grounds 

Pennsylvania  Railroad  tracks 

Pittsburg,  Fort  Wayne  &  Chicago. 
Canarsie  &  Rockaway 

Pittsburg 

Brooklyn 

Brooklyn,  Bath  &  Coney  Island..  . 

Manhattan  Elevated 

Petersburg,  Va 

New  York  City 1 

U.  S.  Military  Railway 

}.3» 

326      CHAP.   VIII.— CURVATURE— EFFECT  ON  EXPENSES. 

The  curve  last  given  was  thus  described  in  a  discussion,  by  Mr.  C.  L.  McAlpine,  of  a 
paper  by  Mr.  C.  Whinery  (Trans.  Am.  Soc.  C.  E.,  1876),  and  is  one  of  the  most  remark- 
able on  record : 

"  Petersburg  and  Richmond,  Virginia,  fell  into  the  hands  of  the  Federal  troops  near  the 
close  of  the  war.  The  base  of  the  latter  for  many  months  had  been  at  City  Point,  on  the  James 
River. 

"  Early  one  morning  imperative  orders  were  received  to  run  the  trains  of  the  United  States 
Military  Railways  into  Petersburg  with  the  least  possible  delay.  This  was  done  by  noon  of 
the  same  day,  under  circumstances  that  would  be  most  interesting,  but  foreign  to  the  subject 
under  discussion. 

•■  This  order  was  followed  up  bj^  another — that  railroad  communication  with  Richmond 
should  be  efEected  at  once. 

"  The  railroad  bridge  at  Petersburg,  over  the  Appomattox,  had  been  burned.  No  connec- 
tion at  that  place  had  ever  been  made  in  peace  times,  and  the  first  examinations  showed  that 
heavy  excavations,  etc.,  requiring  ti}ne  (for  which  the  department  never  made  allowance), 
must  be  made,  before  any  reasonable  connection  with  the  Richmond  line  could  be  effected. 
This  drove  the  engineer  in  charge  into  the  apparently  inadmissible  curve  adopted. 

"  Contrary  to  the  advice  of  trackman  and  bridge-builers,  a  sharp  curve  was  laid  out,  of 
more  than  one  hundred  degrees,  with  a  radius  of  fifty  feet,  on  what  was  to  become  the  main 
line.  The  curve  was  on  trestle-work,  and  the  outside  posts  were  framed  eight  inches  longer 
than  the  inner  ones.  The  ties  were  of  sound  white  pine,  three  inches  in  thickness,  and  the 
rails  were  double  spiked.     Two  guard  rails  were  used,  also  double  spiked. 

"  The  locomotive  engineers  generally  condemned  the  bridge  and  curve  at  first  sight  after 
completion,  and  a  strong  prejudice  was  created  against  it.  But  the  writer  selected  the  worst 
curve-following  engine  in  the  service,  the  '  Government,'  and  ordered  her  to  make  the  first 
trial. 

"  Walking  backwards,  and  in  front,  as  this  engine  slowly  made  its  way,  it  was  easy  to  per- 
ceive her  action  on  this  sharp  curve. 

"  A  little  pressure  on  the  outer  rail  seemed  to  drive  the  wheels  (both  of  the  trucks  and 
drivers)  down  on  to  the  inner  rail,  and  demonstrated  practically  what  had  been  intended,  that 
the  trains  must  be  passed  through  the  curve  at  greater  speed. 

"  Thereafter,  when  the  locomotive  men  became  accustomed  to  the  curve,  the  speed  through 
it  was  usually  from  eight  to  ten  miles  an  hour. 

"  A  very  large  traffic  passed  over  this  curve  for  months  afterwards,  supplying  the  armies  of 
occupation  in  Richmond,  and  at  other  points  to  the  southward,  and  no  accident  or  trouble 
whatever  was  experienced  at  the  place  in  question." 

On  the  4  per  cent  grades  of  the  Mexican  Railway,  reversed  curves  of  150  ft.  radius  on 
temporary  track  around  tunnels  were  operated  by  ordinary  locomotives  for  a  year  or 
more  at  its  first  opening,  and  many  other  cases  of  such  temporary  use  of  very  sharp 
curves  might  be  adduced.  All  of  the  above  curves,  however,  are  in  permanent  track,  al- 
though most  of  them  are  in  localities  where  it  is  convenient  to  operate  them  at  very  slow 
speeds.     The  sharpest  curves  on  the  open  road  of  three  of  the  trunk  lines  are  : 

New  York,  Lake  Erie  &  Western, 10° 

P-ennsylvania, 8° 

Baltimore  &  Ohio, 9°  3°' 

The  first  of  these  curves  is  a  reversed  curve  at  Passaic,  a  few  miles  out  of  New  York, 
and  an  enormous  traffic  passes  over  it.  It  could  be  taken  out  at  very  moderate  expense, 
but  has  not  proved  sufficiently  objectionable  to  make  this  appear  worth  while.  The  New 
York  Central  has  one  very  sharp  curve  of  about  14°  on  its  main  line,  but  in  a  yard 
where  speed  is  slow. 

Narrow-gauge  roads  have  rarely  used  sharper  than  24°  curves  in  any  part  of  the 
world,  although  a  few  as  sharp  as  30°  are  in  use  in  Colorado  and  elsewhere. 


CHAP.   IX.— RISE  AND  FALL.  327 


CHAPTER   IX. 

RISE    AND    FALL. 

361.  The  expense  of  gradients,  as  we  saw  in  part  in  Chapter 
VI.,  arises  from  two  causes,  which  are  totally  distinct  and  must 
be  kept  so  to  form  any  correct  estimate  of  their'cost  or  of  their 
proper  adjustment.  The  association  between  them  is  accidental. 
The  distinction  between  them  is  vital  and  fundamental. 

The  first  of  these  causes  is  the  direct  cost,  for  wear  and  tear 
and  fuel,  of  ascending  to  and  descending  from  any  given  eleva- 
tion, instead  of  running  on  a  level ;  in  other  words,  the  cost  of 
RISE  AND  FALL.  This  is  the  branch  of  the  subject  that  we  pro- 
pose now  to  consider. 

The  SECOND  objection  to  gradients  is  the  effect  which  the 
maximum  or  rather  ruling  grade  (since  the  ruling  grade  may, 
owing  to  the  effect  of  variations  of  velocity,  be  either  greater  or 
less  than  the  nominal  maximum  of  the  profile)  has  to  increase 
the  cost  of  operating  the  entire  line,  however  short  the  ruling 
grade  itself  may  be,  not  by  increasing  the  direct  expense  per 
train-mile,  but  by  limiting  the  number  of  cars  to  a  train. 

362.  This  latter  objection  to  gradients*  (i.e.,  to  one  particular 
gradient,  the  worst  one  on  the  line)  is  greatly  more  important 
than  the  former,  but  it  has  no  real  connection  with  it  whatever, 
being  different  both  in  its  nature  and  in  its  effect  in  detail  on  the 
operating  expenses. 

In  fact,  it  is  not,  properly  speaking,  an  attribute  of  gradients 
at  all,  except  that,  owing  to  the  limitations  of  the  locomotive 
engine,  gradients  happen  to  be  the  most  usual  cause  which 
limits  the  weight  of  trains.  But  this  is  not  invariably  so.  Some- 
times curvature,  and  not  gradients,  is  the  limiting  agent.  For 
example,  the  Hudson  River   Railroad  probably  approaches  the 


328  CHAP,   IX— RISE  AND  FALL. 

nearest  to  being  on  a  direct  level  throughout  of  any  line  of  its 
length  in  the  world,  yet  in  laying  out  that  line  the  locating  en- 
gineer has  freely  introduced,  upon  slight  occasion,  short  gra- 
dients of  0.3  to  0.5  per  cent  (15  to  25  ft.  per  mile),  which  could 
have  been  avoided  at  slight  expense  ;  and  wisely  so,  because  the 
unavoidably  sharp  curvature  of  the  line  effectually  limits  the 
weight  of  trains  to  such  as  is  easily  hauled  on  a  considerable 
gradient.  Up  to  a  certain  grade,  therefore,  curvature  takes  on 
this  line  the  place  of  gradients  as  a  limiting  agent.  Had  the 
topography  of  the  Hudson  River  permitted  such  an  alignment  as 
that  of  the  Canada  Southern  Railway,  for  example,  which  has 
no  curvature  to  speak  of,  a  very  great  expenditure  might  have 
been  justifiable  to  eliminate  these  same  gradients  which  have 
thus  been  freely  and  wisely  introduced. 

363.  And  if  at  some  time  in  the  future  the  locomotive  engine 
should  be  so  improved,  or  such  new  motor  discovered,  as  to  be  able 
to  exert  an  indefinitely  varying  power  according  to  the  need  at 
various  points  on  the  line  (even  if  the  cost  for  power  were  no 
less  per  foot-pound  than  now),  all  objections  to  both  grades  and 
curvature  except  such  as  is  inherent  in  them — the  resulting 
wear  and  tear  and  waste  of  fuel — would  disappear,  and  they 
might  be  introduced  with  great  freedom  ;  for  neither  of  them 
would  then  have  in  addition  to  their  own  inherent  disadvanjtages 
the  further  effect  of  limiting  the  weight  of  trains. 

The  strength  of  couplings  would  then,  perhaps,  become  the 
limiting  agent,  and  all  that  great  value  which  now  attaches  to  the 
reduction  of  the  rate  of  grades  would  be  taken  bodily  from  it 
and  transferred  to  securing  the  strongest  possible  coupling.  The 
direct  cost  of  the  rise  and  fall  on  those  gradients,  however  (its 
effect  to  cause  wear  and  waste  power),  might  remain  entirely  un- 
affected. 

Some  radical  change  of  this  kind  seems  possible — it  might  almost  be 
said  imminent — from  the  development  of  electricity  as  a  motive-power. 
An  electric  motor  so  simple  that  it  could  be  applied  to  each  axle  of  every 
car  would  revolutionize  the  art  of  laying  out  and  operating  railways. 

364.  To  put  into  technical  terms  the  whole  distinction  between  rise  and 
fall  proper  and  limiting  effect  on  trains.  The  cost  of  rise  and  fall  bears  a 


CHAP.   IX.— RISE  AND  FALL.  329 

closely  approximate  ratio  to  the  foot-pounds  of  work  required  to  lift  a 
train  a  feet  high,  which  is  independent  of  the  rate  of  the  grade.  Any  new 
electrical  or  other  motor  might  and  probably  would  leave  the  cost  of 
power  per  foot-pound — which  is  a  small  matter  as  it  is — entirely  unaf- 
fected. But  the  great  objection  to  heavy  gradients  on  railways  as  at 
present  operated  lies,  not  in  their  effect  to  increase  the  foot-pounds  of 
work  to  be  performed,  but  in  the  increase  which  they  cause  in  the, pou?tds 
of  tenszoft  which  the  locomotive  is  required  to  exert  while  on  them.  The 
pounds  of  tension  which  the  locomotive  can  exert  being,  from  its  con- 
struction, strictly  limited,  we  are  obliged  to  increase  Xhefeet  passed  over 
in  surmounting  elevations  (i.e.,  to  reduce  the  rate  of  grade)  by  every  pos- 
sible device,  and  at  large  expense,  in  order  to  enable  the  locomotive  to 
pull  large  trains. 

This  lack  of  adaptability  in  the  locomotive,  i.e.,  inability  to  exert  any 
pull  whatever  if  the  speed  be  reduced  enough,  or  to  give  any  speed  what- 
ever if  the  resistance  be  reduced  enough,  is  its  greatest  mechanical  defect. 
A  partial  remedy  has  been  found  in  rack  railways,  etc.,  as  noted  in 
Chap.  XL 

365.  It  therefore  results  that  the  cost  of  a  ruling  grade  is 
directly  as  the  rate  of  grade  and  independent  of  its  length  or  of 
the  elevation  surmounted,  while,  per  contra,  the  cost  of  rise  and 
fall  is  directly  as  the  elevation  surmounted,  and  (within  moder- 
ate limits)  independent  of  the  rate. 

366.  This  contrast  alone  is  enough  to  show  the  radical  dis- 
tinction between  them  ;  but  while  the  distinction  is  readily 
enough  admitted  in  the  abstract,  it  is  frequently  confused  in 
practice,  and  such  a  practical  confusion  of  these  two  wholly  dis- 
tinct objections  to  gradients  destroys  the  value  of  any  discus- 
sion or  estimate  of  either,  and  forbids  any  clear  understanding 
of  the  proper  adjustment  of  grades  ;  leading,  on  the  one  hand, 
to  very  erroneous  theories  that  "undulating  gradients"  (in  other 
words,  mere  surface  roads  on  any  convenient  grade)  are  not 
seriously  objectionable, — which  in  some  cases,  on  some  parts  of 
a  line,  may  be  very  nearly  the  case, — and,  on  the  other  hand,  to 
equally  mistaken  expenditures  to  introduce  as  long  and  as 
nearly  level  grades  as  possible  at  all  points  of  the  line  indiscrim- 
inately.    The  latter  is  a  particularly  dangerous  and  common 


330  CHAP.    IX.— RISE  AND  FALL. 

error.  B}^  trusting  chiefly  to  one's  impressions  or  "experience" 
in  such  matters,  habit  may  make  it  a  second  nature  to  reduce  all 
grades  as  much  and  as  speedily  as  possible,  and  to  stretch  out 
the  longest  piece  of  thread  which  can  be  made  to  lie  on  the  pro- 
file in  fixing  the  grades.  A  thousand  feet  further  is  not  far  on 
the  profile,  but  it  often  entails  a  considerable  expense  for  con- 
struction to  no  purpose  whatever.  On  the  other  hand,  the  con- 
trary error — an  undiscriminating  readiness  to  use  "  undulating 
grades" — has  seriously  reduced  the  value  of  more  miles  of  railway 
in  the  Western  United  States,  perhaps,  than  all  the  other  causes 
combined ;  because,  unfortunately,  nature  has  left  it  possible  in 
that  region  to  run  almost  from  anywhere  to  anywhere  in  very 
nearly  an  air-line  if  we  are  willing  to  accept  what  are  euphem- 
istically called  "  moderate"  grades  of  25  to  75  feet  per  mile ;  in- 
stead of  the  dead  level,  or  nearly  that,  which  in  many  cases  was 
equally  easy  to  obtain  by  moderate  deviations  from  some  "  50- 
mile  tangent." 

367.  To  some  extent  the  cost  of  rise  and  fall,  as  well  as  the 
limiting  effect  of  gradients,  depends  upon  the  rate  of  grade,  for 
it  must  be  divided,  as  respects  cost  and  disadvantages,  into  three 
quite  distinct  classes,  according  to  the  grades  on  which  it 
occurs. 

These  classes  are  : 

A.  Rise  and  fall  on  grades  so  light  or  so  situated  as  never  to 
require  the  use  of  brakes  nor  variations  in  the  power  of  the 
engine. 

B.  Rise  and  fall  on  grades  heavy  enough  to  require  the 
slight  use  of  brakes  or  shutting  off  steam,  or  both,  in  descend- 
ing, but  not  such  as  to  be  a  serious  tax  upon  the  engine  in 
ascending. 

C.  Rise  and  fall  on  maximum  grades,  requiring  the  full  power 
of  the  engine  in  ascending,  with  more  or  less  use  of  sand,  danger 
of  slipping  drivers,  and  the  use  of  brakes  m  descending. 

To  which  one  of  these  classes  any  given  grade  will  belong, 
will  depend  m  good  part  upon  the  general  character  of  the  line  ; 


CHAP.  IX,— RISE  AND  FALL— EFFECT  OF  VELOCITY.     331 

but   as   between  the  classes   themselves   there  is   a  marked  and 
decided  difference  in  cost,  in  passing  from  one  to  the  other. 

In  order  to  determine  the  method  by  which  they  may  be  cor- 
rectly distinguished  from  each  other,  it  will  be  necessary  to 
consider  now  one  of  the  most  important  departments  of  the 
subject  of  ruling  or  limiting  gradients,  as  well  as  of  rise  and 
fall,  viz.: 

THE  LAWS  OF  ACCELERATED  AND  RETARDED  MOTION,  AND  THE 
EFFECT  THEREOF  ON  THE  MOVEMENT  OF  TRAINS. 

368.  We  cannot  go  into  the  general  theory  of  this  question  as  fully  as 
might  be  desirable,  because  the  final  results  of  such  a  discussion,  which  we  shall 
need  to  use,  will  be  in  so  simple  a  form  that  any  one  can  use  them  almost  me- 
chanically. The  student  is  urgently  recommended,  if  not  already  familiar  with, 
the  general  laws  of  mechanics,  to  study  and  master  the  elementary  principles  at 
least  of  theoretical  mechanics,  which  it  requires  no  great  labor  to  do.  Almost 
any  treatise,  thoroughly  mastered,  will  suffice,  but  Todhunter's  "Mechanics 
for  Beginners"  (the  title  being  somewhat  misleading)  is  particularly  useful  for 
those  who  desire  to  go  thoroughly  into  the  subject,  and  test  their  knowledge  by 
example.  In  this  respect  Todhunter's  entire  mathematical  series  are  quite  un- 
equalled. A  fair  but  in  some  respects  deficient  general  idea  can  be  obtained 
from  Trautwine's  "  Pocket-Book,"  which  may  be  assumed  to  be  in  the  hands  of 
every  engineer.  The  writer  knows  of  no  treatise  in  which  the  important  prac- 
tical applications  of  these  general  principles  which  we  are  about  to  discuss  are 
more  than  obscurely  hinted  at. 

369.  A  railway  train,  or  any  other  body,  acted  upon  by  any  force  or 
any  number  of  forces,  as  gravity,  the  tractive  power  of  the  locomotive, 
friction,  etc.,  which  are  for  the  time  being  uniform  in  their  action  and 
yet  do  not  exactly  balance  and  destroy  eacti  other,  is  under  the  condition 
technically  known  as  uniformly  accelerated  or  retarded  motion,  the  laws 
of  which  are  the  same  as  for  a  body  falling  freely  in  a  vacuum,  acted  upon 
by  gravity  alone.  Rather,  the  latter  also  is  but  one  particular  case  of  a 
general  law. 

When  one  of  the  forces,  as  train  resistance  or  air  resistance,  is  not 
constant,  but  increases  or  decreases  with  the  velocity,  the  body  will  not 
be  governed  by  the  laws  of  uniformly  accelerated  motion,  but  by  laws 
much  more  complicated.  Within  moderate  limits,  however,  and  within 
limits  sufficiently  broad  for  our  present  purposes,  the  motion  may  be  as- 
sumed to  be  uniformly  accelerated  or  retarded  without  sensible  error, 
and  we  shall  so  consider  it,  except  where  otherwise  explicitly  stated. 


332     CHAP.  IX.— RISE  AND  FALL— EFFECT  OF  VELOCITY. 


370.  All  energy  or  work  communicated  to  any  body  must  be  em- 
ployed either  (i)  in  overcoming  frictional  or  other  resistances,  or  (2) 
stored  up,  so  to  speak,  within  the  body,  in  the  form  of  an  increase  of 
velocity.  The  energy  so  stored  up  is  reconvertible  into  work  at  any 
time  without  loss,  and  its  amount,  for  any  given  velocity,  may  be  very 
simply  determined  by  formula,  or  instantly  from  a  table  (Tables  117  and 
118). 

371.  To  determine  by  formula  the  work  represented  by  a  given  ve- 
locity, or  the  velocity  attainable  by  a  given  amount  of  work :  It  was 
found  experimentally  long  since— by  Galileo,  at  the  leaning  tower  of 
Pisa — that  a  body  falling  freely  toward  the  earth,  with  no  opposing  re- 
sistances to  impede  its  motion  (in  other  words,  a  body  continually  acted 
upon  by  a  force  equal  to  what  we  term  its  weight),  will  fall  through  16.08 
feet  in  one  second  of  time  (in  the  latitude  of  Italy  or  New  York,  16.04  at 
the  equator,  16.095  at  London,  51°  31'  N.;  16.127  at  80°  N.),  and  will  then 
be  moving  with  a  velocity  of  twice  its  average  velocity,  or  32.16  feet  per 
second.  In  the  second  second  the  velocity  previously  acquired  will  carry 
it  through  32.16  feet,  and  the  continuous  action  of  the  original  force  will 
carry  it  through  an  additional  distance  of  16.08  feet,  and  communicate  an 
additional  velocity  of  32.16  feet  per  second,  making  the  total  distance 
fallen  through  in  the  second  second  48.24,  and  the  final  velocity  acquired 
64.32  feet  per  second.  By  this  process,  which  can  be  varied  in  many 
ways,  and  which  was  in  the  beginning  purely  empirical,  the  general  laws 
have  been  determined  which  may  be  summarized  thus : 

The  total  time  being  as  i,  2.  3,  4,  etc.,  the  velocity,  either  average  or 
final,  will  be  as  i,  2,  3,  4,  etc.  The  total  spaces  passed  through  will  be  as 
the  square  of  the  velocities,  or  i,  4,  9,  16,  etc.,  and  the  spaces  for  each 
time  as  I,  3,  5,  7,  9,  etc.  The  final  velocity  is  always  twice  the  average 
velocity. 

The  height,  =  h,  through  which  a  body  must  fall  to  acquire  a  velocity 
of  V  feet  per  second  is 

^"^"^  "64.32' 

5280 
or  to  acquire  a  velocity  of  V  miles  per  hour ;  since  v  =  ^^  ^  ^^  Vy 

V60    X     60/  T-2 

^  =   -^ -— f =   0.033445  ^'. 

64.32 


CHAP.  IX.— RISE  AND  FALL— EFFECT  OF  VELOCITY.     333 


372.  Why  the  constant  64.32  in  this  equation  should  be  precisely 
what  it  is,  instead  of  54.32  or  74.32,  is  unknown,  and  science  does  not 
even  tend  to  determine  it ;  but  it  is  known  that  this  constant,  which  is 
called  the  acceleration  of  gravity,  wmU  vary  directly  with  the  force, 
if  the  latter  be  greater  or  less  than  gravity ;  so  that  with  this  change 
made,  the  formula  is  of  general  application  to  a  body  acted  on  by  any 
uniformly  accelerating  force  whatever. 

373.  From  this  formula  Table  117  is  calculated.  It  gives  at  once  the 
velocity  in  miles  per  hour  which  will  be  acquired  by  a  train  (or  any  other 
body)  falling  without  frictional  resistance  through  a  given  vertical  dis- 
tance (acted  on  by  a  force  equal  to  its  weight  for  a  given  distance)  and 
hence,  conversely,  the  vertical  distance  through  which  momentum  alone 
will  lift  the  train  moving  at  any  given  velocity  against  the  force  of  grav- 
ity. Nothing  more  than  this  table  and  a  general  understanding  of  the 
subject  is  needed  to  solve  all  ordinary  problems  connected  with  location 
arising  from  variations  of  velocity,  except  for  one  detail,  which  makes 
Table  118  the  better  one  to  use. 

Table  117. 


Height  in  Vertical  Feet  through  which  a  Body  must  Fall  to  acquire 

A  Given  Velocity  in  Miles  Per  Hour. 

Or  the  height  through  which  the  energy  due  to  that  velocity  will  lift  the  body  against 

gravity  only  before  it  comes  to  rest. 


Miles 

Per 

Hour. 

0. 

1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

0 

10 

20 

30 

40 

50 

0.00 
3-34 
13-38 
30.10 
53-51 
83.61 

0.03 
4-05 
14-75 
32.14 
56.22 
86.99 

0.13 
4.82 

16. ig 
34-25 
58-99 
90-43 

0.30 
5.65 
17.69 
36.42 
61.84 
93-94 

0.54 

6.55 
19.26 
38.66 
64-75 
97-52 

0.84 
7-52 
20.90 
40.97 
67.72 
101.17 

1.20 

8.56 

22.61 

43-34 
70.77 
104.88 

1.64 
9.67 
24.38 
45-78 
73-88 
108.66 

2.14 
10.84 
26.22 
48.29 
77-05 
112.50 

2.71 
12.07 
28.13 
50.87 
80.30 
116.42 

Formula 


/    5280   \2 

( •  )    V^  (in  miles  per  hour) 

h  =  ^^X^/ =  o, 

64.32 


033445  V^' 


For  computations  connected  with  the  movement  of  trains  the  following  Table  118 
should  be  used. 


374.  The  formula  of  par.  371  assumes  that  the  body  is  in  motion  as 
a  whole,  but  that  its  parts  are  at  rest  relatively  to  each  other.     In  a  mov- 


334     CHAP.  IX.— RISE  AND  FAIL— EFFECT  OF  VEIOCITY. 

ing  train  this  is  not  so ;  for  the  wheels  and  axles,  in  addition  to  their  for- 
ward motion,  are  in  rapid  rotation,  so  that  additional  energy  is  stored  up 
within  them  as  in  so  many  fly-wheels.  To  put  the  same  truth  in  another 
way :  Each  particle  in  the  wheels  and  axles  (except  on  the  axis)  moves 
more  feet  per  second  through  space  (albeit  in  a  curved  path)  than  the 
train  as  a  whole,  so  that  they  necessarily  have  more  energy  stored  within 
them. 

The  energy  due  to  the  rotation  of  the  wheels  and  stored  up  in  them 
as  in  a  fly-wheel  is  usually  computed  separately  from  that  which  they 
have  in  common  with  the  rest  of  the  train,  when  it  is  computed  at  all ; 
but  for  all  purposes  in  connection  with  the  motion  of  trains  for  which 
the  one  is  required  to  be  known,  the  other  may  be  said  to  be  also,  and  in 
Table  ii8  the  two  are  included  together.  If  the  wheels  were  not  in  con- 
tact with  the  rails,  but  were  mounted  like  fly-wheels  within  the  car,  they 
would  exercise  no  effect  upon  the  forward  motion  of  the  train.  After 
the  train  had  been  brought  to  a  stop  they  would  continue  to  spin  around 
indefinitely  until  stopped  by  their  own  friction ;  but,  being  in  contact 
with  the  rails  (or  if  mounted  on  the  body  of  the  car  and  connected  with 
the  wheels  by  gearing),  they  act  very  effectually  to  carry  the  train  along 
just  so  much  farther,  in  the  same  way  as  the  rotating  fly-wheel  on  the 
little  toy  locomotives,  which  almost  every  one  has  seen,  causes  the  latter 
to  move,  being  in  that  case  the  only  motive-power. 

375.  The  amount  of  energy  in  any  rotating  body  is  determined,  as  may  be 
seen  in  any  treatise  on  mechanics,  by  determining  the  position  and  velocity  of 
a  point  called  the  radius  of  gyration,  which  is  the  radius  at  which,  if  the  whole 
mass  of  the  rotating  body  were  concentrated,  any  given  force  would  communi- 
cate the  same  velocity  of  rotation  as  it  does  to  the  acutal  body.  Motion  in  a 
circular  or  other  curved  path  at  any  given  linear  velocity  means  the  accumula- 
tion of  the  same  amount  of  energy  as  i'f  the  body,  as  a  whole,  were  moving  in  a 
right  line  at  the  same  velocity,  and  if  the  body  be  both  revolving  and  moving 
forward,  like  the  wheels,  the  two  are  separate  and  in  addition  to  each  other. 

376.  The  manner  of  determining  this  radius  of  gyration  it  is  needless  to  go 
into  detail.  According  to  the  pattern  of  wheel,  it  will  vary  between  0.7  and  0.8 
of  the  actual  radius,  being  in  car  wheels  nearer  0.7  and  in  locomotive  drivers 
fully  0.8.  Assuming  a  minimum  radius  of  0.7,  it  will  be  plain  that  points  on 
that  circle  are  rotating  with  a  hnear  velocity  of  0.7  times  the  velocity  of  the 
train,  and  hence  that  the  rotative  energy  only  of  the  wheels  will  be  0,7^  or  0.49 
— in  round  numbers  one  half  that  due  to  the  forward  modon  of  the  wheels  in 
common  with  the  rest  of  the  train.  Really  it  should  be  a  little  more  than  this 
even  figure  for  ordinary  patterns  of  wheels,  and  in  locomotives  it  is  fully  six- 
tenths. 


CHAP.  IX.— RISE  AND  FALL— EFFECT  OF  VELOCITY.     335 

Estimating  ordinary  car  wheels  to  weigh  2^  tons  per  8-wheeled  car,  or  561 
pounds  per  wheel,  the  ratio  of  the  weight  of  the  wheels  to  the  total  weight  will 
be  about — 


Weighing 

Per  cent  of  weight  of  wheels 

Making  an  addition  to  the  total 
energy  of  the  train  of  about... . 


In  a  Passenger 

or  Loaded 

Freight  Car. 


22^  tons. 
10  p.  c. 

5  p.  c. 


In  an  Empty 
Freight  Car. 


9  tons. 
25    p.  c. 

I2i  p.  c. 


In  Locomotive  and 
Tender. 


10  to  I2|  p.   C. 

6  to    7i  p.  c. 


We  may  say,  therefore,  that  the  rotative  energy  of  the  wheels  will  add 
about  6  per  cent  as  a  minimum  to  the  accumulated  energy  or  "velocity  head  " 
of  the  train  as  a  whole,  in  the  case  of  ordinary  passenger  or  loaded  freight 
trains,  which  with  very  heavily  loaded  cars  may  be  a  little  less,  but  in  the  case 
of  long  trains  of  empty  cars  may  be  some  4  or  5  per  cent  higher.  Under  this 
assumption,  assuming  6.14  per  cent  for  ease  of  computation.  Table  118  was 
computed,  which  is  the  proper  one  for  use  in  all  computations  concerning  the 
energy  stored  in  trains  at  various  velocities. 


Table  118. 

Total  Energy  of  Potential  Lift  in  Vertical  Feet  (or  Velocity  Head) 
IN  Trains  moving  at  Various  Velocities. 

Including  the  Effect  of  the  Rotative  Energy  of  the  Wheels  for  Passenger  or  Loaded 
Freight  Trains,  assumed  at  6. 14  per  cent  of  the  total  energ>^  For  trains  of  empty- 
fiat  or  coal  cars  add  about  4  per  cent  to  the  quantities  below,  and  proportionately  for 
mixed  trains. 


Miles 
Per 

Hour. 
Vel.  ft.. 

0. 
0.00 

1. 

0.04 

2. 

0.14 

3. 
0.32 

4. 
0.57 

5. 

0.89 

6. 
1.28 

7. 
1.74 

8. 
2.27 

9. 

2.88 

Miles 

Per 

Hour. 

.0 

.1 

.2 

.3 

.4 

.5 

.6 

.7 

.8 

.9 

10 

3-55 

3-62 

3.69 

3 

77 

3.84 

3-92 

3-99 

4 

07 

4-15 

4.22 

II 

12 

13 

14 

18 

19 

4.30 
6.00 
6.96 

7-99 
9.09 

10.26 
11.50 
12.82 

4.38 
5-19 
6.09 

7.06 
8.10 
9.21 

10.39 
11.63 
12.96 

4.46 
5.28 
6.19 

7.16 
8.21 
9-32 
10.51 
11.76 
13.09 

4 
I 

9 

10 
II 

13 

54 
37 
28 

27 
32 
44 

64 
90 
23 

4.62 
5-46 
6.38 

7-37 
8.43 
9-55 
10.76 
12.03 
13-37 

4.70 

If 

9.67 

10.88 
12.16 
13-51 

4-79 
5.64 
6-57 

It 

9-79 

II. OT 

12.20 
13.64 

4 

I 

9 
II 
12 
13 

87 

68 
76 
90 

13 

43 
78 

6.76 

8.87 
10.02 

11.26 
12.56 
13.92 

5-03 
5-91 

6.86 

IOyI4 

11.38 
12.69 
14.06 

20 

14.20 

■  14-34 

14.49 

14 

64 

14.78 

14-93 

15.08 

15 

23 

15-38 

15-52 

336     CHAP,  IX.— RISE  AND  FALL— EFFECT  OF  VELOCITY. 


Table  118. — Continued. 


Miles 
Per 

Hour. 
Vel.  ft.. 

0. 
o.oo 

1. 

0.04 

2. 
0.14 

3. 

0.32 

4. 
0.57 

5. 

0.89 

6. 

1.28 

7. 
1.74 

8. 
2.27 

9. 
2.88 

Miles 

Per 

Hour. 

.0 

.1 

.2 

.3 

.4 

.5 

.6 

.7 

.8 

.9 

20    ... 

14. 

20 

14-34 

14.49 

14.64 

14.78 

14-93 

15.08 

15-23 

15.38 

15^52 

21 

22 

23 

24 

27 

28 

29 

15- 
17- 
18. 

20 

22 
24 

25 
27 
29 

67 
19 
79 
46 
20 
00 

88 
83 
86 

15-82 
17-35 
18.95 
20.63 
22.38 
24.18 

26.07 
28.03 
30.06 

15-97 
17.51 
19.11 

20.80 
22.56 
24-37 
26.27 
28.23 
30.27 

16.13 

17.67 
19.27 

20.98 
22.74 
24.56 

26.46 
28.43 
30.48 

16.28 
17-83 
19.44 

21.16 
22.92 
24-75 
2'S.66 
28.64 
30.69 

16.43         16.58 
17.99         18.15 
19.61         19.78 

21.34        21.51 
23.10        23.38 
24.93        25.12 

26.85        27.05 
28.84  1     29.05 
30.90  i     31.11 

16.73 
18.31 

19-95 
21.68 
23.46 
25-31 
27.24 
29.25 
31^32 

16.88 
18.47 
20.12 

21.84 
23.64 
25.50 

27.44 
29.46 

31.53 

17.04 
18.63 
20.39 

21.02 
23.82 
25.69 

%% 

31-74 

30 

•      31 

95 

32.16 

32.18 

32.60 

32-81 

33-03  i     33-25 

33^47 

33-69 

33-90 

31   

32 

33 

.34  ••••• 

%■::::. 
li:;;;:: 

39 

38 
41 

% 

48 
51 

54 

12 

i 

04 
49 
01 

60 
.26 
.00 

34-34 
36.58 
38-90 
41.28 

46.26 

48.87 

51-53 
54-28 

34-57 
36.81 

39-13 

41-53 
44.00 

46.52 

49  13 
51,80 

54-56 

34-79 
37^04 
39^37 

44  25 
46.78 

49^39 
52.08 
54  84 

35-01 
37^27 
39.61 

42.02 
44-50 
47-04 
49.66 
52.36 
55^12 

35-24  1     35-46 
37-50  1     37.74 
39.85  1     40.08 

42.26        42.51 
44.75        45-00 
47-30        47.56 

49-93        50-20 
52.63  1     52.91 
55.40  \     55.68 

35^68 
37^97 
40.32 

42-75 
45.26 
47.82 

50^47 
53.18 
55.96 

35-91 
38.20 
40.56 

43.00 
45^51 
48.08 

50  •73 
56.24 
59^10 

36.13 
38.43 
40.80 

43.24 

'it 

51.00 

53^73 
56.52 

40.   ... 

56 

.80 

57^09 

57-37 

57-66 

57^95 

58.24  a   58.52 

58.81 

59^39 

41 

42 

43 

44   

%■::::. 
%■■:::. 

49 

59 
62 
65 
68 
71 
75 
78 
81 
85 

.68 
.62 
.64 

73 
89 
.12 

42 
79 
.24 

59-97 
62.92 
65-94 
69.05 
72.21 
75-45 

78.75 
82 .  13 
85-59 

60.27 
63.23 
66.25 

69.36 
72.54 
75-78 

85-94 

60.56 

69.68 
72.86 
76.11 

79-43 
82.82 
86.29 

60.86 
6383 
66.87 

70.02 
73.18 
76.44 

79.76 

83^i7 
86.64 

61.15 
64.13 
67.18 

70.34 
73-50 
76.77 

80.10 
83-51 
86.99 

61.45 
64-43 
67.69 

70.65 
73.82 
77.10 

80.44 
83-85 
87-34 

61.74 

64.73 
67.80 

70.97 
74-15 
77-43 

80.77 
84.20 
87.69 

62.04 
65.03 
68.11 

71.28 
74^47 
77.76 

81.  II 

!155 
88.04 

60.33 
65^34 
68.42 

71.60 

74^79 
78.09 

81.45 
84.89 
88.39 

50.    ... 

Diffs... 

60 

Dififs  .. 

70 

Diffs... 

88 

3 

127 

4 

173 
5 

-75 
•59 
.80 
•30 

•95 
.01 

92-34 
3.65 

132.10 
4-36 

178.96 
5.07 

95-99 

3-73 

136.46 

4.44 

184.03 
5^15 

99.72 
3.80 

140.90 
4-51 

189.18 
5-22 

103.52 
3^87 

145^41 
4.58 

194.40 
5^29 

107.39 
3-94 

149.99 
4-65 

199.69 
5-36 

111.33 
4-OI. 

154-64 
4-72 

205.05 
5-43 

115-34 
4.08 

159-36 
4-79 

210.48 
5.50 

119.42 
4.16 

164.15 
4.87 

215.98 
5.58 

123.58 
4.22 

169.02 

4.93 

221.56 

564 

Formula  :  Vel.  head  = 


v"^  in  ft.  per  sec.  _  1.4672  V^  (in  miles  per  hour)    _ 


0.033445 


JZ2 


64.32  64.32 

To  which  add  6.14  per  cent  for  rotative  energy  of  the  wheels  =  0.002055  V^ 
Giving  as  the  final  formula,  by  which  the  table  is  computed,  Vel.  head  =  0.035500  r» 

The  above  table  is  exact  for  the  even  miles.  The  heights  for  tenths  of  a  mile  per  hour 
were  filled  in  by  interpolation,  and  the  last  digit  may  be  in  error. 

The  process  of  computing  the  result  of  a  brake-test  by  the  aid  of  this  table,  which  may 
be  useful  for  reference  in  connection  with  it,  is  as  follows  : 


CHAP.  IX.— RISE  AND  FALL— EFFECT  OF  VELOCITY.     337 

FIELD   NOTES   REQUIRED    FOR   COMPUTING   BRAKE   TESTS. 

1.  Speed  in  miles  per  hour  at  instant  of  applying  brakes. 

2.  Distance  run  after  applying  brakes,  in  feet. 

3.  Rate  of  grade.,  ascending  or  descending,  in  per  cent,  i.e.,  feet  per  station  of  100  ft. 

4.  Proportion  of  the  total  weight  of  the  train  to  which  brakes  were  applied.  (Except 
as  necessary  to  determine  this  proportion,  the  total  weight  of  the  train,  or  the  total  weight 
on  braked  or  unbraked  wheels,  is  unessential,  and  does  not  enter  into  the  computation.) 

To  these  essential  notes  should  preferably  be  added  : 

5.  Time  of  stop  in  seconds  (best  taken  with  a  stop-watch). 

PROCESS   OF   COMPUTATION. 

1.  Take  from  the  table  the  height  in  vertical  feet  corresponding  to  its  speed,  i.e.,  the 
"Vel.  head."  Divide  it  by  the  length  of  the  stop  in  stations  of  100  ft.  The  quotient 
(which  will  in  all  ordinary  cases  be  between  the  extreme  limits  of  2.00  and  20.00)  is  the 
equivalent  guide  of  retardation  for  a  stop  on  a  level  grade. 

2.  To  this  quotient  add  the  acttial  rate  of  grade,  if  descending,  or  subtract  it  if  ascend- 
ing. Subtract  also  the  grade  representing  the  average  train  resistance  during  the  entire 
stop,  which  may  be  approximately  assumed  as  follows  : 

Miles  per  hour. 


Initial  speed, 25        30        40        50        55        60 

and  less. 

Pounds  per  ton  (2000  lbs.). 


Average  resistance  during  stop,    ,     .    8         9        10        12        14        16 

Per  cent  (or  feet  per  100). 

Equivalent  grade, 0.4     0.45      0,5       0.6       0.7      0.8 

3.  The  resulting  sum  or  difference  is  the  actual  equivalent  grade  of  retardation.,  in  feet 
per  100  :  or  the  effect  of  the  brakes  as  a  whole  on  the  train  as  a  whole.  The  figures  ex- 
pressing this  grade,  as  5.00,  8.50,  12.45,  express  also  the  efficiency  of  the  brakes  upon  the 
train  as  a  whole,  in  percentages  of  the  total  weight  of  the  train. 

4.  Divide  this  grade  or  percentage  by  the  per  cent  of  the  total  weight  of  the  train 
upon  which  brakes  acted  or  were  adapted.,  ijitended,  or  expected  to  act.  The  quotient  is 
the  actual  efficiency  of  the  brakes  upon  the  load  carried  by  the  braked  wheels,  or  upon 
that  portion  thereof  which  it  was  intended  to  rely  upon  in  proportioning  the  brakes. 
This  quotient  will  always  lie  between  the  extreme  limits  of  25.00  and  i.oo,  usually  be- 
tween 3.00  and  14.00,  and  is  the  only  one  by  which  comparisons  with  different  trains 
having  differently  distributed  brakes  can  properly  be  made. 

By  formula :  Grade  of  retardation  =  —  Jl!^  i  +  rate  of  descending  grade,  or  )    _ 

Distance  (  —  ascending        "  j 

,       r      ,,.       r  .  ^.  J  Grade  of  retardation 

grade  of  rolhng  friction  ;  and -~- — ——. ,  .  ,    ^— =  Efficiency  of 

p.  c.  of  wt.  of  tram  on  which  brakes  acted 

brakes  in  per  cent  of  weight  on  which  they  acted. 

EXAMPLES. 

I.  Train  with  %,  (75  per  cent)  of  weight  braked ;   20  miles  per  hour ;  2.84  ft.  (284 
stations),  distance  run  ;  grade,  52.8  ft.  per  mile  (i.o  per  cent)  descending. 
22 


338     CHAP.  IX.— RISE  AND  FALL— EFFECT  OF  VELOCITY. 

Assumed  average  grade  of  rolling  friction,  as  above,  =  0.4.     Then 

14.20  (from  table) 

=  5.00  +  i.oo  -  0.4  =  5.6  -f-  0.7s  =  7.47, 

2.04 

being  the  percentage  of  the  efficiency  of  the  brakes  or  rate  of  an  equivalent  grade  ;  and 
grade  of  7.47  X  20  =  159.4  lbs.  per  ton  retarding  force  from  brakes. 

2.  Train  go  per  cent  braked  ;  60  miles  per  hour  ;  1014  ft.  length  of  stop  ;  grade,  26.4 
ft.  per  mile  (0.5  per  cent)  ascending. 

Assumed  average  grade  of  rolling  friction,  as  above,  =  0.8. 

127.80  (from  table)  ^  00 

— =  12.00  —  I.oo  —  0.8  =  10.80  -4-  0.90  =  12.00. 

10.14 


377.  The  magnitude  of  any  force  is  expressed  (in  English)  in  pounds 
or  some  multiple. 

The  work  done  (or  which  has  been  or  can  be  done)  by  the  continued 
application  of  any  force  is  expressed  in  foot-pounds,  i.e.,  by  the  force  in 
pounds  multiplied  by  the  distance  in  feet  through  which  it  acts  or  has 
acted  or  can  act.  A  Consolidation  locomotive  has  a  tractive  force  of,  say, 
20,000  lbs.  The  work  done  by  such  an  engine  in  running  a  mile  is 
20,000  X  5280  =  105,600,000  foot-pounds.  A  horse-power  is  33,000 
foot-pounds  per  minute.     If,  therefore,  such  an  engine  run  a  mile  in  4 

105,600,000      .      ,  ^..  ,, 

minutes  its  horse-power  is =  800  horse-power,  if  it  run  a  mile 

^  33,000  X  4 

.                                   105,600.000 
in  5  minutes  it  is  exertmg  a  force  of  only  — — —  =  640  horse-power. 

If  a  train  at  a  certain  velocity  has  an  average  resistance  of  10  pounds 
per  ton,  the  power  consumed  by  it  will  be  10  foot-pounds  per  ton  per 
foot,  or  52,800  foot-pounds  per  ton  per  mile.  If,  again,  the  resistance  of 
brakes  be  added,  assuming  the  total  pressure  on  the  brake-blocks  to  be 
equal  to  half  the  weight  of  train  or  1000  lbs.  per  ton,  and  assuming  the 
coefficient  of  friction  to  be  at  0.16  (it  is  in  reality  very  variable),  the  re- 
tarding force  of  the  brakes  will  be  1000  x  o.  16  —  160  lbs.  per  ton,  and 
the  work  done  per  ton  by  the  brakes  (in  dissipating  energy)  will  be  160 
foot-pounds  per  foot  through  which  the  brakes  act. 

378.  The  same  amount  of  energy  (in  excess  of  all  retarding  forces) 
communicated  from  any  source  to  any  body  moving  in  any  direction 
will  cause  that  body  to  move  through  space  with  the  same  velocity. 
The  DIRECTION  of  the  motion  may  vary.  The  velocity  of  motion  will 
not  vary,  and  will  always  be  equal  to  that  required  to  lift  the  body 
through  the  vertical  height  through  which  the  body  would  have  to  fall 
freely  in  a  vacuum  to  acquire  that  velocity. 


CHAP.  IX.— RISE  AND  FALL— EFFECT  OF  VELOCITY.     339 


379.  From  the  above  it  necessarily  results  that  it  is  a  general  law  of 
-motion  on  inclined  planes 
that  a  body  descending 
freely  along  any  incline, 
regular  or  irregular,  as 
AC,  AD,  AE,  or  AF,  Fig. 
62,  under  the  action  of 
the  same  vertical  force,  as 
gravity,  will  be  moving 
through  space  at  any  point,  C,  D,  E,  or  F,  which  lies  at  the  same  verti- 
cal distance  below  A,  with  the  same  velocity  as  it  would  have  at  B  if  it 
had  fallen  vertically  through  AB.  The  direction  of  motion  will  vary 
in  each  case.  The  time  of  descending  to  the  line  bb  will  also  vary  in 
each  case,  but  the  velocity  with  which  the  body  is  moving  through  space 
as  it  passes  any  given  level  bb  will  always  be  the  same,  by  whatever  path 
it  has  reached  that  level,  and  always  that  "due"  to  the  vertical \\^\^\.  of 
the  plane  (less  the  loss  by  friction),  this  being  the  necessary  result  of 
the  fact  that  the  same  number  of  foot-pounds  of  work  have  been  com- 
municated to  the  body  in  either  case. 

380.  The  time  occupied  in  the  descent,  if  it  be  a  regular  plane,  will 
be  greater  than  that  "  due"  to  the  vertical  fall  in  the  ratio  of  the  length 
of  the  plane  to  its  height.  If  it  be  a  curved  or  broken  surface,  the  time 
of  descent  will  bear  no  such  constant  ratio,  but  the  final  velocity  at  a 
given  vertical  distance  below  A  will  in  all  cases  be  the  same. 

381.  Conversely,  the  accelerating  or  retarding  effect  of  gravity  on 
any  incline,  and  in  the  direction  thereof,  as  on  a  railway  grade,  Fig.  63, 
is  less  than  the  weight  of  the  body  in  the  same  ratio  as  the  height  ab 
of  the  plane  is  less  than  its  length 
ac ;  that  is  to  say,  the  force  W^ 
Fig.  63,  which  represents  the 
weight  of  the  body  O  acting  verti- 
cally downward,  may  be  resolved 
— or  rather  resolves  itself — into 
the  force/ acting  parallel  with  the 
plane  and  tending  to  produce  mo- 
tion down  it,  and  the  force  W — (al- 
ways less  than  W) — acting  in  the 
direction  R,  perpendicular  to  the 
rail,  ac  representing  the  actual  pressure  of  the  wheel  thereon.  It  is  geo- 
metrically evident  from  Fig.  63  (on  account  of  the  similarity  of  triangles) 


^ 

^-- 

^/t 

r 

/     1 

^^""SL^^^ 

/^l 

^}       ^^^^^^^--^ 

, 

7 1 

j 

1 

1 
1 
» 

/ 
/ 

1 

i 

1 
/ 

Fig.  63. 


340     CHAP.  IX.— RISE  AND  FALL— EFFECT  OF  VELOCITY. 

that  the  force  /  (technically  known  as  the  grade  resistance,  although  in 
descending  it  is  not  a  resistance  but  an  accelerating  force)  bears  the  same 
ratio  to  the  weight  that  the  rise  in  any  distance  does  to  the  length  ac, 
measured  on  the  slope,  attd  not  horizontally.  Practically,  however,  on  any 
ordinary  railway  grade  the  horizontal  distance  be  is  not  sensibly  differ- 
ent from  the  length  measured  along  the  surface  of  the  rails  ac,  and  hence 
it  is  customary  and  proper  to  assume  ab  =  ac  )  whence  we  have,  approxi- 
mately, 

f_  _ab 

IV^Jc' 

or,  if  we  let  the  horizontal  distance  be  =  lOo,  and  the  height  ab  =  r  = 
rate  of  grade  or  rise  in  loo  (whether  feet  or  other  horizontal  unit,  if  we 
use  the  same  for  both  vertical  and  horizontal),  then  we  have 

_f  _L-  ^^ 

W"~  loo      -^  ~  loo* 

382.  If,  in  this  equation,  we  let  W  ^  2000  =  the  number  of  pounds  in 
a  ton,  we  have 

/  =  2or, 

or,  The  grade  resistance  in  lbs.  per  ton  =  rate  of  grade  per 
CENT  20.  This  rule  should  be  memorized  by  every  railroad  engineer, 
preferably  in  the  still  simpler  form  :  "  Rate  of  grade  in  tenths  X  2."  E.  g. 
on  a  I  per  cent  or  i.o  grade  the  grade  resistance  is  20  lbs.  per  ton  ;  on  a 
0.4  grade,  8  lbs.  per  ton. 

For  the  long  ton  of  2240  lbs.  it  is  only  necessary  to  increase  the  re- 
sult by  12  per  cent.  The  rule  amounts  to  no  more  than  saying  that  if 
the  rate  of  grade  be  y^,  the  resistance  per  ton  will  be  y^  ton,  which  is 
20  lbs. 

383.  The  trifling  importance  of  the  error  in  assuming  in  Fig  63,  that,  for 
all  practical  purposes,  the  hypothenuse  ac  and  the  base  ab  may  be  assumed 
equal,  when  computing  grade  resistance,  is  shown  by  Table  119. 

On  a  4  per  cent  grade,  which  may  be  considered  the  utmost  limit  of  ordi- 
nary practice,  the  error  in  the  computed  resistance  is  only  0.0008,  or  less  than 
one  tenth  of  I  per  cent.  On  the  heaviest  grade  on  which  the  locomotive  has 
ever  worked,  10  per  cent,  the  error  is  only  one  half  of  one  per  cent. 

The  error  can  be  avoided  by  substituting  for  the  actual  weight,  W,  Fig.  63, 
the  value  of  the  component  W  at  right  angles  to  the  plane;  but  for  any  grade 
less  than  the  most  extreme  this  is  unnecessary  trouble,  as  the  error,  what  there 
is  of  it,  tends  to  safety  by  exaggerating  the  grade  resistance. 


CHAP.  IX.— RISE  AND  FALL— EFFECT  OF  VELOCITY.     341 


Table  119. 

Comparative  Length  Per  Station  of  100  Ft.  (or  other  Unit)  of  Various 
Grades,  measured  Horizontally  and  Along  the  Slope. 

Giving  also  the  percentage  of  excess  in  the  computed  grade  resistance  under  the  rule 

f  =  2or  of  par.  382. 


Rise  in  100. 

{ab.  Fig.  63.) 

(=  rate  of  grade 

per  cent.) 

Length  on  Slope 

{ac) 

for  Horizontal  Distance 

{be)  of  100. 

1,00 

100.005 

2.00 

100.020 

3.00 
4.00 

100.045 

100. oSo 

5.00 

6.00 

100.125 
100.180 

7.00 

8.00 

100.245 
100.319 

9.00 
10.00 

100.404 
100.499 

Note. — This  table  likewise  affords 
a  good  opportunity  for  testing  the 
convenient  rule  elsewhere  given  for 
solving  right  -  angled  triangles  of 
small  altitude,  viz. : 

Diff.  between  hyp.  and  base  =  ht.^ 
-^  twice  hyp.  or  base  (whichever  is 
known). 

It  will  be  seen  to  be  correct  with 
these  triangles  to  within  a  very  mi- 
nute percentage. 


384.  The  grade  which  produces  a  longitudinal  force  precisely  equiva- 
lent in  pounds  per  ton  (or  any  other  unit)  to  the  "rolling  friction"  of  the 
car  at  any  given  velocity  is  called  the  grade  of  repose  for  that  velocity, 
being  that  grade  on  which,  if  a  car  or  train  were  descending,  the  accel- 
erating force  of  gravity  would  just  balance  the  resistance  to  motion,  and 
hence  enable  it  to  continue  in  motion  forever  at  the  same  speed,  neither 
gaining  nor  losing  velocity,  which  is  the  theoretical  condition  of  all 
bodies  to  which  a  given  velocity  has  once  been  communicated,  accord- 
ing to  Newton's  first  law  of  motion. 

385i  As  the  frictional  resistance  per  ton  varies  with  either  the  veloc- 
ity or  the  length  of  train,  the  "  grade  of  repose"  will  also  vary  with  either  ; 
but  these  grades,  as  determined  by  Table  150,  in  Chap.  XIII.,  are  given 
in  Table  120. 

386.  The  term  "  grade  of  repose"  is  ill-chosen,  and  originated  in  the  mistaken 
idea  that  a  grade  which  was  heavy  enough  to  more  than  equal  the  resistance  of 
motion  when  a  train  was  once  moving,  was  heavy  enough  to  start  a  train  from 
a  state  of  rest.  In  reality,  a  grade  several  times  heavier  is  necessary,  and  this 
latter  grade  only  can  properly  be  called  a  "grade  of  repose."  But  the  ill- 
chosen  term  is  still  the  common  one,  as  is  likewise,  unhappily,  the  erroneous 
idea  in  which  it  originated.  Otherwise,  probably,  there  would  be  fewer  stations 
on  limiting  grades. 


342     CHAP.  IX.— RISE  AND  FALL— EFFECT  OF  VELOCITY. 

387.  When  a  railway  train  descending  a  grade,  or  any  other  falling 
body,  is  acted  upon  by  an  accelerating  force  which  remains  uniform, — 
like  the  traction  of  a  locomotive  or  gravity, — in  opposition  to  a  retarding 
force  which  increases  with  the  velocity, — like  the  resistance  of  a  train, — 
the  velocity  of  motion  will  continue  to  increase  until  the  retarding  force 
becomes  equal  to  the  accelerating,  and  thereafter  the  body  will  continue 
in  motion  indefinitely  at  a  uniform  velocity.  The  net  resultant  of  all 
the  forces  acting  is  then  zero,  and  consequently  the  body  continues 
indefinitely  in  motion  at  an  unvarying  velocity,  as  theory  requires. 

388.  This  statement  should  be  read  over  until  its  meaning  is  fully 
grasped.  A  railway  train  in  motion  at  a  uniform  velocity  is  acted  on  in 
one  sense  by  two  forces,  but  in  a  truer  sense  by  no  force.  The  frictional 
and  other  resistances  and  the  traction  of  the  locomotive  act  upon  and 
destroy  each  other  within  the  body,  without  either  acting  upon  the  body 
itself,  except  to  produce  internal  stress.  Such  a  body  is  therefore  one  of 
the  nearest  examples  in  practical  mechanics  of  Newton's  abstract  con- 
ception of  a  body  moving  on  indefinitely  iti  vacico  from  original  impulse, 
without  gain  or  loss  of  energy,  as  do  the  heavenly  bodies. 

389.  Under  such  conditions  any  new  force— whether  accelerating 
or  retarding,  like  a  change  in  the  rate  of  grade  or  in  the  tractive  force  of 
the  locomotive — will  act  upon  the  body  precisely  as  if  no  other  forces 
existed  to  act  upon  it ;  i.e.,  the  whole  of  the  new  force,  undiminished 
by  frictional  or  other  losses,  will  act  upon  the  body  to  vary  its  velocity, 
and  will  vary  it  precisely  as  theory  requires.  This  fact  bears  with  it  im- 
portant consequences. 

To  illustrate  this  interconvertibility  of  work  and  velocity  :  Let  us  assume 
any  body,  as  a  car,  weighing  20,000  pounds  to  have  fallen  freely  (i.e.,  without, 
or  in  excess  of,  the  loss  by  friction)  16.08  feet.  It  would  then  have  20,000  X 
16.08  =  321,600  foot-pounds  of  work  stored  up  in  it,  and  would  be  moving 
through  space  with  the  precise  velocity  of  32.16  feet  per  second  or  about  21 
miles  per  hour. 

If,  instead  of  having  fallen  vertically,  either  gravity,  or  the  tension  on  the 
draw-bar,  or  any  other  force,  had  been  communicating  to  that  same  car  body 
continuously  a  force   of   20   pounds   (or  one   pound  per  ton  in  excess   of  all 

resistance!  the  car  would  have  to  move  through  a  distance  of '- =  16,080 

'  20 

feet  to  store  up  within  itself  321,600  foot  pounds,  and  hence  to  acquire  the  same 
velocity  that  it  acquires  when  falling  freely  through  space,  or,  when  acted  upon 
(in  any  direction)  by  a  force  equal  to  its  weight,  in  16.08  ft. 

390.  This  velocity  once  acquired,  the  corresponding  amount  of  energy  stored 
in  the  car  may  be  expended  in  any  one  of  the  followir:g  ways  : 

First.   It  may  (theoretically)  by  proper  mechanical  appliances  be  made  to  lift 


CHAP.  IX.— RISE  AND  FALL— EFFECT  OF  VELOCITY.     343 

the  body  vertically  through  a  height  of  16.08  feet,  which  it  will  do  in  one  second 
of  time,  and  bring  it  to  a  state  of  rest. 

391.    Secondly.   It  may  be  made  to  lift  the  body  up  an  inclined  plane  A,  A', 
A",  A'",  Fig.  64,  as  on  a  grade  of  any  rate,  against  the  action  of  gravity.     In 


Fig.  64. 

this  case,  if  there  be  no  other  resisting  force  but  gravity,  the  body  will  rise 
through  the  same  vertical  height  in  all  cases  before  coming  to  rest.  The  dis- 
tance run  and  the  time  occupied  in  the  ascent  will  alone  vary.  The  vertical 
elevation  surmounted  will  not  vary.  But  as  there  is  a  resisting  force  (rolling 
friction)  which  is  so  much  per  foot  run,  these  conditions  do  not  precisely  obtain 
in  practice. 

392.  Thh-dly.  It  may  be  made  to  propel  the  body  on  a  level  against  the 
resistance  of  axle  and  rolling  friction.  If  the  natural  resistance  to  motion  be 
7  lbs.  per  ton,  or  70  lbs.  for  the  car,  its  accumulated  energy  of  321,600  foot- 

321.600 
pounds  will  continue  it  in  motion  for  a  distance  of —  =  4594  feet  before  it 

comes  to  a  state  of  rest. 

This  "rolling  friction,"  so  called,  of  7  or  a  pounds  per  ton  of  2000  pounds  is 
precisely  equivalent  in  its  mechanical  effects  to  a  grade  rising  7  or  a  feet  in 
2000,  or  to  the  "  grade  of  repose"  before  explained  (par.  384). 

It  follows,  therefore,  that  any  given  grade  other  than  a  level  is  equivalent  in 
its  mechanical  effect  upon  the  train,  if  it  be  an  ascending  grade,  to  the  actual 
rate  of  grade //z/j-  the  grade  of  repose;  and  if  it  be  a  descending  grade,  to  the 
actual  rate  minus  the  grade  of  repose. 

393.  Foiirthly.  The  accumulated  energy  of  the  car  may  be  sooner  exhausted 

by  calling  in  the  action  of  brakes  in  addition  to  the  resistances  of  gravity  and 

rolling  friction.     If  there  be  brake-blocks  on  half  the  wheels  only  (which  has 

until  recently  been  the  general  custom  for  freight  service),  and  the  pressure  on 

them  be  equal  to  the  load  on  the  wheel,  which  is  somewhat  more  than  that 

which  the  ordinary  brake  leverage  is   intended  to  give  (modern  experiments 

indicate  that  not  more  than  two  thirds  of  the  load   on  the  wheels   is  a  safe 

pressure),  and  if  the  coefficient  of  friction  between  brake  and  wheel  be  \  which 

is  about  an  average  (it  varies  in  reality  from  \  to  -1^)  then  the  retarding  forces 

on  the  car  will  be  — 

20  000 
Brakes,  — ^ X  i  X  i  =  1,667  lbs. 


Normal  rolling  friction  as  above  =       70 
Resistance  of  grade  if  on  a  level  =        o 


Total  resistances  on  a  level  =  1,737  Ihs.  or  173.7  lbs.  per 


344    CHAP.  IX.— RISE  AND  FALL— EFFECT  OF  VELOCITY. 

ton  of  2O0O  lbs.     The  car  will,  consequently,  come  to  a  state  of  rest  on  a  level 

J     •          J.                r  321,600  ft. -lbs.          „      ,  .         ,  , 

grade  m  a  distance  of =  185    feet,  supposing  the  brakes  to  be 

instantly  applied  and  with  their  full  force,  neither  of  which  is  very  likely  to  be 
the  case. 

If  the  car  be  on  an  ascending  or  descending  grade  instead  of  on  a  level  the 
-|-  or  —  resistance  of  the  grade  is  to  be  included  annong  the  resistances.      If  the 

car  stood  on  a  descending  grade  of  — ~-  =  8.6q  per  cent,  or  458  ft.  per  mile,  it 

2000  ^  ^  .        tj  r 

would  continue  in  motion  forever  at  the  same  velocity  even  with  brakes  set. 

This  has  repeatedly  been  proven  practically  on  8  and  10  per  cent  grades. 

If  there  were  10  cars  in  the  train,  moving  at  the  velocity  of  32.16  feet  per 

second,  and  only  one  of  them,  as  above,  had  brakes  set,  then  we  should  have — 

Brake  resistance,  1,667  lbs. 

Rolling  friction  70  X  10,  700     " 


Total  resistances  on  a  level,  2,367  lbs. 

,  3.216,000  ft. -lbs.  .  ^     ^.  

and -z — r- =  1359  feet,  as  the  distance  in  which  the  train  would  come 

2,367  lbs. 

to  a  state  of  rest.* 

394i  Fifthly.  The  accumulated  energy  of  the  car  may  be  made  to  act  con- 
jointly with  the  full  power  of  the  loco- 
^.^-^l  motive  to  carry  it  over  a  particularly 

^*''''       <Q-{  difEcult  gradient.     If  the  full  power 

^^''        ^      J^ of  the  locomotive  is  just  sufficient  to 

-^^ !!L  ^^■^ '  carry  the  car  or  train  over  any  grade 

^^-^^,,,,.,--''''''^  I  of  a  per  cent,  Figs.  65  to  67,  the  en- 

_-i^^^£rrI__ i__  ergy  of  momentum  will  carry  the  car 

Fig.  65.  or  train  up  a  grade  which  rises  in  all 

16.08  feet  higher;  whether  that  rise 
be  by  a  uniform  excess  of  rate,  as  in  Fig.  65,  or  in  a  local  excess  at  certain 
points,  as  in  Figs.  66  and  67. 

In  this  case  the  office  of  the  locomotive  is  simply  to  neutralize  all  grades 
and  rolling  resistances  due  to  the  a  per  cent  grade.  All  extraneous  forces  thus 
neutralizing  and  destroying  each  other,  the  vis  viva  of  the  body  lifts  it  through 
the  additional  rise  of  16.08  feet,  precisely  as,  and  to  the  full  extent  that,  theory 
requires;  but  if  the  power  of  the  locomotive  is  completely  used  up  on  the  a  per 

*  This  calculation  is  not  quite  correct,  because  the  wheels,  in  addition  to  their  linear 
velocity  in  common  with  the  remainder  of  the  car,  have  an  energy  of  rotation  which  adds 
some  6  per  cent  to  the  total  vis  viva  of  the  car,  as  noted  in  par.  374  et  seq.  Nor  should 
computations  of  this  kind  be  ordinarily  made  as  above,  but  by  the  "  velocity-heads" 
given  in  Table  118,  which  include  the  rotative  energy  of  the  wheels. 


CHAP.  IX.— RISE  AND  FALL— EFFECT  OF  VELOCITY.     345 

cent  grade,  the  train  will  come  to  a  state  of  rest  at  the  summit,  which  is  16,08 
feet  higher,  in  spite  of  the  exertion  of  the  full  power  of  the  locomotive  and  the 
aid  of  the  stored  energy  jointly.     Grades   so  operated  are  called  momentum 

GRADES. 


Fig.  66.  Fig.  67. 

395.  Sixthly.  The  accumulated  energy  in  the  car  may,  in  theory,  be  made 
by  proper  mechanical  appliances  to  compress  a  spring,  drive  a  pile,  or  do  any 
other  kind  of  work  whatsoever  capable  of  measurement  in  foot-pounds.  If  a 
spring  required  a  force  of  10,000  pounds  to  compress  it  one  inch  and  its 
resistance  continued  uniform,  then  the  energy  of  the  car  body  would  compress 

321,600 
the  spring =  32.16  inches.     A  perfectly  elastic  body,  to  which  a  spring 

approximates,  would  immediately  give  back  this  energy  to  the  car  and  repel  it 
with  equal  velocity.  A  perfectly  inelastic  body,  such  as  a  bank  of  earth,  which 
required  a  pressure  of  10,000  pounds  to  enable  a  body  of  the  size  of  the  car  to 
penetrate  it  one  inch,  would  (if  the  resistance  continued  uniform)  be  likewise 
penetrated  32.16  inches,  and  would  not  repel  the  body.  The  energy  would  be 
converted  into  heat. 

A  pile  which  opposed  a  static  resistance  to  motion  of  100,000  pounds  would 

in  theory  be  driven  - — '- =  3.21  feet,  or  322  similar  piles  would  be  driven 

100,000 
o.oi  feet,  if  the  resistance  to  motion  were  uniform,  which  it  is  not. 

396.  A  rod  of  iron  of  one  square  inch  section,  which  would  require  a  load 
of  26,000.000  pounds  to  extend  it  to  double  its  length  if  its  resistance  to 
extension  continued  uniform, — i.e.,  whose  modulus  of  elasticity  was  26,000,000, 
— would  sustain  a  force  of  only  some  50,000  pounds  without  rupture,  and  say 
25.000  pounds  without  producing  a  permanent  set.  Therefore,  if  those  effects 
are  to  be  avoided,  the  stress  on  the  rod  must  at  no  time  exceed  that  limit;  and 
since,  if  the  car  is  to  be  stopped  by  the  rod,  321,600  foot-pounds  are  to  be 
absorbed,  by  reaction  against  a  force  beginning  at  zero  (since  the  slightest 
force  will  extend  the  bar  somewhat)  and  gradually  increasing  to  50,000  or  25,000 
pounds  respectively,  we  have 

321,600  n   ^       I       . 

— =  128.64  feet 

50,000  -j-  2 

as  the  length  which  the  rod  would  have  to  stretch  to  avoid  the  rupture,  and 

321.600  „  , 

-~ ■  =  257.28  feet 

25,000  -f-  2 


346     CHAP.  IX.— RISE  AND  FALL— EFFECT  OF  VELOCITY. 

as  the  length  which  the  rod  would  have  to  stretch  to  avoid  exceeding  the  elastic 
limit.     But  (assuming  uniformity  of  elasticity)  the  rod  can  only  stretch  in  any 

case  the  — part  of  its  length  ( 1  without  rupture,  and  only  half  that 

26,000,000  \i,300/ 

without  permanent  set. 

Therefore,  to  avoid  these  effects  and  yet  enable  the  bar  to  do  (or  use  up)  the 
requisite  amount  of  work  in  stopping  the  car,  it  would  have  to  be 

128.64  X  1300  =  167,232  ft.  long  to  avoid  the  rupture,  and 
257.28  X  2600  =  668,928  ft.  long  to  avoid  permanent  set; — 

which  are  rather  long  bars.  The  consequences  to  the  car  body  also  we  will  not 
consider,  but  the  example  will  serve  to  illustrate  the  laws  of  the  mutual  converti- 
bility of  energy  or  work,  and  velocity. 

397.  From  this  ready  interconvertibility  of  velocity  and  work 
results  the  undoubted  fact — too  little  considered  by  engineers — 
that  train  resistance,  in  practical  operation  (i.e.,  as  measured  by 
the  tension  on  the  draw-bar  of  the  locomotive,  or  graphically 
recorded  by  a  dynamometer)  bears  no  very  close  and  apparent 
relationship  to  what  may  be  called  the  dead  resistance,  as  deter- 
mined by  adding  the  nominal  grade  resistance  to  a  certain 
rolling  friction,  without  paying  any  regard  to  the  effect  of 
differences  of  velocity.  This  is  well  understood  by  all  those 
who  have  had  occasion  to  deal  with  dynamometer  experiments, 
and  is  the  greatest  difficulty  in  deducing  valuable  results  from 
such  experiments.  It  is  also  well  understood  in  a  practical  way 
by  locomotive  engineers,  who  appreciate  the  great  advantage  of 
a  "  run  at  a  hill  "  and  the  disadvantage  of  a  stop  on  it. 

398.  Now  the  object  before  the  engineer  in  laying  out  a  rail- 
way is,  obviously,  to  lay  out  his  line  so  that  the  demand  on 
THE  LOCOMOTIVE,  and  not  the  absolute  grade  resistance  (which 
latter  is  in  itself  a  thing  of  no  moment),  shall  be  as  nearly  uni- 
form as  possible,  under  the  conditions  which  actually  exist  in 
the  daily  routine  of  operation.  If,  at  a  certain  point,  the  veloc- 
ity of  the  trains  has  certainly  to  be  increased,  in  addition  to 
overcoming  the  normal  grade  and  rolling  resistances,  the  gradi- 
ent is  in  effect  increased  at  that  point.  If  at  a  certain  other 
point  velocity  can  safely  be  acquired  before  reaching  it  and  then 


CHAP.  IX,— RISE  AND  FALL— EFFECT  OF  VELOCITY.     34/ 

surrendered,  the  grades  are  in  effect  reduced.  The  virtual  or 
equivalent  profile,  including  these  effects  of  velocity,  is  what  the 
engineer  should  study,  and  should  consider  as  the  true  profile 
of  the  line  for  operating  purposes,  as  distinguished  from  the 
nominal  grades  shown  by  the  levels  and  the  plotted  profiles. 

399.  The  two  are  widely  different  even  in  freight  service, 
and  much  more  so  in  passenger  service.  Thus,  when  a  train 
starts  out  from  a  station  it  has  to  acquire  a  certain  velocity  as 
speedily  as  possible — say  15,  20,  or  40  miles  per  hour;  giving 
which  velocity  is  mechanically  equivalent  to  lifting  the  train 
vertically  (see  Table  118)  7.99,  14.20,  or  56.80  feet.  This  rise, 
divided  by  the  distance  in  which  the  velocity  is  or  must  be  at- 
tained, gives  a  grade  which  is  in  effect  an  additionto  the  actual 
grade.  Thus,  if  there  be  a  station  at  A^  Fig.  dZ^  on  a  nominally 
level  grade,  and  it  be  necessary  to  acquire  a  velocity  of  21.3 
miles  per  hour  (corresponding  to  a  "velocity-head,"  as  per 
Table  118,  of  16.08  feet),  and  it  be  necessary  to  acquire  that 
velocity    in    at    most    2000    feet,   the    "virtual"    grade    is    that 

shown  by  the  solid  line  in  Fig.  68,  or  — '- —  =  .804  per  cent. 

20 

If  the   train    then   strikes   a  down   grade,  no  change   in    the 
strain  upon  the  draw-bar  necessarily  takes  place,  nor  probably 
will  take  place,  if  the  grade  be  short 
or  the  speed  high.     More  probably, 
the    same    steam-power   and    ten- 
sion on  the  draw-bar  will  be  contin-  ^ 
uousl}^  exerted,  and   the   excess   of  Fig.  68. 

power  over  that   consumed   by  the 

resistances  will  be  stored  up  in  the  train  as  velocity,  to  be 
surrendered  in  part  on  the  next  up  grade;  and  so  on  indefi- 
nitely. 

In  fast  passenger  service,  with  a  sufficiently  good  track  and 
alignment  to  admit  of  high  speed,  the  amount  of  energy  required 
to  cause  even  slight  modifications  of  speed  between  stations  is 
so  great  that  the  effect  of  undulations  of  gradients,  even  of  con- 
siderable size,  is  almost  wholly  eliminated. 


CHAP.  IX.— RISE  AND  FALL. 

400.  Thus,  Fig.  69  is  an  ex- 
ample from  actual  practice  of  a 
very  bad  undulatory  profile  (for 
freight  service),  which  not  only 
may  be,  but  actually  is,  operated 
by  express  passenger  trains  almost 
as  a  level  grade. 

To  determine  in  practice  how 
velocity  affects  the  operation  of 
this  or  any  other  similar  profile  is 
a  problem  of  the  simplest  possible 
character.  We  require  nothing 
to  aid  us  but  Table  118.  Thus, 
let  us  suppose  that  an  express 
passenger  train  approaches  the 
point  A,  Fig.  69,  as  it  actually 
does,  at  a  velocity  of  about  50 
miles  per  hour,  the  point  being 
situated  at  the  foot  of  a  long  gen- 
tle incline.  This  velocity  being 
given,  in  order  to  run  without  a 
stop  to  the  point  B,  a  distance  of 
about  eleven  miles,  no  further 
burden  is  laid  upon  the  locomo- 
tive than  to  furnish  the  power 
which  is  necessary  to  keep  the 
train  moving  on  the  "  equivalent" 
maximum  grade,  which  in  this 
case  is  a*  dead  level,  despite  the 
fact  that  the  profile  maximum  is 
I  per  cent  or  52.8  ft,  per  mile. 

The  process  of  determming  in 
advance  whether  it  will  be  possi- 
ble to  operate  this  undulating 
grade  as  a  level  gradient  in  this 
manner,  and  what  the  fluctuations 
of  velocity  must  be  to  do  it,  is  as 
follows : 

401.  The  train  at  the  point 
A,  moving  (by  assumption)  at  50 
miles  per  hour,  has  sufficient  vis 


CHAP.  IX.— RISE  AND  FALL— EFFECT  OF  VELOCITY.     349 

viva  or  "velocity-head"  (Table  118)  to  lift  it  through  88.75  feet  verti- 
cally before  coming  to  a  state  of  rest.  In  running  to  b,  it  makes  a 
rise  of  130—80  =  50  feet,  and  if  the  engine  is  to  do  only  the  v^rork  due  to 
a  level  grade  all  the  work  of  lifting  the  train  through  this  50  feet  must 
be  done  from  the  energy  stored  as  velocity,  and  there  will  consequently 
be  left  in  the  train,  on  reaching  b,  only  88.75  —  50  =  38.75  vertical  feet  of 
"  head,"  which  corresponds  (Table  118)  to  33  +  miles  per  hour.  The  par- 
ticular grade,  and  hence  the  horizontal  distance,  between  A  and  b  makes 
no  difference,  because  the  engine,  if  it  is  to  operate  the  grade  as  a  level, 
furnishes  the  power  to  overcome  the  frictional  resistances  on  a  level,  and 
no  more ;  and  these  alone  are  affected  by  the  horizontal  distances. 

From  bx,o  c  the  train  descends  30  feet.  Therefore,  the  engine  being 
supposed  to  continuously  exert  the  same  amount  of  force  to  overcome 
the  frictional  resistances,  ail  the  additional  accelerating  force  due  to  the 
descending  grade  will  be  communicated  to  the  train  in  the  form  of  ve- 
locity, and  at  the  foot  of  the  grade,  at  c,  the  train  will  be  moving  with 
the  velocity  due  to  38.75  +  30=  68.75  vertical  feet,  which  (Table  118)  is 
44  miles  per  hour. 

From  c  to  d  there  is  a  vertical  rise  of  20  feet,  and  consequently  the 
train  will  be  moving  at  d  at  the  speed  due  to  68.75  —  20=  48.75  feet,  or 
(Table  18)  37  +  miles  per  hour. 

402.  So  the  undulations  of  speed  continue,  as  shown  by  figures  and 
the  dotted  diagram,  until  on  reaching  the  points,  which  is  neither  higher 
nor  lower  than  the  initial  point  A,  the  train  is  found  to  be  moving  with 
the  same  velocity  as  at  a,  or  50  miles  per  hour.  Whether  this  will  be  the 
case  at  any  point  we  can  determine  at  once,  without  tracing  up  the  inter- 
mediate velocities,  simply  from  its  relative  level  compared  with  A. 

Thus,  the  highest  point  on  the  stretch  is  at  elevation  140,  or  60  feet 
above  A.  The  train  here,  consequently,  will  have  only  the  velocity  due 
to  88.75  —  60  =  28.75  vertical  feet,  or  nearly  28i  miles  per  hour.  The 
lowest  point  is  the  point  n,  which  is  70  feet  below  A,  and  the  velocity 
at  that  point  will  consequently  be  that  due  to  88.75  +70=  158.75  vertical 
feet,  or  66.9  miles  per  hour. 

403.  Now  if  we  had  a  dynamometer  record  of  the  tension  on  the 
draw-bar  during  such  a  run  as  this  (which  the  writer  has  made  many 
times  over  that  identical  piece  of  track  at  approximately  the  assumed  ve- 
locities) we  should  find  it  absolutely  uniform  and  unvarying,  without  any 
appreciable  trace  or  evidence  in  the  recorded  strains  that  there  were  any 
undulations  in  grade  or  deviations  from  a  perfecTt  level  on  the  stretch 
passed  over.     If  we  were  to  stand  and  watch  any  coupling  of  the  train 


350     CHAP.  IX.— RISE  AND  FALL— EFFECT  OF  VELOCITY. 


we  should  be  led  to  the  same  conclusion.  Assuming  the  vertical  curves 
connecting  the  grades  to  have  been  properly  put  in,  there  would  be  no 
*' slack"  at  any  time,  nor  crowding  of  one  car  upon  another;  but,  on  the 
contrar}^  there  would  be  a  continuous  and  substantially  uniform  tension 
on  every  draw-bar,  whether  going  up  hill  or  down,  and  the  motion  of  the 
train  would  be  as  steady  as  if  the  grade  were  in  fact  level,  as  to  all  intents 
and  purposes  it  is — at  that  velocity.  At  slower  velocities,  or  with 
intervening  stops,  or  with  very  high  summits,  the  conditions  are  widely 
different. 

404.  To  determine  the  effect  of  all  these  and  similar  facts  in  advance 
for  any  piece  of  track  and  any  assumed  speeds,  we  have  only  to  construct, 
with  the  assistance  of  Table  ii8,  what  may  be  termed  the  equivalent  or 
VIRTUAL  PROFILE,  whicli  is  the  actual  profile  so  modified  as  to  include 
these  effects  of  probable  or  admissible  variations  of  velocity.  Thus  at.^. 
Fig.  69  or  70,  moving  at  50  miles  per  hour,  the  train  is  in  the  same  con- 


A'(Oi-MilesperH.)Jb' 


Fig.  70. 

dition  mechanically,  as  respects  demands  upon  the  motive-power,  as  if  it 
were  at  A',  Fig.  70,  88.75  ^^^^  higher,  moving  at  0+  miles  per  hour.  In 
either  case  it  would  arrive  at  the  point  b',  on  a  level  with  A'y  at  a  velocity 
of  0+  miles  per  hour.  As,  however,  it  has  only  to  rise  50  feet  to  b,  it 
will,  on  arriving  at  b,  still  retain  a  velocity  which  will  lift  it  through 
38.75  vertical  feet,  and  consequently  the  point  for  the  equivalent  profile 
is  at  b'  38.75  feet  above  b.  To  have  the  equivalent  pr^'^le  continue  a  level 
line,  its  altitude  above  ^  at  c'  must  be  68.75,  and  the  train,  consequently, 
must  be  moving  at  c  at  44  miles  per  hour.  As  this  is  an  admissible  pas- 
senger velocity,  to  operate  the  line  ac  as  a  virtual  level  at  passenger 
speed  is  not  impossible. 

405.  If,  at  the  point  c,  it  were  necessary  to  slow  up  to  a  velocity,  say, 
of  20  miles  per  hour,  to  pass  through  a  town  or  for  sharp  curvature,  or 
any  other  reason,  this  level  virtual  profile  could  not  be  maintained. 
What  the  equivalent  profile  would  actually  be  equivalent  to,  must  be 
determined  by  laying  off  above  c  the  vertical  altitude  due  to  a  velocity 


CHAP.  IX.— RISE  AND  FALL— EFFECT  OF  VELOCITY.     35 1 

of  20  miles  per  hour,  or  14.20  feet.  We  then  find  that  the  equivalent 
profile  becomes  a  sharp  descent  to  c, — requiring  the  excessive  use  of 
brakes,— and  an  equally  sharp  ascent  to  d' :  thus  showing  that  it  is 
practically  impossible  to  resume  the  original  velocity  at  d. 

406.  To  determine  what  velocity  we  might  obtain  at  d :  Determine 
by  computation,  or  from  experience  elsewhere,  what  is  the  maximum 

grade,   /,    Fig,    71,   up    which    the ^- -Jfn?p 

full  power  of  the  engine  could  keep  |  y^{ 

the   train    moving  at   20  miles  per  J^        ^  ^'''     { 

hour,   which   will   be   a   pretty  stiff  ^"•'"^^  ^'^  .5L,-^<^ 

grade.     The  difference,  dd",  Fig.  71,  1  <i<J^-— "^  ^ 

between   the    elevation    which    the  '^     I      1     "^     1      1      !     f     1 

train   might  attain    on   such  grade  ^^^-  7i- 

and  that  which  it  actually  has  to  attain  at  d  will,  if  the  engine  does  so 
exert  its  full  power  between  c  and  d,  be  communicated  to  the  train  in 
the  form  of  velocity,  and  it  will  be  moving  at  ^  with  the  velocity  due  to 
14.20  +  dd"  feet.  If  the  equivalent  grade  were  2  per  cent,  or  105.6  feet 
per  mile,  instead  of  the  actual  grade  of  0.5  per  cent  mile,  the  value  of  dd" 
would  be  30  feet,  and  the  train  would  be  moving  at  d  with  the  velocity 
due  to  14.20  +  30  =  44.20  feet  =  35.3  miles  per  hour.  The  point  at  which 
it  will  be  mechanically  possible  for  the  train  to  entirely  recover  from  the 
effect  of  a  check  or  stop  at  c  may  be  determined  with  equal  simplicity 
(assuming  that  the  train  resistance  did  not,  as  it  would,  increase  with 
speed)  by  prolonging  the  2  per  cent  equivalent  grade  cd"  until  it  inter- 
sects at/  the  level  equivalent  grade  for  the  run  without  a  stop.  At  that 
point  the  traction  of  the  engine  may  be  reduced  to  that  due  to  a  level 
grade  and  the  run  continued  as  before,  as  shown  in  Fig.  69. 

407.  In  this  simple  manner,  it  will  be  evident,  an  equivalent 
profile — which  for  all  operating  purposes  is  the  profile,  and 
which  is  consequently  the  only  one  which  the  engineer  should 
consider  in  laying  out  the  line — may  be  constructed  almost  by 
inspection,  assisted  by  Table  n8,  for  any  grade  or  section  of  line 
whatever,  and  for  any  speed  or  variations  of  speed  whatever. 
Such  an  equivalent  profile,  if  constructed  for  high-speed  trains, 
will  bear  little  or  no  resemblance  to  the  actual  profile;  and  even 
at  low  freight  speeds  it  will  be  very  seriously  modified,  and  widely 
different  in  appearance  from  the  actual  profile.  At  points  where 
a  stop  or  a  slackening  of  speed  occurs  the  equivalent  grade  may 
be  very  much  higher  than  the  actual.     At  other  points  where 


352     CHAP.  IX.— RISE  AND  FALL— EFFECT  OF  VELOCITY. 


I  oy 


considerable  velocity  at  the  foot  of  grades  is  probable  and  ad- 
missible it  will  be  very  much  lower. 

In  only  one  respect  is  such  a  profile 
liable  to  be  deceptive.  The  profile  it- 
self demands  no  allowances,  but  the 
hauling  power  of  an  engine  is  materially 
greater  in  making  a  start  from  what  it 
is  at  speeds  above  lo  or  15  miles  per 
hour,  at  which  latter  speeds  or  higher 
it  is  not  possible  ordinarily  to  utilize 
the  full  adhesion  of  the  locomotive,  for 
reasons  given  in  Chapter  XI.  and  XIII. 
Therefore  a  higher  virtual  grade  at 
o/  /  -I     J    stopping  points  only  is  not  necessarily 

a  limiting  gradient. 

408.  Fig.  72  is  a  representation  of  a  vir- 
tual and  actual  profile,  constructed  in  the 
above  manner,  for  an  assumed  maximum 
freight  speed  of  25  miles  per  hour.  We 
have  only  to  take  each  governing  point  in 
succession  ;  determine  for  each  what  is  the 
actual,  probable,  necessary,  or  safe  velocity 
at  that  point ;  lay  off  vertically  above  it  the 

■^  f^  vertical  feet  to  which  this  velocity  is  equiva- 
lent, as  given  in  Table  118 ;  and  connect  the 
points  thus  fixed  by  right  lines.  This  gives 
the  equivalent  and  for  all  operating  purposes 
the  actual  profile,  except  that  the  varying 
train  resistance  at  various  speeds  must  be 
remembered,  and  likewise  the  greater  adhe- 
sive power  of  the  locomotive  when  starting 
and  using  sand. 

409.  Thus  at  c,  where  a  stop  is  neces- 
sary, the  velocity  will  be  zero,  and  the  virtual 
and  actual  profiles  will  coincide.    The  grades 

—0*'-*  approaching  this  position  on  each  side  are 

necessarily  much  heavier  in  the  virtual  than 
in  the  actual  profile.  At  other  points,  as  at  the  depression  d,  the  veloc- 
ity will  be  considerable,  and  the  approaching  grades  on  each  side  are 


'OZh 


'OZ1- 


"^  \oo\ 


\ 


a 


CHAP.  IX.— RISE  AND  FALL— EFFECT  OF  VELOCITY.     353 

on  the  virtual  profile  very  much  reduced  by  that  fact.  At  still  other 
points,  as  at  the  foot  of  the  long  grade  e,  the  velocity  of  approach  may  be 
considerable,  and  yet  the  grade  so  long  that  this  velocity  has  but  a  slight 
effect  in  reducing  the  virtual  grade.  If  there  were  a  station  or  a  pretty 
heavy  minor  grade  near  the  foot  of  the  long  grade,  as  is  apt  to  be  the 
case,  no  surplus  velocity  at  all  could  be  assumed,  and  the  virtual  and 
actual  profile  would  again  coincide. 

For  a  further  example  from  practice  of  the  effect  of  varying  velocity  to  mod- 
ify gradients,  and  of  the  deceptive  indications  of  the  power  of  engines  obtained 
by  neglecting  it,  see  the  close  of  Chapter  XX. 

410.  It  will  be  evident  that,  in  practical  work,  a  virtual  profile  need 
not  be  constructed  for  the  entire  length  of  the  line,  but  only  at  points 
where  it  is  likely  to  make  an  important  difference.  On  long  stretches 
of  level  or  minor  gradients  we  need  feel  no  anxiety,  unless  at  stopping 
points.  On  long  stretches  of  maximum  grade  we  know  that  we  must 
:iccept  the  actual  as  the  virtual  grade.  In  such  a  sag  as  that  at  d,  Fig. 
72,  it  is  plain  that  virtual  profile  will  differ  importantly,  but  it  is  unneces- 
sary to  draw  it  as  in  the  cut.  Granting  our  assumed  safe  velocity  in  the 
hollow  ^,  of  25  miles  per  hour  (vel.-head,  by  Table  118,  22.2  ft.),  and  the 
assumed  velocity  of  10  miles  per  hour  (vel.-head,  3.55  ft.)  on  the  summits- 
on  each  side,  the  assumed  difference  of  velocity  in  effect  ?nakes  a  Jill  at 
^of  22.2  —  3.5  =  16,7  feet.  We  have  therefore  merely  to  lay  off  vertically 
16.7  feet  above  d  and  connect  the  point  thus  fixed  and  the  actual  sum- 
mits by  a  dotted  grade  line,  and  we  obtain  the  same  virtual  profile  as 
that  shown  in  Fig.  72,  but  3.55  feet  lower,  so  as  to  touch  the  actual 
grade  line  at  the  summit ;  and  so  at  any  other  point. 

411.  The  danger  in  using  such  a  process  as  this  as  a  basis  for 
laying  out  grades  is  solely  one  common  to  most  engineering 
and  other. work — bad  judgment  as  to  the  practical  possibilities 
and  necessities.  Thus,  a  stop  may  be  required  where  one  is  not 
anticipated,  or  a  velocity  may  be  assumed  which,  owing  to  cur- 
vature or  other  cause,  may  not  be  practicable  or  expedient.  The 
possible  use  of  sand  in  starting  or  at  particular  points,  or  the 
varying  power  of  the  locomotive,  may  be  forgotten,  or  a  speed 
may  be  assumed  at  summits  so  low  as  to  leave  an  insufficient 
margin  for  head  winds  and  similar  contingencies.  The  lowest 
speed  that  can  properly  be  assumed  at  a  summit,  as  a  general 
rule,  in  view  of  these  contingencies,  is  about  10  miles   per  hour 


354    CHAP.  IX.— RISE  AND  FALL— EFFECT  OF  VELOCITY. 

for  freight  trains  and  20  miles  per  hour  for  passenger  trains. 
Even  that  is  leaving  very  little  margin,  for  when  a  train  has 
fallen  below  a  speed  of  10  miles  per  hour  it  requires  very  little 
to  stall  it. 

Nevertheless  with  reasonable  care  and  skill  it  is  a  simple  mat- 
ter to  construct  such  a  profile  and  save  the  consequences  of  the 
vague  and  rash  guesses  as  to  the  effect  of  '*  taking  a  run"  at 
grades,  which  are  sometimes  made,  when  the  effect  of  momentum 
is  considered  at  all. 

This  most  important  caution  should  be  remembered,  however: 
With  the  virtual  profile  once  properly  constructed,  no 
FURTHER  LIBERTIES  CAN  BE  TAKEN  WITH  IT.  The  maximum  vir- 
tual grade  represents  precisely  the  power  of  th-e  engine;  and 
whether  the  virtual  gradient  be  100  feet  or  100  miles  long,  it  is 
equally  decisive  of  the  power  of  the  engine,  except  as  the  latter 
may  itself  vary. 

412.  It  will  be  evident  from  the  preceding  discussion  that 
rise  and  fall  has  the  most  serious  effect  on  slow  freight  service, 
and  will  in  all  cases  become  inadmissible  for  such  service  con- 
siderably before  it  becomes  of  serious  moment  for  passenger 
trains.  Such  an  undulation  of  profile  as  is  shown  at  d,  Fig. 
72,  for  example,  produces  hardly  any  measurable  effect  upon 
the  speed  of  a  fast  passenger  train,  simply  causing  an  undula- 
tion of  a  few  miles  per  hour  in  ordinary  passenger  speed  (say 
from  50  to  55  miles  per  hour),  which  is  hardly  perceptible  to  the 
senses.  In  this  rise  and  fall  is  unlike  curvature,  for  the  latter  (if 
the  grades  have  been  properly  compensated)  is  most  objection- 
able for  high-speed  service. 

413.  The  extremely  important  effect  which  even  very  mod- 
erate fluctuations  of  velocity  may  have  to  modify  nominal 
grades,  even  for  slow  freight  trains,  is  illustrated  in  Fig.  73. 
According  to  the  profile  this  is  a  0.8  per  cent  (42  feet  per  mile) 
maximum  grade,  and  even  allowing  somewhat  for  the  effect  of 
**  momentum"  it  would  be  very  apt  to  be  classed  as  a  0.6  grade. 
In  reality,  the  0.8  grade  at  the  top  of  the  hill  may  be  one  mile 
long,  and  it  can  still  be  operated  as  a  virtual  0.4  grade  (21  feet 


CHAP.  IX.— RISE  AND  FALL— EFFECT  OF  VELOCITY.     355 


per  mile)  if  we  may  count  with  certainty  on  approaching  the  foot 
of  the  hill  at  a  speed  of  23I ,  ^  miles   per   hour.     We   shall    still 
be  able  to  turn  the  hill  with 
a  velocity  of  nearly  10  miles 
per  hour,  our  highest  inter- 
mediate  velocity    being    2 
miles  per  hour. 

If  we  cannot  count  on  a 
higher  velocity  than  15  miles 
per  hour  at  the  foot  of  the 
hill,  whether   because   curva- 
ture, a  station,  or  bad  grades, 
we  cannot  quite  do  this.     We 
shall  have   only  18   instead  of 
24  vertical  feet   of   "  head  "  in 
the  train  at  elevation  120,  3  of 
which    we    must    have    at    the 
summit  to  avoid  danger  of  stall- 
ing.     As   we   use  up  0,4  feet  of 
head  for  each  station  of  0.8  grade 
the    0.8    grade,    at     the     top     of 
the    hill    cannot    be    longer    than 

■-  =  —  =  37.5   stations,   if  the 

0.4         0.4 


entire  grade  is  to  be  operated  as  a 
virtual  0.4. 

Such  undulations  are  often  ex- 
tremely desirable  for  economy's  sake, 
or  to  make  an  otherwise  impossible  lo- 
cation feasible.  Let  us  therefore  deter- 
mine their  exact  effect  on  slow  train 
service  and  the  consequent  limits  of  safe 
practice  ;  since  if  these  limits  are  passed 
unnecessary  injury  may  be  done  to  the 
line.  In  Fig.  73,  for  example,  the  virtual  gradient  shown  is  a 
reasonable  one  because  at  no  point  does  it  reduce  the  speed  very 
low,  but  if  the  points  at  elevations  60  and  no  were  ten  or  fifteen 
feet  higher  it  would  no  longer  be  so. 


356 


CHAP.  IX.— RISE  AND  FALL—SAFE  LIMITS  OF. 


SAFE    LIMITS    OF    UNDULATIONS    OF    GRADE. 

414.  We  will  suppose  a  train  of  40  cars,  say  1300  feet  long  and  weigh- 
ing 1600  tons,  to  be  moving  with  a  uniform  velocity  of  15  miles  per  hour 
(22  feet  per  second)  toward  station  100,  Fig.  74.  The  pull  of  the  loco- 
motive is  perhaps  16,000  lbs.,  being  in  any  case  precisely  that  required 
to  move  the  train  at  15  miles  per  hour  on  a  long  0.2  grade. 

It  has  been  already  stated  (pars.  399,  403)  that  so  long  as  the  steam- 
power  of  the  locomotive  is  unvaried  the  relative  motion  of  the  train  and 


"is. 


Cr.55; 


I 

100  125  t^O 

W/es  per  Hour. 

/S.  Z2.S  ^e.ty 

Ve/,  Heads, 


(7.^9) 


Or.99) 

Fig.  74. 


(iZ3.9S) 


the  tension  on  each  draw-bar  will  be  practically  uniform  and  unvarying, 
whatever  the  variation  of  grade,  the  change  in  resistance  taking  the  form 
of  increased  or  decreased  velocity.  The  only  time  when  the  tension  on 
the  draw-bar  is  not  absolutely  fixed  and  unvarying  is  in  passing  from 
one  grade  to  another,  and  this  occurs  as  follows  : 

415.  As  the  engine  passes  over  station  100,  Fig.  74,  continuously 
exerting  the  same  steam-power,  the  change  in  the  rate  of  grade  (from 
+  0.2  to  —  0.2)  makes  a  difference  of  8  lbs.  per  net  ton  of  its  weight,  or, 
say,  8x62.5  =  500  lbs.  in  all,  in  its  pull  on  the  draw-bar,  thus  increasing 
its  pull  on  the  train  for  the  moment  from  16,000  to  16,500  lbs.,  or  about 
3  per  cent.  This  increased  traction  will  immediately  begin  to  make  the 
train  move  faster,  and  as  some  of  it  must  be  absorbed  in  making  the 
engine  itself  move  faster,  not  all  of  it  will  be  transmitted  backward  to 
the  train. 

Three  seconds  afterwards,  two  other  cars  will  have  passed  over  sta- 
tion 100,  and  will  increase  the  traction  on  the  draw-bars  behind  them  by 
some  320  lbs.  more.  This  increase  of  tractive  force,  likewise,  having  no 
extra  resistance  to  use  it  up,  will  take  the  form  of  an  increase  in  velocity. 

So  as  each  car  in  succession  passes  over  the  break  of  grade  the  accel- 


CHAP.  IX.— RISE  AND  FALL— SAFE  LIMITS  OF.  357 

crating  force  gradually  increases  from  zero  (as  the  engine  approaches 
station  100)  to  8  lbs.  per  ton  of  weight  of  the  whole  train,  when  the 
entire  train  has  finally  passed  over  the  apex. 

416.  The  instant  that  this  occurs  the  tension  on  the  draw-bars  will  be 
precisely  the  same  as  before  throughout,  viz.,  that  due  to  the  work  of  the 
engine  only,  and  will  be  employed  in  the  same  manner — in  overcoming 
the  normal  train  resistance  on  a  grade  of  +  0.2  at  the  original  velocity; 
while  the  extra  accelerating  force  from  the  change  of  grade  will  be  act- 
ing upon  the  train  independently  to  communicate  velocity,  precisely  as 
if  it  were  descending  the  same  plane  without  resistance  and  with  no 
other  force  acting. 

The  final  velocity  at  stations  125  and  140  will  be  precisely  the  same  as 
if  it  had  fallen  freely  through  a  height  equal  to — not  the  actual  differ- 
ence of  level  between  100  and  140 — but  through  a  vertical  height  equal 
to  the  drop  in  the  actual — 0.2  grade  from  the  dotted  +  0.2  grade,  on 
which,  by  assumption,  the  locomotive  was  exerting  just  enough  power  to 
keep  the  train  moving  at  15  miles  per  hour. 

What  will  be  the  velocity  of  motion,  then,  at  125  }  Computing  it  as 
before,  we  have — 

The  original  velocity  of  15  miles  per  hour  is  equivalent  to  a 

fall  through  space  of  (see  Table  118) 7.99  feet. 

The  dip  in  the  grade  is 10.00    " 

Hence  the  train  at  125  will  have  the  velocity  "  due"  to  a  free 

fall  of 17.99    " 

whieh  by  Table  118  will  be  22.5  miles  per  hour. 

This  is  an  entirely  safe  and  unobjectionable  velocity.  At  station  140 
the  "dip"'  is  16  feet  instead  of  100  feet,  and  the  velocity  acquired  is 
16.0  -f  7.99  =  23.99  vert,  feet  =  a  velocity  of  26.0  miles  per  hour,  which 
may  be  claimed  to  approach  the  utmost  limit  of  expediency  for  freight 
service. 

Had  the  dip  been  20  feet,  the  velocity  acquired  would  have  been 
about  28.1  miles  per  hour.  A  dip  of  20  feet  may  therefore  be  considered 
about  the  maximum  which  it  is  permissible  to  ride  over  in  freight  ser- 
vice without  shutting  off  steam,  on  good  track  and  with  favorable 
alignment. 

417.  These  velocities  would  actually  be  somewhat  less  than  the  fig- 
ures given,  owing  to  the  fact  (i)  that  the  centre  of  gravity  of  the 
train  does  not  rise  quite  as  high  or  fall  quite  as  lev/  as  the  highest  or 
lowest  point  of  the  track,  and  (2)  that  the  resistance   of  the  train   in- 


358 


CHAP.  IX.— RISE  AND  FALL— SAFE  LIMITS  OF. 


creases  with  the  velocity  (see  Table  120  and  Chap.  XIII.),  whereas  we 
have  assumed  it  to  be  constant;  but  as  the  difference  is  of  no  great 
moment  in  the  details  we  are  now  considering,  and  as  the  neglect  of  it 
tends  to  safety,  it  is  not  here  considered. 


Table  120. 

Approximate  Grades  of  Repose  for  Various  Trains  (as  Determined  in 
Table  166).     See  also  Table  180. 


Velocity. 

Miles 

Per. 

Hour. 

Freight 
of 

Trains 

Passenger  Trains 
of — 

Approximate  General 
Average. 

Twenty- 
Cars. 

Fifty 
Cars. 

Four 
Cars. 

Twelve 
Cars. 

Grade 
Per  Cent. 

Feet 
Per  Mile. 

10 

15 

20 

25 

30 

40 

50 

60 

70 

0.30 
0.36 
0.46 
0.58 
0.73 
1. 10 

0.28 

0.33 
0.40 
0.48 

0.59 
0.90 

0.34 
0.40 
0.52 
0.69 
0.88 
1.38 
2.02 
2.81 
3-74 

0.27 

0.34 
0.42 

0.53 
0.65 
0.98 

1-39 
1.89 

2.49 

0.30 
0.35 
0.40 
0.50 
0.65 
1. 00 
1.50 
2.25 
3.00 

16.84 
19.48 
21.12 
26.40 
36.32 
52.80 
79.20 
118.80 
168.40 

The  resistance  in  pounds  per  ton  is  given  by  multiplying  the  above  by  20. 

418.  Now,  what  takes  place  in  the  hollow  at  140,  when  the  engine  be- 
gins to  ascend  }  Here,  if  anywhere,  is  the  point  of  danger,  and  here  is  in 
fact  a  very  great  danger,  the  precise  nature  and  limits  of  which  should  be 
determined.  The  danger  arises  from  the  fact  that  in  the  hollow  of  a 
grade,  where  the  head  of  the  train  is  on  an  up  grade  and  the  rear  of  the 
train  on  a  down  grade,  there  is  liable  to  be  a  momentary  crowding  to- 
gether of  the  train. 

This  liability  occurs  only  when  the  head  and  rear  of  the  train  are  on 
different  grades.  We  have  just  seen  (pars.  415,  416)  that  when  the  whole 
train  is  on  the  same  grade,  however  great  its  rate  of  ascent  or  descent,  the 
tension  on  the  draw-bars  will  remain  the  same,  being  that  arising  from  the 
traction  of  the  locomotive,  and  the  additional  energy  communicated  to  or 
taken  from  the  train  by  the  grade  will  take  the  form  of  an  increase  or 
decrease  of  velocity,  which  is  uniform  throughout  the  train  because  the 
grade  is  uniform. 

419.  In  the  hollow  of  a  grade  this  is  not  so,  and  hence  arises  the 
tendency  for  the  rear  of  the  train  to  run  up  against  the  front  when  pass- 
ing such  points  under  certain  conditions,  taking  all  the  "  slack"  out  of 


CHAP.  IX.— RISE  AND  FALL— SAFE   LIMITS  OF.  359 

the  train  and  bringing  the  draw-bars  into  more  or  less  compression.  The 
next  instant,  when  the  hollow  is  passed  and  the  uniform  grade  (whatever 
it  may  be)  is  struck,  the  normal  condition  of  tension  throughout  the  train 
returns,  but  returns  with  a  jerk;  for  with  the  present  awkward  style  of 
couplings  the  difference  in  length  of  a  train  in  tension  or  compression  is 
very  considerable.  The  "  slack"  varies  from  4  to  6  inches  or  more  per  car, 
according  to  the  degree  of  force  with  which  the  springs  are  compressed 
and  extended,  so  that  a  train  of  60  or  80  empty  cars  may  shorten  as  much 
as  30  to  40  ft.  The  jerk,  when  this  slack  is  "taken  out,"  is  exceedingly 
apt  to  break  the  train  in  two,  and  it  is  at  such  hollows  in  grades  that  most 
of  such  breakages  occur. 

420.  The  reality  of  the  danger  may  be  illustrated  by  a  literally  truthful 
anecdote :  In  the  old  days  of  iron  rails,  some  thirty-five  years  ago,  when 
derailments  were  much  more  frequent  and  more  easily  caused  than  now,  a 
certain  especially  poor  road  was  having  very  frequent  derailments,  so  that 
each  conductor  was  having  derailments  every  few  days.  One  of  the  older 
conductors  was  singularly  exempt  from  such  accidents,  for  which  no 
reason  appeared.  In  answer  to  repeated  questions,  he  at  last  confessed 
that  he  "always  kept  his  caboose  brake  set  up  a  little."  This  was  con- 
trary to  orders,  but  it  had  the  practical  effect  of  keeping  the  draw-bars 
always  in  tension,  and  at  the  cost  of  a  slight  waste  of  power  prevented 
the  more  serious  danger. 

Such  crowding  together  is  dangerous,  not  only  for  the  quick  jerk 
which  must  almost  inevitably  follow  it,  but  because  it  tends  to  crowd  the 
cars  out  sidewise  against  one  or  the  other  rail,  and  so  produce  irregularity 
of  motion,  causing  the  wheels  to  hunt,  as  it  were,  even  more  zealously 
than  they  ordinarily  do,  for  the  first  defect  by  which  they  may  escape 
from  the  track.     Especially  on  curves  this  is  very  dangerous. 

421.  The  philosophy  of  trains  breaking  in  two  is  simply  this :  At  the  top  of 
the  grade  the  steam  is  partially  shut  off  and  the  brakes  put  on  shghtly  ;  but 
before  reaching  the  foot  of  the  grade  the  brakes  are  almost  always  let  off,  and 
the  train  strikes  the  foot  of  the  ascent  "full  of  slack."  A  careful  engineman 
will  then  let  on  steam  gently,  and  all  will  be  well.  The  more  careless  will  "  pull 
out"  with  a  jerk,  and,  if  he  be  careless  enough,  he  will  be  almost  certain  to 
break  a  link  or  pull  out  a  draw-head,  for  such  parts  can  hardly  be  made  strong 
enough  (at  least  in  the  present  fashion)  to  resist  a  too  sudden  exertion  of  the 
power  of  the  engine.  To  a  great  extent  the  number  of  such  accidents  is  en- 
tirely in  the  hands  of  the  engineer.  It  has  not  unfrequently  happened  that, 
when  the  employes  were  annoyed  by  an  increase  of  train  or  other  cause,  the 
feeling  of  annoyance  has  taken  the  form  of  a  jerky  fashion  of  pulHng  out  the 
throttle,  which  has  resulted  in  an  alarming  increase  in  such  accidents  and  ter- 


360  CHAP.  IX.— RISE  AND  FALL— SAFE   LIMITS  OF. 

rifled  a  doubting  or  inexperienced  superintendent.  So,  too,  the  introduction  of 
heavier  engines  has  had  and  will  almost  certainly  have  dangerous  consequences, 
— for  a  time, — partly  because  the  enginemen  are  really  inexperienced  in  hand- 
ling such  powerful  machines  and  partly  from  a  secret  willingness  to  throw  dis- 
credit upon  them. 

422.  We  will  consider  the  mechanical  reasons  why  a  very  slight  set- 
ting up  of  brakes  on  a  rear  car  should  reduce  these  dangers,  and  how — 
as  that  remedy  is  objectionable  as  a  regular  reliance — it  also  can  be  safely 
dispensed  with  in  passing  sags. 

A  train  of  cars  coupled  together  may  be  considered  as,  mechanically, 
a  single  solid  body.  All  solid  bodies  have  m  ore  or  less  elasticity,  and 
alter  their  dimensions  under  exterior  force  applied  to  certain  parts  only. 
A  train  has  more  than  usual  longitudinal  elasticity :  that  is  all. 

The  motion  of  such  a  body,  as  respects  the  action  of  gravity,  is  the 
same  as  if  its  mass  were  concentrated  at  its  centre  of  gravity. 

423.  The  centre  of  gravity  of  such  a  train  does  not  descend  into  the 
apex  of  the  hollow  in  Fig.  74  or  75  (assuming  such  sharp  intersections  of 


Levef. 

Fig.  75. 

grade  to  exist  in  practice),  although  each  individual  car  does.  Its  path 
lies — for  simple  geometrical  reasons  which  the  student  may  be  assumed 
either  to  understand  or  to  take  for  granted — at  a  uniform  distance  above 
a  circular  arc  or  parabola  (according  to  the  assumptions  made)  tangent  to 
the  two  grades  at  the  points  e.g.,  one  half  train-length  from  the  apex.  In 
Fig.  75  we  assume,  as  the  simplest  case,  that  a  level  grade  intersects  an 
0.6  per  cent  ascent,  instead  of  a  —  0.2  and  -f  0.4  grade  in  Fig.  74.  The 
results  we  shall  reach  are  not  essentially  varied,  whatever  the  rates  of  the 
separate  grades,  if  their  angle  of  intersection  is  the  same. 

Let  us  assume  for  the  moment  the  train  in  Fig.  75  to  be  exerting 
within  itself  just  energy  enough  to  balance  its  own  resistances,  so  that  it 
is  in  the  theoretical  condition  of  a  body  moving  in  vacuo  without  either 


CHAP.  IX.— RISE  AND  FALL— SAFE  LIMITS  OF. 


361 


gaining  or  losing  velocity,  and  moving  at,  say,  26  miles  per  hour,  equal 
to  a  "velocity-head"  (Table  118)  of  23.99  feet.  For  simplicity  we  will 
assume  the  train  to  be  1200  feet  long  and  to  weigh  uniformly  one  ton 
per  foot,  and  we  will  assume  it  to  consist  of  only  8,  12,  or  more  very  long 
cars  instead  of  some  40,  as  it  probably  would. 

424.  Under  these  conditions,  when  the  train  has  reached  the  position 
mdicated  by  the  black  line  OC  in  Fig.  76,  with  the  rear  car  just  past  the 
apex  6>,  its  centre  of  gravity  B  will  be  precisely  6.00  x  0.6  -  3.6  feet  higher 
than  at  A,  and  the  train  as  a  whole  will  have  surrendered  an  amount  of 
energy  and  of  velocity  corresponding  to  that  height.     The  centre  of 


LA 


Leve/. 


Fig. 


gravity  will  have  moved  in  the  arc  A  OB,  and  the  velocity  with  which 
the  train  as  a  whole  is  moving  at  any  point  Oov  B  is  given  with  absolute 
precision  by  substracting  the  ordinates  to  the  curve  from  the  base-line 
AA'  from  the  initial  "  velocity- head,"  as  is  done  in  Fig.  76.  At  B  the 
velocity  will  be  only  24.0  miles  per  hour. 

With  the  train  in  this  position,  each  car  considered  separately  would 
have  surrendered  the  energy  and  velocity  represented  by  the  successively 
diminishing  ordmates  aa',  and  if  the  train  were,  as  assumed,  a  body 
moving  through  space  from  original  impulse  without  resistance  or  com- 
municated force,  the  inevitable  effect  of  such  conditions  would  be  to  pro- 
duce a  uniform  compression  throughout  the  body  at  all  the  points  aa' 
(each  rear  particle  pressing  against  that  in  front  of  it)  whenever  the  path 
of  the  body  were  deflected  upward,  however  slightly. 

425.  But  the  train,  although  as  a  whole  it  is  in  the  condition  stated, 
yet  mternally  to  itself  is  in  very  different  condition.  A  strong  acceler- 
atmg  force  (the  engine)  is  acting  in  front  at  C;  a  strong  retarding  force 
(say  10  lbs.  per  ton)  throughout  the  rear  of  the  body.  The  two  counter- 
act and  destroy  each  other,  their  net  resultant  being  zero  ;  but  in  so  doing 
they  produce,  or  tend  to  produce,  a  state  ot  tension  throughout  the  train. 


362 


CHAP.  IX.— RISE  AND  FALL—SAFE  LIMITS  OF. 


What  is  required  is,  not  that  this  tension  shall  not  be  reduced  in 
passing  changes  of  grade,  but  that  it  shall  not  be  exchanged  in  any  part 
of  the  train  (or  only  in  a  very  small  part)  for  a  state  of  compression.  A 
train  may  be,  as  respects  its  couplings,  in  three  conditions  : 

1.  In  tension,  its  normal  condition,  which,  whether  greater  or  less,  will 
only  extend  the  springs  a  little  more  or  less,  but  make  no  material  differ- 
ence in  the  whole  length  of  the  train. 

2.  In  neither  te?tszo?t  nor  co7npression,  the  two  adjacent  cars  tending 
for  the  moment  to  move  with  the  same  velocity,  so  that  no  force  of  any 
kind  is  communicated  from  one  to  the  other.  This  condition  can  only 
be  momentary. 

3.  hi  compression,  the  cars  behind  crowding  upon  those  in  front. 

In  the  transition  from  the  first  to  this  last  condition  lies  the  whole 
danger.  So  long  as  we  do  not  pass  the  second  (which  is  more  properly 
merely  a  line  of  demarcation  between  the  first  and  third)  we  are  safe. 

426.  This  we  shall  avoid  if  the  rear  car  (or  cars),  wliere  the  tension  is- 
least,  nowhere  itself  tends  to  move  faster  than  the  train  as  a  whole  is 
moving  at  the  same  moment,  during  the  period  of  transition  from  one 
grade  to  another,  Figs.  75,  76,  or  78. 

The  rear  car,  when  travelling  on  a  grade  of  any  rate,  as  a,  b,  or  c,  Fig. 

jj,  has  a  certain  frictional  resistance 
which  will  make  it  of  itself,  without 
exterior  assistance,  surrender  veloc- 
ity as  if  it  were  moving  on  the  dot- 
ted grade  without  friction,  instead  of 
on  the  actual  grade  with  friction. 
The  difference  between  the  dotted  and  actual  grade  is  the  so-called 
"grade  of  repose,"  marked^  in  Fig.  78.  By  even  a  slight  application  of 
brakes  this  grade  of  repose  may  be  very  greatly  increased. 

Since  the  train  as  a  whole,  then,  is  moving,  mechanically,  without 
friction,  and  surrendering  velocity  at  the  same  rate  as  if  its  mass  were 
concentrated  at  its  centre  of  gravity  and  moving  in  the  path  thereof  {A 

B,    Figs.  j6   and  78),  at 


Fig.  77. 


/<T=  GracfeofR^pose  of/^st  Car. 


Fig.  78. 


each  point  in  the  passage 
from  A  to  B  the  tram 
as  a  whole  is  surrender- 
ing velocity  at  the  rate 
due    to     the    grade     on 


which  the   centre  of  gravity  is  for  the  moment  moving  m  its   path  AB. 
The  steepest  point  on  this  curve  is  at  the  tangent  point  B,  at  which  same 


CHAP.  IX.— RISE  AND  FALI—SAFE  LIMITS  OF.  363 

instant  the  rear  car  of  the  train  itself  strikes  the  up  grade  at  O,  and  en- 
counters the  same  retarding  resistance  as  the  rest  of  the  train,  so  that 
the  danger  of  its  crowding  up  on  it  is  then  past. 

427.  By  comparison  of  the  conditions  just  stated  for  the  last  car  and 
the  whole  train  we  deduce  this  simple  rule : 

To  OBVIATE  ALL  DANGER  OF  THE  REAR  PORTION  OF  THE  TRAIN 
CROWDING  UPON  THE  CARS  IN  FRONT,  WITHOUT  THE  USE  OF  BRAKES, 
AT   ANY   SAG   IN   A    GRADE   LINE: 

The  rate  of  the  grade  on  which  the  head  of  the  train  stands  7nust  in  no 
case  exceed  that  on  which  the  rear  of  the  trai7i  stands  by  7nore  than  the 
"grade  of  repose"  of  the  last  car.  Otherwise  the  latter  will  crowd  tip- 
upon  the  train. 

428.  The  grade  of  repose  may  be  increased  for  the  time  being  above 
the  normal  (i)  by  applying  brakes,  and  (2)  by  the  engineman  "pulling 
out  "or  beginning  to  exert  more  force  upon  the  train  at  or  quite  near  to 
the  apex  O,  In  the  latter  case,  until  the  train  has  acquired  a  velocity 
corresponding  to  the  new  tractive  force,  the  "  grade  of  repose"  of  the  rear 
car,  or  its  resistance  to  moving  with  the  train,  will  be  considerably  greater. 
The  first  of  these  remedies  is  objectionable  as  a  regular  reliance,  and  the 
second  is  too  uncertain.  Therefore  the  rule  above  may  be  considered 
one  which  it  is  desirable  to  adhere  to  strictly  whenever  possible. 

429.  Since  the  conclusions  reached  above  depend  on  the  DIFFER- 
ENCES in  the  rate  of  grade  (see  Figs.  ^,-.^^ 
']']  and  'jZ),  it  is  obvious  that  they  ap- 
ply alike  to  all  hollows  in  grade  lines, 

whether  both  be  ascending,  both  de-  F'g.  79. 

scending,  or  one  descending  and  one 
ascending.     To  see  this  more  clearly 

(which  should  be  almost  self-evident),  S^^'' 

.      ^.         r.  .  .  ,.  .  Fig.  80. 

tip  Fig.  78  m  various  directions  so  as 

to  correspond  to  all  the  conditions  of  practice.     It  will  be  obvious  that 

although  the  changes  in  the  absolute  velocity  of  the  train  and  every  part 

of  it  will  be  greatly  modified,  yet  that  the  relation  of  the  motion  of  the 

rear  car  to  the  whole  train  will  not  be  modified. 

430.  We  see  in  what  has  preceded  the  urgent  reasons  why  the 
use  of  long  and  easy  vertical  curves  in  the  hollows  of  grade  lines 
should  never  be  neglected.  The  conditions  are  entirely  different 
in  a  salient  or  rising  angle  in  a  grade-line  like  Fig.  79  and  in  a 
hollow  like  Fig.  80.     In  passing  over  the  former  there  is  only  a 


364  CHAP.  IX,— RISE  AND  FALL— SAFE  LIMITS  OF. 

momentary  increase  in  the  normal  tension.  If  too  sudden,  this 
is  objectionable,  so  that  vertical  curves  should  be  used  in  all 
cases;  but  it  is  the  reversal  of  strain  in  a  hollow  which  is  par- 
ticularly objectionable,  and  for  them  the  rule — The  cnange  in  ' 
rate  of  grade  in  a  train-length  should  never  exceed  the  grade  of 
repose  of  the  last  car — should  be  strictly  adhered  to  when  the 
cost  of  doing  so  is  not  too  great. 

431.  From  this  it  follows  that  the  longer  the  train  and  the  lower  the 
grade  of  repose  the  easier  should  be  the  vertical  curve,  2S\A  vice  versa. 
As  the  grade  of  repose  increases  with  the  velocity,  it  is  evident  that 
short  trains  at  high  speed,  like  passenger  trains,  are  in  little  danger  of 
any  such  effect,  and  that  to  obviate  it  altogether  the  longest  possible 
train  and  the  lowest  possible  resistance  for  the  last  car  or  cars  should 
be  assumed. 

The  lowest  probable  resistance  for  the  rear  of  the  train  at  any  such 
point  is  about  6  lbs.  per  ton.  Dynamometer  tests  of  freight  trains  show, 
indeed,  average  resistances  of  3^  to  4  lbs.  in  frequent  instances,  but  the 
speed  is  likely  to  be  high  at  the  particular  localities  in  question,  and 
there  is,  moreover,  a  certain  atmospheric  resistance  from  suction  at  the 
rear  of  the  train  (which  may  be  estimated,  by  analogy,  from  experiments 
on  a  small  scale,  at  about  half  as  much  per  square  foot  as  that  at  the 
head  of  the  train)  which  will  increase  the  resistance  of  the  rear  cars 
somewhat  above  the  rest  of  the  train.  Curve  resistance,  if  uncompen- 
sated (and  still  more  when  compensated,  in  descending  a  grade),  may 
affect  the  question  either  way,  according  to  its  location.  Grade  resist- 
ance, as  we  have  seen,  does  not  in  itself  affect  the  question  in  the  slight- 
est. The  difference  between  the  grades  at  the  rear  and  head  of  the  train 
alone  concerns  us. 

432.  The  utmost  length  of  train  will  depend  on  the  ruling  grade 
of  the  road.  An  empty-car  train  will  have  about  twice  the  length  of  a 
loaded  train  ;  but  empty-car  trains  are  unusual,  their  rolling  friction  is 
higher,  and  the  phenomenon  is  not  so  objectionable  that  it  may  not  in 
occasional  instances  be  permitted,  especially  as  it  can  be  avoided  by 
brakes,  or  "  pulling  out,"  if  desired.  A  35-  or  40-car  train  will  be,  say, 
1200  ft.  long,  and  this  may  not  unreasonably  be  taken  as  an  average  maxi- 
mum. On  heavy-grade  lines  a  shorter  assumed  length  of  train  may  suf- 
fice, and  on  low-grade  lines  the  trains  may  be  much  longer. 

433.  Assuming  1200  ft.  (12  stations)  length  of  train,  and  6  lbs.  per 
ton  (0.3  grade)  for  the  resistance  of  the  rear  car  or  cars,  we  have  the  rule — 


CHAP.  IX.— RISE  AND  FALL— SAFE  LIMITS  OF.  365 

Vertical  curves  in  sags  should  be  400  ft,  long,  or  200  ft.  on  each  side  "1 

/l200\ 

of  the  vertex  \  — -^ —  | ,  for  each  tetith  in  change  of  rate  of  grade,  making 

the  change  in  rate  of  grade  per  statio7i  not  over  0.025  P^^  station,  if  ALL 
POSSIBILITY  of  bri7igi7ig  the  draw-bars  of  afiy  part  of  the  train  into  coin-  ■ 
pressio7i  while  passi7ig  over  it  is  to  be  avoided.  With  half  this  length  of  .; 
curve,  which  is  considerably  more  than  is  usual  in  laying  out  vertical  \ 
curves,  all  danger  of  "  taking  out  the  slack  "  in  the  front  half  of  the  train,  J 
^here  there  is  most  danger  of  breaking  in  two,  will  be  avoided. 

434.  A  short  and  simple  method  of  putting  in  vertical  curves  is  given  at 
the  close  of  this  chapter.  The  omission  of  such  curves,  and  the -neglect  to  make 
them  long  enough  when  used  at  all,  is  one  of  the  most  prevalent  and  unfortu- 
nate of  the  minor  errors  of  location,  for  it  often  converts  a  sag  which  would 
otherwise  be  almost  innocuous  into  a  serious  disadvantage.  The  bad  results  in 
such  a  case  will  very  naturally  be  ascribed  to  the  sag  itself  instead  of  to  the 
bad  manner  of  putting  in  the  sag  ;  and  in  this  way  a  prejudice  even  greater 
than  the  facts  justify  exists  against  such  breaks  of  grade.  With  proper  care 
they  may  be  used  harmlessly  with  some  freedom,  especially  as  it  is  nearly 
always  possible  to  take  them  out  in  part  or  whole  at  any  time  when  circumstan- 
ces seem  to  require  and  permit,  by  increasing  the  height  of  the  fills  or  grading 
a  new  line.  In  this  manner,  in  fact,  it  is  often  possible  to  provide  for  eventually 
securing  better  line  and  grades  than  it  would  otherwise  be  possible  to  obtain. 

So  soon  as  an  automatic  close  coupler  shall  be  adopted,  eliminating  all  loose 
slack  from  the  train  (and  it  is  now  clear,  for  reasons  given  in  Chapter  XII., 
that  such  a  coupler  is  the  only  proper  form  to  adopt),  much  of  the  impor- 
tance of  connecting  breaks  of  grade  by  extremely  easy  vertical  curves  will 
disappear.  It  is  hardly  safe,  however,  to  count  upon  any  speedy  and  gen- 
eral action  in  that  direction. 

435.  Let  it  therefore  be  repeated,  that  so  long  as  (i)  it  is  not  neces- 
sary to  alter  in  any  way  the  steam-power  of  the  engine  to  avoid  too  high 
speed,  and  (2)  so  long  as  the  transition  from  one  grade  to  another  is  ex- 
tremely gentle  and  gradual,  such  breaks  are  a  matter  of  the  most  trifling 
moment.  But  to  this  rule  there  are  some  exceptions.  Thus,  a  sag  of  10 
or  15  feet  might  be  entirely  innocuous  on  a  long  tangent  between  sta- 
tions, yet  at  some  other  point  on  the  line,  where  the  profile  is  precisely 
the  same,  it  might  be  a  serious  and  even  dangerous  evil.  A  sharp  curve 
at  the  bottom  of  the  sag  might  necessitate  a  very  low  speed  there,  or  a 
heavy  grade  near  at  hand  make  high  speed  desirable.  A  station,  or  a 
siding,  or  crossing,  or  water-tank  may  in  the  future,  if  not  at  present, 
necessitate  a  stop  there.  In  any  such  case  the  sag  would  at  once  change 
its  character  from  a  harmless  economy  to  a  serious  and  costly  error,  if  it 
be  for  any  reason  a  permanency.     If,  on  the  other  hand,  it  can  be  taken 


366       CHAPriX.—RISE  AND  FALL— LIMITS  OF  CLASSES. 

out  at  any  time  by  simply  filling  up  the  hollow,  of  course  far  greater 
boldness  may  be  used. 

436.  It  will  be  obvious,  furthermore,  that  the  effect  and  disadvan- 
tages of  such  sags  are,  other  things  being  equal,  the  same,  whatever  the 

rate  of  the  grade  on  which  the 
'jS  sag  occurs.  Thus  in  Fig.  8i 
there  is,  literally  speaking,  no  rise 
and  fall  at  all,  because  it  is  a  con- 
tinuous up  grade  ;  yet  if  the  loco- 
motive be  ascending  this  grade, 
and  exerting  just  power  enough 
to  maintain  a  uniform  velocity, 
the  effect  of  the  mere  break  of 
grade  is  precisely  the  same  as  the 
actual  sag  and  rise  and  fall  in  Fig. 
82,  In  each  case,  if  the  train  be 
moving  at  a  uniform  velocity  of  12  or  15  or  20  miles  per  hour  (=  velo- 
city-head, by  Table  118,  of  5. 11,  7.99,  and  14.20  ft.),  the  sag  will  increase 
the  velocity- head  by  4.0  ft.,  to  9. 11,  11.99,  ^^^  18.20  ft.,  and  the  velocity 
in  the  bottom  of  the  hollow  (neglecting  the  fact,  as  heretofore,  that  the 
centre  of  gravity  of  the  train  does  not  rise  quite  so  high  nor  fall  quite  so 
low  as  the  angles  of  the  grade)  will  be  increased  to  16.0,  18.4,  and  22.6 
miles  per  hour.  After  passing  the  bottom  of  the  hollow  the  train  begins 
to  lose  velocity,  and  on  again  reaching  the  main  grade  is  moving  at  the 
same  velocity  as  when  it  left  it. 

437.  The  above  makes  clear  that  it  is  a  fallacy  to  count  up  the  num- 
ber of  feet  of  rise  and  fall  merely  from  the  ups  and  downs  as  shown  by 
the  differences  of  elevation  of  the  profile,  as  one  of  the  criterions  of  the 
excellence  of  a  line.  Ordinarily  this  may  not  prove  very  deceptive  but 
the  true  comparative  importance  to  be  ascribed  to  rise  and  fall,  and 
hence  the  limits  of  the  three  classes  of  rise  and  fall.  A,  B,  and  C,  as  sum- 
marized in  par.  367,  and  again  in  par.  451,  must  be  determined  in  a  dif- 
ferent way. 


LIMITS   OF  THE  CLASSES   OF  RISE  AND   FALL. 

438.  Limits  of  Class  A.  (The  least  objectionable  class.) — The  nor- 
mal freight  speed  may  be  assumed  to  be  15  miles  per  hour,  but  in  certain 
locations  it  is  not  likely  to  be  more  than  10  miles  per  hour,  and  in  other 
locations  it  may  usually  and  naturally  be  as  high  as  20  miles  per  hour. 
Assuming  a  train  to  be  approaching  a  sag  in  any  grade-line  at  these  rates 


CHAP.  IX.— RISE  AND  FALI^LIMITS  OF  CLASSES.       367 


of  speed,  we  have  in  Table  121  the  maximum  velocity  which  sags  of  vari- 
ous depths  will  give  to  the  train. 

Table  121. 

Effect  of  Sags  of  Various  Depths  below  a  Continuous  Grade-Line 
and  having  the  form  of  either  fig.  8 1  or  fig.  82  to  modify  the 
Speed  of  Trains. 

(Computed  by  the  aid  of  Table  ii8,  as  explained  in  par.  400  et  seq,) 


Greatest 

Depth  of 

Sag  in 

Feet. 

Vel.-Head  in  Train  at  Lowest 

Point  of  Sag  for  Speeds  of  Approach 

IN  Miles  Per  Hour  of — 

Maximum  Speed  in  Bottom  of  Sag 

FOR  Speed  of  Approach  in  Miles 

Per  Hour  of— 

10 

15 

20 

10 

15 

20 

None 

5 

10 

15...-.    - 

20 

25 

30 

3 

8 

13 

18 

23 
28 

33 

55 
55 
55 
55 
55 
55 
55 

7-99 
12.99 

17-99 
22.99 

27-99 
32.99 
37-99 

14.20 
19.20 
24.20 
29.20 
34-20 
39 -20 
44.20 

10. 

15-5 

19-5 

22.9 

25.8 

28.3 

30.8 

15- 
19. 1 

22.5 

25.4 
28.1 

30.5 
32.7 

20. 

23.2 

26.1 

28.7 

31-0 

33-2 

35.3 

This  table  assumes  that  the  train  is  approaching  at  a  uniform  speed,  and  that  the 
locomotive  continues  to  exert  the  same  uniform  power  in  passing  the  sag.  The  original 
velocity  will  then  be  resumed  after  passing  it. 

If  there  is  an  excess  of  accelerating  or  retarding  force  in  approaching  the  sag,  both  the 
speed  in  the  bottom  of  the  sag  and  the  speed  after  passing  it  will  be  correspondingly 
higher  or  lower  than  the  speed  of  approach,  but  the  table  will  not  be  essentially  modified. 

The  manner  of  computing  Table  121  should  be  carefully  studied.  It 
will  be  seen  how  little  the  speed  of  approach  affects  the  resulting  speed 
at  the  bottom  of  a  sag  in  grade-line  of  any  considerable  depth.  Twice 
the  speed  of  approach,  20  miles  per  hour  instead  of  10,  increases  the 
speed  in  the  hollow  only  some  15  per  cent,  or  4-I-  miles  per  hour.  It  will 
also  be  seen  how  comparatively  slight  is  the  effect  of  increased  depth  of 
sag.  A  lo-ft.  sag  increases  10  miles  per  hour  to  20,  but  it  takes  20  ft. 
more,  or  a  30-ft.  sag  in  all,  to  increase  the  20  miles  per  hour  to  30.  At  a 
speed  of  approach  of  20  miles  per  hour  a  lo-ft.  sag  increases  the  speed 
6.1  miles  per  hour ;  the  next  10  ft.  (20  ft.  in  all)  only  4.9  miles  per  hour, 
and  the  next  10  ft.  only  4.3  miles  per  hour. 

439.  The  table  likewise  shows  in  part  (for  fuller  explanation  see 
Chap.  XVIII.)  why  a  very  slight  break  upwards  from  a  long  continuous 
grade-line  is  so  very  much  more  injurious  than  even  a  considerable  drop 
below  it.  Sags  even  of  30  ft.  will  not  produce  an  absolutely  dangerous 
speed,  but  a  rise  of  even  3^  ft.  above  a  grade-line  will  bring  a  train  mov- 


368       CHAP.  IX.— RISE  AND  FALL— LIMITS  OF  CLASSES. 

ing  at  10  miles  per  hour  to  a  stop,  or  a  train  moving  at  15  miles  per  hour 
to  a  speed  of  1 1.2  miles  per  hour. 

440.  The  highest  freight-train  speed  which  can  be  regarded  as 
reasonably  safe  and  practical  at  favorable  points  is  about  30  miles  per 
hour.  Such  speeds  are  ordinarily  far  less  objectionable  on  long  straight 
grades  than  on  undulating  grades,  for  the  reason  that  the  true  objection 
to  high  freight  speeds  (within  reason)  is  not  the  speed  itself,  but  abrupt 
alterations  of  speed.  With  long  and  easy  vertical  curves  (usually  want- 
ing), and  with  breaks  of  grade  so  designed  that  their  depth  will  not  give: 
a  dangerous  maximum  speed  if  they  are  operated  as  virtual  continuous 
grades,  by  making  no  change  in  the  work  done  by  the  locomotive  but 
permitting  its  excess  of  work  to  take  the  form  of  velocity,  speeds  of  30 
miles  per  hour  for  the  moment  only  on  good  alignment  cannot  be  con- 
sidered as  in  the  least  objectionable,  and  are  very  common  in  present 
practice,  and  likely  to  become  more  so.     (See  par.  444.) 

If  we  assume  30  miles  per  hour  as  a  maximum  speed  at  certain  favor- 
ably situated  points  where  considerable  speed  is  desirable,  it  results  (see 
Table  121)  that  sags  of  20  or  even  30  ft.  from  a  grade-line,  according  to 
the  speed  of  approach,  may  be  operated  as  a  virtual  continuous  grade. 

441.  We  therefore  conclude  that,  as  a  general  rule,  but 
with  a  number  of  modifying  special  conditions,  a  sag  of  not 
exceeding  20  ft,  in  vertical  depth  from  the  main  grade-line,  if 
eased  off  by  a  long  and  easy  vertical  curve  in  the  hollow,  will 
not  require  any  slacking  up  or  variation  in  steam-power,  and 
that,  if  it  does  not,  it  is  entirely  innocuous,  except  for  the  greater 
wear  and  tear  which  may  result  from  the  higher  speed.  That  ex- 
pense we  will  estimate  in  par.  452  et  seq. 

442.  If  the  sag  be  deeper  than  20  ft.,  and  sometimes  if  it  be  consider- 
ably less  than  20  ft.,  we  have  a  more  objectionable  class  of  rise  and  fall 
(Class  B,  pars.  367  and  451).  It  will  then  be  necessary  either  to  put  on 
brakes  (which  is  really  the  best  practice)  or  to  merely  shut  off  steam  and 
"  pull  out"  again  at  the  foot  of  the  grade,  which  is  the  too  common  prac- 
tice. 

It  is  in  this  latter  kind  of  sags,  especially  if  they  have  no  adequate 
apology  for  a  vertical  curve,  that  most  of  the  draw-heads  are  pulled  out 
and  trains  broken  in  two,  in  the  way  explained  in  par.  418-421.  In  part 
this  is  avoidable  by  care  in  running.  Nevertheless,  with  the  greatest 
practicable  care,  it  is  not  possible  to  prevent  frequent  serious  jerks  to 
trains  in  sags  of  considerable  depth,  which  will  sometimes  break  them 


CHAP.  IX.— RISE  AND  FALI—IIMITS   OF  CLASSES.      369 

in  two.  Such  sags,  therefore,  become  more  and  more  objectionable  as 
the\'  increase  in  depth,  even  when  it  is  not  necessary  to  use  any  brakes. 

443.  The  point  at  which  it  certainly  becomes  7tecessary  to  apply  brakes, 
and  consequently  the  point  at  which  the  cost  of  rise  and  fall  is  materially 
increased  (Class  C,  pars.  367  and  451),  varies  in  part  with  the  rate  of  grade, 
and  may  be  determined  as  follows  : 

The  grades  of  repose  for  various  speeds,  i.e.,  the  grades  on  which  the 
accelerating  force  of  gravity  just  suffices  of  itself  to  keep  the  train  in 
motion  at  the  given  speed  without  resistance  from  the  engine  and  without 
either  gain  or  loss  of  velocity,  are  about  as  given  in  Table  120,  page  358. 

It  follows  from  Table  120,  that  if  the  admissible  limit  of  speed  on  any 
part  of  the  line  be  given,  any  grade,  however  long,  on  a  rate  not  exceed- 
ing the  grade  of  repose  for  that  speed,  may  be  of  indefinite  length  without 
ever  requiring  the  use  of  brakes,  because  all  that  is  necessary  is  to  shut 
off  steam  at  the  top  of  the  grade  A,  Fig.  83  ;  when  the  train,  in  descend- 
ing the  grade,  will  of  itself  either  acquire  or  lose  velocity  until  it  attains 


The  dotted  line  shows 
the  virtual  grade-line  of  a 

train  starting  from  the  top  of  the  hill  with  a  small  ve- 
locity, which  gradually  increases  until  it  becomes  as 
great  as  the  acceleration  of  gravity  is  able  to  maintain. 
On  the  stretch  AB  the  speed  and  resistance  are  small, 
and  the  ordinate  B  represents  the  vertical  energy  stored  in  the  train  as  velocity.  On  the 
next  stretch  the  resistance  is  higher,  because  of  the  higher  speed,  but  there  is  still  an  ex- 
cess of  acceleration.  So  with  the  next  stretch;  but  as  the  resistance  grows  higher  and 
higher  with  each  increase  of  velocity  there  necessarily  comes  a  point  wliere  the  resistance 
and  acceleration  balance  each  other,  as  given  in  Table  120. 


the  velocity  at  which  the  accelerating  force  precisely  balances  the  rolling 
resistance.  This  grade  will  be  seen  to  be  very  high  for  fast  passenger- 
train  speeds,  so  that  there  can  rarely  or  never  be  necessity  for  the  use  of 
brakes  on  descending  grades  of  less  than  i  per  cent  (52.8  ft.  per  mile)  in 
ordinary  passenger  service,  merely  to  avoid  excessive  speed  due  to  the 
gradients  themselves.  Usually,  however,  heavy  gradients  are  accom- 
panied by  heavy  curvature,  which  latter  will  often  necessitate  on  long 
grades  a  rate  of  speed  but  little  higher  than  the  freight  maximum. 

444.  The  customary  speed  in  freight  service  shows  a  steady  tendency 
to   increase  at  points  where  velocity  is  of  assistance  in  hauling   heavy 
trains.  It  is  of  course  greatly  affected  by  the  character  of  the  line  as  to 
24 


370       CHAP.  IX.— RISE  AND  FALL— LIMITS   OF  CLASSES. 

curvature,  but  the  idea  formerly  prevalent  that  the  most  economical 
speed  for  freight  trains  is  a  very  slow  one  has  been  pretty  thoroughly  ex- 
ploded, both  by  theory,  practice,  and  experiment.  Experiments  by  Mr. 
P.  H.  Dudley  on  the  Lake  Shore  &  Michigan  Southern  Railway  have 
shown  directly  that  "  with  long  and  heavy  freight  trains  it  required  less 
fuel  with  the  same  engine  to  run  trains  at  i8  to  20  miles  per  hour  than  at 
10  to  12  miles  per  hour."  *  This  result — as  to  the  substantial  correctness 
of  which  there  is  little  room  for  doubt — is  not  due  to  the  actual  resist- 
ances to  motion  being  any  lower,  or  as  low,  at  the  higher  speed,  but  to 
the  joint  action  of  the  following  causes  : 

1.  To  the  saving  of  power  at  undulations  of  grades,  in  the  manner 
heretofore  discussed  in  this  chapter,  the  extra  velocity  serving  as  a  reser- 
voir of  power  and  so  preventing  waste  thereof. 

2.  To  the  less  time  of  exposure  of  the  locomotive  to  radiation — a  sav- 
ing, in  all  probability,  of  very  great  importance.     (See  pars.  344  et  al.) 

3.  To  the  less  time  for  radiation  from  the  interior  surface  of  a  cylin- 
der into  the  exhaust  steam  ;  also  a  very  important  source  of  loss. 

On  the  other  hand,  evidence  presented  in  Chapter  XIII.  makes  it  at 
least  doubtful  if  the  resistance  is  more  than  a  pound  or  two  per  ton 
greater. 

445.  Whatever  may  be  the  cause,  the  expediency  and  economy  of  in- 
creasing freight-train  speeds,  on  fair  alignment,  up  to  20  and  even  (at 
points)  30  miles  per  hour  is  very  generally  recognized  and  acted  on  by 
the  more  prominent  managing  officers.  This  tendency  will  probably  be 
greatly  strengthened  in  the  near  future  by  (i)  the  general  adoption  of 
some  form  of  freight-train  brake  and  of  a  more  durable  and  stronger 
coupler,  and  by  (2)  the  increase  in  average  car-load  and  consequent  de- 
crease in  number  of  freight  cars  per  train,  with  the  natural  attendant  in- 
crease of  care  in  the  construction  of  freight  cars.  On  lines  using  the 
"speed  gauge"  the  usual  maximum  speed  specified  is  22  miles  per  hour, 
a  rate  in  all  probability  which  at  some  points  on  some  lines  has  been  ex- 
pensively low,  and  would  have  been  still  more  so  except  that  the  grades 
at  stations  are  usually  the  de-facto  limiting  grades,  and  not  those  between 
stations. 

446.  It  will  therefore  be  safe   in  all  cases  to  assume  a  maximum 


*  Trans.  Am.  Soc.  C.  E.,  Oct.  1876.  The  explanation  there  given  by  Mr. 
Dudley,  that  at  the  higher  speeds  "  the  locomotive  seems  to  produce  its  power 
more  economically  by  using  the  steam  expansively  to  a  greater  extent  than  at 
slow  speeds"  would  seem  to  be  certainly  incorrect,  except  as  the  less  time  for 
internal  radiation  may  be  supposed  to  be  referred  to. 


CHAP.  IX,— RISE  AND  FALL— LIMITS  OF  CLASSES.       371 

freight-train  speed  of  about  22  to  25  miles  per  hour  on  long  grades,  cor- 
responding to  a  grade  of  repose  of  something  under  0.5  per  cent,  or  26.4 
feet  per  mile;  and  this,  under  favorable  circumstances,  for  important 
€nds,  may  be  assumed  to  be  increased  to  nearly  30  miles  per  hour,  corre- 
sponding to  a  degree  of  repose  of  something  over  0.6  per  cent,  or  32  feet 
per  mile.  On  grades  not  exceeding  these  limits  rise  and  fall  on  grades 
of  any  length  will  not  be  likely  to  require  the  use  of  brakes,  or  to  en- 
danger objectionable  "  slack"  in  the  train,  with  the  most  moderate  care 
in  running, 

447.  The  point  at  which  a  grade  on  rates  exceeding  these  limits  be- 
comes so  long  that  the  use  of  brakes  will  become  necessary  is  readily 
determined  as  follows  : 

Let  AB,  Fig.  84,  be  such  a  grade  and  AB'  be  the  average  grade  of  repose 
while  attaining  the  assumed  admissible  velocity,  say  0.4  per  cent,  for  a 

D' 


Fig.  84. 

maximum  velocity  of  25  miles  per  hour,  or  0.5  per  cent  for  30  miles  per 
hour.  Let  the  lowest  velocity  at  which  it  is  necessary,  expedient,  or  prob- 
able that  trains  will  approach  A  be  also  determined.  It  will  depend  on  the 
character  of  the  line  back  of  A.  If  A  be  at  the  foot  of  a  long  grade,  no 
lower  velocity  than  the  maximum  admissible  could  safely  be  assumed, 
and  the  application  of  brakes  would  be  immediately  necessary  on  reach- 
ing A.  If  A  were  a  station  the  initial  velocity  would  be  O.  It  is  desira- 
ble that  the  velocity  should  be  as  low  as  possible,  but  as  enginemen  do 
not  always  pay  close  attention  to  little  matters  of  economy  such  as  sav- 
ing the  use  of  brakes — especially  if  behind  time — it  should  not  be  taken 
too  low.     Let  us  suppose  it  to  be  10  or  15  miles  per  hour ;  then  we  have  : 

Initial  velocity  at  A.  10  miles  per  hour.  15  miles  per  hour. 

Corresponding  velocity-head 3-55  ft.  7.99  ft. 

Corresponding  velocity-head  at  maxi- 
mum velocity  of  25  miles  per  hour.  22.20  "  22.20  " 

Difference 18.65"  14.21" 


372       CHAP.  IX.— RISE  AND  FAII— LIMITS  OF  CLASSES. 


which  latter  is  the  vertical  distance  D,  Fig.  84,  which  the  grade  will  have 
to  fall  below  the  grade  of  repose  before  the  train  will  acquire  the  maximum 
admissible  velocity. 

This  being  given,  it  is  a  simple  matter  to  compute  the  horizontal  dis- 
tance AD'  and  the  corresponding  vertical  fall  D  +  D' .  In  the  above 
example,  the  excess  of  the  actual  grade  over  the  assumed  0.4  grade  of 

18.65 


repose  being  0.6  per  cent,  we  find  D  +  D'  to  be — 7-  =31.1  stations  for 

14.21 
an  initial  speed  of  10  miles  per  hour  and  — 7-  =  23.7  stations  for  an  in- 
itial speed  of  15  miles  per  hour.     In  this  manner  we  may  construct  Table 
122. 

44-8.  Any  grade,  at  any  given  rate  whatever,  which  does  not  exceed 
in  length  and  vertical  rise  the  limits  of  Table  122  can  be  operated  in  the 
routine  of  freight  service  without  the  use  of  brakes  (the  cost  of  such  rise 
and  fall  being,  consequently,  very  much  less)  provided  that  there  be  no 
excessive  curvature  or  other  special  cause  near  the  foot  of  the  grade  to 
require  especially  low  speed  at  that  point.     Ordinary  curvature,  with  a 


Table  122. 

Distance  within  which  the  Velocity  of  Trains  descending  Various 
Grades  without  Steam  or  Use  of  Brakes  will  exceed  the  Limits 
OF  25  and  30  Miles  Per  Hour,  starting  with  Various  Initial  Ve- 
locities. 


Rate  of  Grade. 


''er  Cent. 


0.4 
0-5 
0.6 
0.7 
0.8 


1-5 

2.0 

3-0 


Less  Grade 
of  Repose. 


0.0 
0.1 
0.2 
0.3 
0.4 
0.5 
0.6 
I.I 
1.6 
2.6 


Admissible  Maximum  Velocity 
OF  25  Miles  Per  Hour. 


Initial  Velocity  at  Top  of 
Grade,  in  Miles  Per  Hour. 


0  + 

10 

15 

Infinite 

Infinite 

Infinite 

222.0 

166.5 

142. 1 

III.O 

83.2 

71.0 

74.0 

55-5 

47-4 

55-5 

41.6 

35-5 

44-4 

33-3 

28.4 

37-0 

27.7 

23-7 

20.2 

^5-1 

12.9 

13-9 

10.4 

8.9 

8.5 

6.4 

5-5 

20 

Infinite 

80.0 

40.0 

26.7 

20.0 

16.0 

13-3 
7-3 
50 
3-1 


Admissible  Maximum  Velocity 
OF  30  Miles  Per  Hour. 


Initial  Velocity  at  Top  of 
Grade,  in  Miles  Per  Hour. 


04- 

iO 

IS 

Infinite 

Infinite 

Infinite 

319-5 

284.0 

239.6 

159 

7 

142.0 

119 

8 

106 

5 

94-7 

79 

9 

79 

9 

71.0 

59 

9 

63 

9 

56.8 

47 

9 

32 

0 

28.4 

24 

0 

21 

3 

18.9 

16 

0 

12 

8 

II. 4 

9 

6 

20 


Infinite 
(( 

177-5 
88.8 
59-2 
44.4 
35-5 
17.7 
II. 8 
7-1 


CHAP.  IX.— RISE  AND  FALL— LIMITS  OF  CLASSES.       373 

Table  122. — Continued. 

Total  Vertical  Fall  in  Feet  from  Top  of  Grade  to  Point  where  the 
admissible  maximum  velocity  is  attained,  as  above. 


0.4 
0.5 
0.6 
0.7 
0.8 
0.9 
i.o 
1-5 
2.0 
3-0 


Infinite 

Infinite 

Infinite 

Infinite 

Infinite 

Infinite 

Infinite 

III.O 

83.2 

71.0 

40.0 

*' 

" 

e6.& 

49-9 

42.6 

24.0 

191. 7 

170.4 

143-8 

51-8 

38.8 

33-2 

18.7 

III. 8 

99.4 

83-9 

44.4 

33-3 

28.4 

16.0 

85.2 

75.8 

64.0 

40.0 

30.0 

25-5 

14.4     \ 

72.0 

63-9 

54-0 

37-0 

27.7 

23-7 

13-3      i 

63-9 

56.8 

47-9 

30.3 

22.6 

19.4 

10.9 

48.0 

42.6 

36.0 

27.8 

20.8 

17.8 

10. 0 

42.6 

37-8 

32.0 

17.0 

12.8 

II. 0 

6.2 

38.4 

34-2 

28.8 

Infinite 

(4 
106.5 
62.2 

47-4 
40.0 
35-5 
26.6 
23.6 
21.3 


Computed  as  follows ; 


At  speed  of 

Vel.-head 

Do.  at  25  (and  30)  m.  p.h. 

Difference 

Assumed  average  grade 
of  repose 


0 

10 

15 

20 

0.00 

3-55 

7-99 

14.20 

0.00 

3-55 

7-99 

22.20 

22.20 

22.20 

22.20 

31-95 

3^-95 

31-95 

22.20 

16.65 


14.21 

8.00 
.40 

31-95 

28.40 

23.96 

14.20 

31-95 
17-75 

-50 


Then  the  actual  rate  of  grade,  less  the  grade  of  repose,  gives  the  fall  per  station  which 
goes  to  increase  the  velocity,  and  the  "  differences"  above,  divided  by  the  surplus  fall  per 
station,  gives  the  number  of  stations  within  which  the  permitted  maximum  velocity  will 
be  attained,  as  in  the  first  part  of  the  table  above.  The  number  of  stations  X  rate  of 
grade  per  cent  gives  the  second  part  of  the  table. 


road-bed  in  good  condition,  can  be  operated  by  all  trains  with  almost  as 
great  safety  at  25  to  30  miles  per  hour  as  at  any  lower  speed,  if  the  speed 
does  not  require  to  be  suddenly  checked.  In  ascending  such  a  grade 
the  same  conditions  obtain  as  in  descending,  except  (i)  that  the  locomo- 
tive ascends  the  grade  using  steam,  whereas  it  descends  without  steam  ; 
and  (2)  that  it  starts  or  may  start  with  the  high  velocity  ^which  gradually 
decreases  instead  of  with  the  low  velocity  which  gradually  increases. 
We  are  not  now  considering  the  effect  of  limiting  gradients,  which  is  an 
entirely  different  matter,  but  assuming  that  the  locomotive  has  sufficient 
power  to  ascend  all  grades  at  necessary  speeds,  as  of  course  in  all  cases 
it  must.  The  cost  of  decreasing  the  length  and  increasing  the  number 
of  trains  to  effect  this  end,  which  constitutes  the  chief  objection  to  gradi- 
ents, is  not  now  under  consideration  at  all. 


374       CHAP.  IX.— RISE  AND  FA II— LIMITS  OF  CIASSES. 

449.  Summarizing  the  preceding  discussion  of  the  nature 
of  rise  and  fall,  we  have  found  that  it  may  be  divided  into  the 
following  classes,  having  a  very  different  effect  on  operating 
expenses : 

Class  A.  Rise  and  fall  on  minor  gradients  and  for  small  un- 
dulations, not  sufficient  to  make  it  necessary  to  vary  the  power 
of  the  engine,  but  merely  causing  a  momentary,  gradual,  and 
unobjectionable  fluctuation  of  speed. 

Class  B.  Rise  and  fall  similar  to  class  A,  in  its  effect  in  speed, 
provided  steam  be  shut  off  in  descending,  but  not  requiring  the 
use  of  brakes  in  descending,  nor  seriously  taking  the  power  of  the 
engine  on  the  ascent.    Tables  121-2  give  the  limits  of  this  class. 

Class  C.  Rise  and  fall  requiring  the  use  of  brakes  in  descend- 
ing, in  addition  to  shutting  off  steam,  in  order  to  avoid  exces- 
sive velocities,  and  consequently,  in  almost  all  cases,  more  or 
less  use  of  sand  in  ascending. 

450.  Rise  and  fall  is  most  conveniently  estimated  by  the 
number  of  vertical  feet  of  it,  since  the  cost  of  it  (which  in- 
cludes no  limiting  effect  on  trains)  depends  primarily  on  the 
length  of  grades  and  not  at  all  on  their  rate,  except  as  the  rate 
may  change  the  rise  and  fall  from  one  to  the  other  of  the  above 
classes.  A  foot  of  "rise  and  fall"  is  ordinarily  considered  as. 
one  foot  of  ascent  with  its  corresponding  foot  of  descent,  so  that 
in  passing  over  a  hill  100  feet  high  there  are  100  feet  of  rise  and 
fall,  and  not  100  feet  ascending  -}-  100  feet  descending  =  200  feet. 

451.  The  amount  of  rise  and  fall  of  each  kind  on  the  profile 
should  be  determined  thus  : 

A.  All  rise  and  fall  arising  from  hollows  in  grade-lines  not. 
exceeding  the  limits  specified  in  connection  with  Table  121  (par. 
435  et  seq.)^  if  the  grades  are  connected  by  easy  vertical  curves  and 
are  not  too  near  stations,  or  very  bad  curvature,  will  belong  to 
the  least  objectionable  class,  A.  If  the  hollows  are  sharp  and 
abrupt,  however,  even  if  quite  small,  the  rise  and  fall  will  be 
more  objectionable  than  the  worst  class  here  considered. 

B.  All  rise  and  fall  on  grades  too  long  to  come  under  Class  A,, 
but  on  rates  of  grade  so  easy  that  the  train  can   never  obtain 


CHAP.  IX.— RISE  AND  FALL— COST  OF.  375 

a  dangerously  high  velocity  when  running  without  brakes  with 
steam  shut  off,  will  belong  to  Class  B.  So  also  will  rise  and  fall 
on  any  grade,  however  steep,  which  is  not  long  enough  for  the 
train  to  obtain  a  dangerously  high  velocity,  as  fixed  in  Table  122 
and  par.  447  et  seq.  So  also,  strictly  speaking,  will  the  upper 
part  of  any  grade,  however  steep  and  however  long,  on  which 
no  dangerously  high  velocity  can  result  according  to  Table  122  ; 
but  it  would  be  an  objectionable  refinement,  tending  to  an  under- 
estimate of  the  cost  of  bad  details  of  location,  to  so  consider. 

C.  Class  C,  therefore,  should  be  considered  to  include  the 
entire  length  of  all  grades  so  long  and  steep  as  to  require  the 
use  of  brakes  in  descending. 

The  ruling  grade  of  the  line  may  belong  to  either  Class  B  or 
Class  C.  In  either  case  it  will  involve  the  occasional  use  of 
sand  and  more  or  less  slipping  of  wheels,  and  perhaps  breaking 
in  two  of  trains  in  ascending,  and  thus  make  an  addition  to  the 
cost  of  either  class  which  would  not  apply  to  the  same  grades  if 
they  were  not  ruling  grades,  and  hence  did  not  so  severely  tax 
the  power  of  the  engine. 

The  limit  of  these  classes  will  vary  in  every  case,  but  there  is 
a  tolerably  sharp  line  of  demarcation  between  the  cost  of  each, 
which  may  be  estimated  as  follows  : 

THE  COST   OF  RISE  AND   FALL. 

452.  Fuel. — Except  as  wasted  by  brakes,  there  is  no  loss  of  power 
(energy),  and  except  as  wasted  by  brakes  and  radiation  combined,  there 
is  no  loss  of  either  fuel  or  power,  from  any  amount  of  rise  and  fall  of 
Class  A,  if  we  neglect  the  slight  difference  in  frictional  resistances  result- 
ing from  a  (so  to  speak)  regularly  irregular  speed  instead  of  from  a  uni- 
form speed  averaging  the  same  in  miles  per  hour.  This  necessarily  fol- 
lows from  elementary  dynamic  laws.  Even  if  there  be  a  difference  in 
the  level  of  the  two  termini,  what  power  is  lost  in  going  in  one  direction 
is  regained  in  returning. 

When,  in  the  case  of  rise  and  fall  on  easy  gradients  requiring  no 
brakes  (Class  B),  we  run  a  part  of  a  distance  of  one  or  two  miles  (the 
ascent)  under  steam  and  another  part  of  it  (the  descent)  with  steam  shut 
off,  assisted  by  gravity  only, — or  in  other  words,  assisted  by  the  energy 


3/6  CHAP.  IX.— RISE  AND  FALL— COST  OF. 

stored  in  the  train  during  the  run  over  the  up  grade  by  the  act  of  lifting 
it  against  gravity,— the  total  time  that  the  locomotive  is  exposed  to  ex- 
terior radiation  is  the  same,  and  probably  also  the  loss  of  heat.  The  loss 
from  interior  radiation  in  the  cylinders,  a  very  important  loss,  explained 
in  Chapter  XL,  is  affected  as  follows : 

It  is  increased  by  the  (probable)  lower  piston  speed  in  ascending  the 
up  grade. 

It  is  decreased  by  the  (probable)  later  point  of  cut-off,  and  hence  less 
oscillation  of  temperature  in  the  cylinder  ;  the  disadvantage  of  this  latter 
very  nearly  balancing,  as  experiment  shows,  the  theoretical  gain  from  an 
earlier  point  of  cut-off.  This  is  to  say,  from  both  of  these  causes  com- 
bined, the  steam  used  for  equal  work  in  the  locomotive  engine  is  about 
the  same  at  all  points  of  cut-off  less  than  half  stroke ;  which  leads  to  the 
conclusion  that  the  steam  (not  fuel)  used  to  run  an  engine  two  miles 
will  be  about  the  same  whether  the  work  is  uniform  for  the  whole  run  or 
is  all  done  during  the  first  mile  in  taking  the  engine  up  an  easy  grade, 
down  which  it  runs  by  gravity  for  the  second  mile.  The  loss  by  ex- 
ternal radiation  during  the  last  mile  will  be  a  net  loss.  The  fuel  used 
will  probably  be  much  more  increased,  not  only  by  possible  blowing-off 
of  steam  from  the  safety-valve,  but  by  blowing  out  more  unconsumed  coal 
from  and  wasting  more  heat  through  the  smoke-stack,  owing  to  the 
stronger  draft.  In  Chapter  XI.  it  is  shown  that  in  proportion  as  the  work 
of  the  engine  is  increased,  economy  of  fuel  consumption  is  decreased. 

From  all  these  causes  combined  a  locomotive  running  w^ithout  brakes 
or  steam  down  grades  too  steep  to  continue  the  steam-power  unchanged, 
but  not  steep  enough  or  long  enough  to  require  the  use  of  brakes,  will 
burn  probably  one  fourth  to  one  fifth  more,  and  certainly  not  over  one 
third  more  fuel  in  ascending  one  mile  on  the  grade  equal  to  the  grade  of 
repose  (assumed  at  26  feet  per  mile,  or  0.5  per  cent),  and  then  descend- 
mg  one  mile  without  steam,  than  in  running  two  miles  on  a  level.  Al- 
lowing one  third  more,  80  vertical  feet  of  rise  and  fall  on  such  grades 
will  waste  fuel  equal  to  the  average  consumption  per  mile. 

453.  When  brakes  are  required,  owing  to  the  grade  being  either  too 
steep  or  too  long  to  permit  of  operating  it  without  them,  the  power  used 
in  ascending  is  entirely  lost,  except  that  portion  of  it  which  is  just  suffi- 
cient to  keep  the  train  in  motion  on  the  grade  of  repose.  That  is  to  say  : 
The  rise  and  fall  at  BC,  Fig.  85,  consists  of  two  parts,  the  upper  part,  B, 
belonging  to  Class  B,  and  the  lower  part  only,  C,  belonging  to  Class  C, 
which  is  very  much  more  costly,  objectionable,  and  dangerous.  In  laying 
out  a  line  this  fact  must  be  borne  in  mind  ;  the  lower  portion,  C,  estimated 


CHAP.  IX.— RISE  AND  FAIL— COST  OF.  377 

at  its  true  value  and  avoided  if  possible  ;  the  upper  portion,  B,  less  care- 
fully avoided.  The  limit  between  classes  B  and  C  may  be  taken  in  round 
figures  as  the  height  of  the  point  b.  Fig.  85,  above  or  below  the  grade  of 

repose  descending  from  A,  ^^^^ _^ 

although,  strictly  speaking,  J>^^'^^'*^"^^^**^^'S=-— 

the  grade  of  repose  should    ^^x"*^"^  ^**"""*"^2?^"^^'^/?e^'-^~ 

be  drawn  in  starting  from  ^^^^^<p°^^* 

the    point    on    the   grade  ^^^'>>, 

where  the  limits  of  Table  ^ 

,  Fig.  85. 

122  and  par.  447  are  passed, 

so  that  dangerously  high  speed  before  reaching  the  foot  of  the  grade  is 

certain.     But  when  this  point  is  once  passed  great  care  in  handling  the 

train  on  a  grade  where  brakes  are  known  to  be  essential  cannot  fairly 

be  assumed,  so  that  it  is  fairer  and  more  reasonable  to  assume  that  all 

the  fall,  C,  Fig.  85,  will  be  of  the  objectionable  class. 

When  an  engine  is  descending  a  grade  without  steam,  the  wastage  of 
fuel  by  radiation  and  slow  combustion  is  at  first  (say  for  10  or  15  minutes) 
very  considerable — about  one  fourth  of  the  usual  consumption  per  mile. 
The  loss  of  fuel  on  this  most  objectionable  class  of  rise  and  fall  may  be 
taken  as  equal  to  the  average  consumption  in  running  a  mile  for  every 
26  feet  of  rise  and  fall. 

454.  Repairs  of  Cars  and  Locomotives. — The  use  of  brakes  is 
excessively  destructive  to  wheels.  Table  114,  page  318,  will  make  it 
clear  that  something  like  one  third  of  the  total  cost  of  wheels  arises  from 
this  cause,  and  other  data  that  as  much  as  forty  or  fifty  per  cent  arises 
from  them.  Brakes,  however,  are  used  even  more  for  stopping  and 
starting  than  on  grades — sometimes  very  much  more;  and  the  whole 
cost  of  wheels  is  only  some  30  per  cent  of  freight-car  repairs  and  very 
much  less  of  passenger  cars.  The  records  of  wheels  drawn  on  the 
Pennsylvania  Railroad  indicate  (a)  that  about  30  per  cent  of  passenger- 
car  wheels  are  drawn  for  being  "worn  flat  from  sliding,"  and  that  their 
life  is  from  this  cause  abbreviated  from  one  third  to  one  half.  About 
one  sixth  of  the  wheels  are  drawn  for  being  "worn  flat  or  hollow  on 
tread."  which  class  of  wear  is  distinctly  ascribed  in  the  Pennsylvania 
classification  to  "  wear  from  rail." 

If  we  should  consider  only  such  facts  as  these,  we  might  reach  the 
conclusion  that  the  wear  due  to  grades  must  be  a  very  important  element 
in  the  cost  of  freight-car  repairs ;  but  by  referring  to  Table  86,  page  203, 
and  remembering  that  grades  are  only  one  of  many  causes  for  wear  and 
tear  of  cars,  we  shall  see  reasons  for  concluding  that,  while  it  is  exceed- 


378 


CHAP.  IX.— RISE  AND  FALL— COST  OF. 


ingly  difficult,  in  fact  impossible,  to  reach  an  exact  estimate  in  such  a 
mattter  as  this,  yet  that  it  is  not  probable,  if  all  grades  were  levelled  down 
fiat  so  as  not  to  require  in  any  case  the  use  of  brakes,  except  for  stops, 
wheel  renewals  would  not  be  reduced  more  than  one  sixth  nor  car 
repairs  as  a  whole  more  than  one  tenth.  The  only  item  of  car  repairs 
other  than  the  wheels  affected  to  an  important  extent  is  the  cost  of 
draw-gear  and  links  and  pins,  and  the  loss  in  this  respect,  as  we  have 
seen  (par.  419),  arises  more  from  lack  of  proper  vertical  curves  at  breaks 
of  grade  than  from  the  grades  themselves. 

Table  123. 

Variations  in  the  Quality  of  Water  Supply,  Chicago,  Burlington  & 
QuiNCY  Railroad. 


Grains  Per  Gallon. 

Lbs. 

Incrusting 

Matter  in  Tank 

of  2750 

Gallons. 

Comparative 
Incrusting 

Locality. 

Incrusting 
Solids. 

Alkalies  and 
Non-crusting. 

Matter. 

Lake  Michigan 

=  1. 00. 

Chicago  Division  : 

Best 

Worst 

10.666 
28.851 

1-365 
10.788 

4.19 
11-33 

1.5 
3.9 

Average 

16.405 

4.898 
20.178 

2.853 

1.458 
2.449 

6.44 

1.92 
7.93 

2.2 

St.  Louis  Division  : 
Best 

0.7 

2.8 

Worst 

Average 

11.490 

1.678 

4-51 

1.6 

Lake  Michigan 

Hudson  River 

7-305 
7.177 
5.362 
0.9II 

0.626 
1. 136 
I. 511 
1-333 

2.87 
2.82 
2. II 
0.36 

I.O 
I.O 

Croton  River,  N.  Y 

Loch  Katrine,  Scotland.. 

0.7 
0.1 

Incrusting-  solids  include  silica,  oxide  of  iron  and  alumina,  carbonates  of  lime  and 
magnesia,  and  sulphates  of  lime  and  magnesia. 

The  standard  tank  of  the  road  carries  2750  gallons. 

The  non-incrusting  matter  may  be  partly  deposited  as  mud  and  partly  mechanically 
combined  with  the  scale.  According  to  this  table,  an  engine  consuming  three  full  tanks 
of  water  per  day  would  in  a  week's  work  with  the  average  water  in  the  Chicago  Division 
accumulate  at  least  116  lbs.  of  incrustation.  With  the  best  water  on  the  St.  Louis 
Division  (taken  from  the  Mississippi  at  Rock  Island)  the  result  of  a  similar  week's  work 
would  be  only  345^  lbs.  of  incrustation.  The  difference  shows  the  importance  of  good 
water. 

The  water  of  Loch  Katrine,  Scotland,  from  which  Glasgow  derives  its  supply,  is  about 
the  purest  and  softest  known. 


CHAP.  IX.— RISE  AND  FALL— COST  OF.  379 

455.  The  cost  of  locomotive  tires  will  be  affected  in  much  the  same 
way  and  to  the  same  extent  as  the  cost  of  car  wheels.  The  life  of  the 
boiler  is  likewise  unfavorably  affected  by  an  intermittent  instead  of 
regular  demand  for  power,  although  this  effect  is  slight  in  comparison 
with  the  injury  suffered  from  the  cooling  off  of  boilers  at  the  end  of  the 
trip,  from  the  effect  of  bad  water  and  many  other  causes  not  connected 
with  the  grades  between  stations.  Table  123  gives  an  idea  of  how  im- 
portant is  the  effect  of  bad  water  on  locomotive  repairs. 

456.  It  is,  moreover,  true  of  both  engine  and  car  repairs  that,  as 
noted  in  par.  164,  when  we  search  for  evidence  of  the  effect  of  much 
rise  and  fall,  or  curvature,  or  (as  usually  happens)  both  together,  by 
comparing  the  cost  of  engine  and  car  service  per  mile  run  on  roads  or 
divisions  having  much  and  having  little  curvature  and  rise  and  fall,  we 
fail  to  find  it.  As  respects  grade,  this  results  in  part,  no  doubt,  from 
lower  speed  and  more  careful  handling  on  them ;  but  as  this  costs  the 
company  nothing  except  a  slight  delay,  we  may  fairly  regard  it  as  an 
offset,  to  some  extent.  In  the  first  edition  of  this  treatise  the  writer 
estimated  the  effect  of  rise  and  fall  at  5  per  cent,  on  the  total  cost  of 
repairs  of  engines  and  cars  per  mile,  for  each  25  feet  per  mile  (0.5  per 
cent,  nearly)  which  would  amount  in  2  per  cent  grades  to  something 
over  20  per  cent  per  mile  of  ascent  and  descent.  Taking  an  average  of 
the  mountain  divisions  of  the  Pennsylvania  Railroad,  this  would  require 
that  a  difference  of  at  least  15  per  cent  should  be  visible,  and  on  the 
Baltimore  &  Ohio  at  least  20  per  cent,  whereas  in  fact  no  such  difference 
appears  in  either  case.  This  fact,  together  with  a  careful  estimate  by 
items,  which  cannot  be  given  more  fully  than  above,  leads  the  writer  to 
believe  that  his  original  estimate  was  too  high  and  it  is  reduced  in  the 
estimate  below  (Table  123)  to  4  per  cent,  which  is  the  utmost  that  the 
statistical  evidence  seems  to  justify. 

On  Class  A  of  rise  and  fall  there  cannot  be  considered  to  be  any 
measurable  increase  in  the  cost  of  rolling-stock  maintenance  if  proper 
vertical  curves  are  used.  On  Class  B  (requiring  shutting  off  steam  for 
descending,  but  not  the  use  of  sand  or  brakes)  there  is  very  little — cer- 
tainly not  over  one  fourth  of  what  exists  on  the  worst  class,  C. 

457.  Wear  of  Rails. — The  effect  of  grades  on  the  wear  of  rails  is 
exaggerated  in  popular  belief  for  want  of  a  proper  distinction  between 
the  effect  of  a  heavy  ruling  grade,  which  increases  the  number  of  trains 
and  the  proportion  of  engine  tonnage,  and  the  effect  of  rise  and  fall 
simply,  on  which  the  number  of  trains  and  proportion  of  engine  tonnage 
is  the  same  as  on  adjacent  sections  of  level  track.     Thus,  in  an  able  and 


380  CHAP.  IX.— RISE  AND  FALL— COST  OF. 

elaborate  report  on  the  wear  of  rails  on  the  Pennsylvania  Railroad, 
already  quoted,  an  increase  of  some  75  per  cent  in  the  wear  of  rails  on 
grades  over  which  almost  three  times  as  many  engines  pass  as  on  ad- 
jacent sections  of  level  track  was  ascribed  to  the  effect  of  grades  as  such, 
whereas  it  is  in  reality  merely  an  expression  of  the  fact  that  an  engine 
wears  the  rails  several  times  as  much  as  the  same  weight  of  cars  (par. 
115).  In  so  far  as  this  is  the  cause  of  extra  wear  of  rails  it  is  an  effect 
arising  from  the  limiting  effect  of  gradients,  and  not  at  all  an  inherent 
property  of  gradients  as  such. 

When  we  eliminate  this  extraneous  question  we  are  driven  to  the 
conclusion  that  the  wear  of  rails  due  to  gradients  as  such  is  almost  nil, 
except  as  their  rate  may  be  such  to  require  the  use  of  brakes  and  sand. 
The  use  of  sand  is  exceedingly  destructive  to  rails.  The  writer  found 
that  at  specially  exposed  localities  (near  stations  for  the  most  part),  where 
the  use  of  both  brakes  and  sand  was  usual,  the  wear  as  measured  by  loss 
of  weight  was  increased  some  75  per  cent ;  but  loss  of  weight  alone  is  an 
unfair  criterion,  since  the  wear  at  joints  is  a  very  important  factor  in  the 
life  of  rails,  and  often  requires  their  removal  before  they  are  fully  worn 
out.  Such  extreme  use  of  either  brakes  or  sand,  moreover,  is  not 
common  on  any  grade  as  at  the  points  covered  by  the  writer's  tests. 

458.  In  the  first  edition  of  this  treatise,  a  considerable  body  of  sta- 
tistics being  presented  and  discussed  to  which  it  appears  unnecessary  to 
again  give  space,  the  writer  estimated  that  the  wear  of  iron  rails  was  in- 
creased not  over  5  per  cent  per  25  vertical  feet  of  rising  grade  and  the 
same  on  the  corresponding  descent,  or  10  per  cent  for  each  25  feet  of 
rise  and  fall,  making,  on  a  2  per  cent  grade  (106  feet  per  mile)  a  differ- 
ence of  20  per  cent  in  the  aggregate  of  this  item  on  both  the  ascent  and 
corresponding  descent.  He  sees  no  reason  to  believe  that  this  estimate 
is  materially  in  error  in  either  direction  (unless  in  excess)  as  measuring 
the  effect  of  gradients  pure  and  simple,  without  modification  iji  the  7iu7n- 
ber  of  engines  used  for  a  given  7iumber  of  cars,  and  this  latter  occurs  only 
on  the  worst  class  of  rise  and  fall,  C.  For  that  class,  a  proper  estimate 
for  iron  rails  might  be  expected  to  still  hold  good  for  steel,  since  the 
proportions  of  the  grade  near  to  the  level  wear  has  not  been  greatly  af- 
fected by  the  introduction  of  steel  on  such  steep  grades,  where  speed  is 
slow. 

On  Class  A  there  is  certainly  no  direct  evidence  that  the  wear  of  rails 
is  affected  at  all,  with  steel  rails.  With  iron  rails,  which  failed  mostly 
from  lamination  and  which  speedil)'"  wore  to  an  irregular  surface  on  top, 
on  which  any  considerable  increase  of  speed  caused  greatly  increased 
wear  and  tear,  the  case  was  different. 


CHAP.   IX.— RISE  AND  FALL— COST  OF.  38 1 

Class  B  of  rise  and  fall  likewise  has  little  effect  to  increase  rail  wear, 
but  as  it  is  apt  to  cause  a  somewhat  high  velocity  in  the  hollows,  it  un- 
doubtedly has  some  ill  effect ;  possibly  about  one  half  as  much  as  Class  C. 

459.  Maintenance  of  Road-bed  and  Track.— In  the  former 
edition  of  this  treatise  the  cost  of  these  items  was  estimated  as  increased 
in  about  the  same  ratio  as  the  rail  wear,  viz.,  5  per  cent  for  each  25  feet 
per  mile  (0.5  per  cent  nearly)  of  rise  and  as  much  for  the  corresponding 
fall.  A  liberal  estimate  in  such  a  matter  is  proper,  and  we  may  continue 
the  former  estimate  for  Class  C,  although  it  is  probably  somewhat  too 
high  for  average  conditions. 

On  Class  A  and  Class  B  the  disadvantages  and  advantages  of  th-e 
grade  may  be  fairly  considered  to  balance  each  other  as  respects  main- 
tenance of  road-bed  and  track.  A  great  compensating  advantage  from 
the  grade,  besides  the  lower  speed,  is  the  more  perfect  drainage,  giving 
a  firmer  road-bed  and  prolonging  the  life  of  ties  and  ballast  as  well  as 
preserving  the  surface.  Level  cuts  are  always  very  objectionable,  as  has 
been  rediscovered  many  times  since  one  of  the  early  English  engineers 
laid  out  one  several  miles  long,  which  caused  immense  difficulty  (and 
still  causes  it),  several  costly  tunnel  culverts  having  to  be  driven  to  drain 
it.  Grades  of  any  moment  are  usually  situated  in  comparatively  rugged 
and  difficult  regions,  and  the  increased  expense  arising  from  that  cause 
is  very  apt  to  be  erroneously  ascribed  to  the  effect  of  the  gradients 
themselves.  Creeping  of  rails  is  an  annoying  effect  due  in  part  to  gra- 
dients, but  has  been  largely  done  away  with  in  recent  years  by  improved 
forms  of  joints. 

460.  Train  Wages. —  It  is  quite  conceivable  that  one  or  more  addi- 
tional brakemen  may  be  required  on  a  line  of  much  rise  and  fall,  yet  it 
would  ordinarily  be  quite  improper  to  include  this  as  one  of  the  ex- 
penses arising  from  it,  for  this  reason  :  Whether  or  not  such  additional 
force  will  be  required  is  usually  determined  by  the  general  character  of 
the  line  beyond  hope  of  change  by  the  engineer.  In  comparing  two 
radically  different' lines,  it  might  be  an  element  worthy  of  consideration, 
but  the  slight  modifications  which  are  ordinarily  alone  possible  can 
rarely  be  sufficient  to  in  themselves  make  any  difference  in  this  respect. 

461.  Station,  Terminal,  and  General  Expenses,  as  well  as  train 
wages  and  a  large  proportion  of  the  other  running  expenses,  cannot  be 
considered  as  affected  to  any  appreciable  extent  by  any  changes  in  rise 
and  fall  not  of  the  most  radical  and  extensive  nature. 

462.  From  all  that  has  preceded  we  may  deduce  that  no  lead- 
ing item  of  railway  expenditure  is  largely  affected  by  rise  and 


382  CHAP.   IX.— RISE  AND  FALI—COST  OF. 

fall  in  itself,  and  very  many  of  them  not  at  all  affected.  In 
Table  124  appears  a  detailed  summary  of  the  aggregate  effect 
to  increase  expenses  of  each  of  the  three  classes  of  rise  and  fall, 
A,  B,  and  C: 

A.  Not  requiring  shutting  off  steam  nor  change  in  the  natural 
velocity,  nor  use  of  brakes  or  sand.     (See  foot-note  to  Table  124.) 

B.  Requiring  shutting  off  steam  at  the  head  of  the  grade,  but 
not  use  of  brakes  or  sand. 

C.  Requiring  use  of  both  brakes  and  sand. 

463.  The  summary  of  the  cost  per  year  of  a  foot  of  rise  and 
fall  at  the  foot  of  Table  124  shows  its  cost  to  be — 

Class  C.  Class  B.  Class  A. 

Cost  on  minor  gradients $2  67  $0  84  $0  28 

Cost  on  ruling  gradients 3  50  167            

Addition  to  cost  of  same  amount  of  rise 

and  fall  if  on  ruling  gradient o  83  o  83            

These  sums,  divided  by  the  rate  of  interest  on  capital,  what- 
ever it  may  be,  will  give  the  justifiable  expenditure  per 
DAILY  TRAIN  to  avoid  One  foot  of  rise  and  fall.  Thus,  if  capital 
cost  6  per  cent,  the  justifiable  expenditure  per  daily  train  to 
avoid  100  feet  of  rise  and  fall  (i.e.,  100  feet  up,  with  the  corre- 
sponding 100  feet  down)  will  be  for  each  class, — multiplying  the 
above  sums  by  100  and  dividing  by  0.06, — 

Class  C.  Class  B.         Class  A. 

If  on  minor  gradients $4j45o         $ij4oo         $4^7 

If  on  a  ruling  gradient 5)^33  2,783         

To  reduce  the  ruling  to  a  minor  gradi- 
ent (leaving  the  ruling  gradient  else- 
where unchanged) i)383  i>383         

It  would  be  impossible,  however,  that  there  should  be  so 
much  as  100  feet  of  rise  and  fall  of  Class  A  at  any  one  point, 
since  if  there  were  so  much,  or  even  half  or  one  quarter  so  much, 
it  could  not  belong  to  Class  A.  The  value  given  for  reduction 
of  a  ruling  to  a  minor  gradient  refers,  of  course,  merely  to  the 
DIRECT  saving  of  wear  and  tear  by  having  the  grade  easier,  and 


CHAP.   IX.— RISE  AND  FALL— COST  OF. 


383 


Table  124. 

Estimated  Cost  Per  Train-Mile  and  Per  Daily  Train  of  26.4  Feet  of 

THE  Various  Classes  of  Rise  and  Fall. 

(Cost  of  train-mile  assumed  at  $i.oo,) 


Item. 


Total 

Cost  of 

Item, 


Percentage  of  same 
increasing  with  26.4 
feet  of  rise  and  fall 

belonging  to— 
Class  C.       Class  B. 


Cost  per  train-mile 
of  26.4  feet  of  rise 
and  fall  belonging 

to- 
Class  C.       Class  B. 


Fuel 

Water,  oil,  and  waste 

Repairs  of  engines 

Switching-engine  service.. 
Train  wages  and  supplies. 

Rep^airs  of  cars 

Car-mileage 

Renewals  of  rails 

Adjusting  track 

Renewing  ties 

Earthwork,  ballast,  etc... 

Yards  and  structures 

Station  and  general 


7.6 
1.2 
5.6 
5-2 
15-4 

lO.O 

2.0 

2 

6 

3 
4 


p.  c 
100 


30. 


P.O. 

33i 
50  20 

4.0  i.o 

Unaffected. 

4.0  1.0 

Unaffected, 
lo.o  5.0 

5.0  0.0 

5.0  0.0 

5.0  0.0 

Unaffected. 


P.O. 

7.6 
0.6 
0.22 


0.4 

0.2 
0.3 
0.15 
0.2 


p.  c. 
2.53 
0.24 
0.06 


O.IO 

0.00 
0.00 
0.00 


Total, 


9-7 


3.0 


9.67 


3-03 


Per  Foot  of  Rise  and  Fall 

Per  Foot  of  Rise  and  Fall  per  Daily  Train  (round  trip). 


.366 

$2.67 


•115 

$0.84 


If  the  Rise  and  Fall  be  on  the  Maximum  Grade,  whether  on  Class  B  or 
Class  C,  the  wear  and  tear  of  rolling-stock  and  track  will  be  so  increased  as  to  add  at 
least  3.0  cents  per  train-mile  to  the  cost  of  26.4  feet  of  rise  and  fall,  giving  us  the  follow- 
ing comparison  : 

Class  C.    Class  B. 
Cost  per  daily  train  per  foot  of  rise  and  fall  on  Minor  Gradients,  as 

above, 

Addition  to  cost  of  the  same  grade  if  a  Ruling  Gradient  due  to  the 

extra  wear  and  tear  on  ruling  gradients, 0.83 

Giving  as  the  cost  per  daily  train  per  foot  of  rise  and  fall  on  Ruling 

Gradients, $3-5o 


?2.67 


0.83 


;i.67 

A  Foot  of  Rise  and  Fall  means  a  foot  of  ascent  with  its  corresponding  descent 
(par.  450). 

Class  A  of  Rise  and  Fall  is  not  included  in  this  table,  because,  as  will  be  seen 
from  the  preceding  discussion  of  the  details  of  expenses,  no  expense  can  be  directly  traced 
to  it  in  any  single  item.  In  considering  this  apparently  doubtful  conclusion  the  strict 
limitations  laid  down  for  the  class  in  par.  435  et  seq.  are  to  be  remembered.  Moreover, 
although  the  effect  on  expenses  of  rise  and  fall  of  this  class  is  so  small  as  to  defy  separate 
estimation  by  items,  yet  as  it  causes  some  variation  in  the  velocity  of  the  train  there  must 
be  considered  to  be  some  disadvantage  arising  from  such  rise  and  fall  for  this  cause  alone, 
and  it  will  lead  to  no  serious  error  to  assume  its  cost  at  one  fourth  to  07ie  third  the  cost  of 
Class  B. 


384  CHAP.   IX.— RISE  AND  FALL— COST  OF. 

not  at  all  to  the  much  greater  value  which  results  from  reducing 
all  ruling  grades  throughout  the  line,  so  that  the  length  of 
trains  can  be  increased. 

464.  The  above  values  are  to  be  further  multiplied  by  the 
estimated  number  of  trains  per  day  (round  trip).  Thus,  if  there 
are  expected  to  be  10  trains  per  day  each  way,  the  value  of  sub- 
stituting a  level  for  a  hill  100  feet  high  becomes  $14,000  to 
$44,500  for  minor  gradients,  and  $27,830  to  $58,330  for  ruling 
gradients — which  are  very  considerable  sums  if  we  remember 
that  they  are  quite  apart  from  all  limiting  effect  of  the  gradi- 
ents. The  value  of  changing  the  rise  and  fall  from  Class  C  to 
Class  B  is  nearly  $30,000,  and  of  reducing  a  ruling  gradient  to  a 
minor  gradient  without  changing  the  class,  nearly  $14,000. 

465.  In  the  first  edition  of  this  treatise  the  cost  of  rise  and  fall  on  all  grades 
of  over  40  feet  per  mile  was  found  to  be — 

On    12^        feet  per  mile  (about  0,25)  grades $1  04 

0.5  )       "      I  56 

0.7  )       "     I  87 

0.8  to  I. o  )       "     2  08 

1.5  )       "     2  29 

2.5  )       "     2  40 

The  writer  has  been  forced  to  the  conclusion  that  these  estimates  were  too 
small  to  be  on  the  safe  side,  and,  despite  the  fact  that  the  steel  rail  and  other 
mechanical  betterments  have  materially  reduced  the  disadvantages  of  rise  and 
fall,  has  increased  its  estimated  cost  as  above. 

466.  It  will  be  clear  from  all  that  has  preceded  in  this  chapter 
that  the  disadvantages  of  rise  and  fall  are  measured  more  truly 
by  the  number  of  breaks  of  grade  than  by  the  actual  amount 
of  it  in  vertical  feet,  except  on  the  worst  class  of  all,  C,  on  which 
both  brakes  and  sand  have  to  be  constantly  used.  Even  on  the 
heaviest  grades  this  is  in  a  measure  true.  Thus,  the  long  i  per 
cent  grade  in  Fig.  86,  belonging  to  Class  C,  will  be  considerably 
more  objectionable  to  operate  than  a  corresponding  easy  grade 
belonging  to  Class  A  or  B  of  rise  and  fall,  as  the  0.5  continuous 
grade  in  Fig.  86;  but  the  breaking  up  of  the  i  per  cent  grade 
at  frequent  intervals  by  stretches  of  lighter  grade,  so  that  the 


I2i        feet 

per 

mile  (about 

25 

35 

40  to  50  " 

"     (    "  0. 

80 

125 

CHAP.    IX.— RISE  AND  FALL— VERTICAL    CURVES.        385 

descent  is  made  half  on  one  grade  and  half  on  the  other,  so  far 
from  decreasing  the  aggregate  cost  of  the  grade  over  the  straight 


O  sM.  lOM,  I5M, 

Fig.  86. 

I  per  cent,  will  in  fact  make  it  considerably  more  expensive  to 
operate. 

467.  Again,  1000  feet  of  rise  and  fall  concentrated  on  a  single 
grade  is  not  nearly  so  expensive  in  wear  and  tear  as  when  the 
same  amount  of  it  is  scattered  around  in  a  dozen  or  more  shorter 
and  widely  scattered  grades  of  the  same  rate  and  class  (par. 
462).  If  its  class  is  changed  by  such  breaking  up  the  case  is 
different.  Thus,  the  least  objectionable  class,  A,  of  rise  and  fall 
can  only  exist  when  there  is  very  little  at  one  point. 

468.  We  have  seen  (par.  414  et  seq.)  that  long  and  easy  verti- 
cal curves,  properly  used,  very  largely  obviate  the  disadvantages 
of  every  class  of  rise  and  fall,  however  much  broken  up  into 
short  sections;  in  fact,  properly  used,  they  forbid  the  breaking 
it  up  into  over-short  sections. 

It  is  so  extremely  important  that  vertical  curves  should  be 
sufficiently  long  and  should  be  properly  put  in,  that  we  may 
anticipate  here,  from  the  field-book  which  follows  this  volume, 
some  notes  as  to  the  proper  manner  of  putting  in  such  curves: 

469.  We  have  seen  (par.  426  et  seq.)  that  the  length  of  vertical  curves 
should  be  determined,  not  arbitrarily,  regardless  of  the  angle  between 
gradients,  but  by  the  amount  of  change  of  grade  per  station  which  is 
admissible ;  the  safest  rule  being  as  already  given— that  the  difference  in 
the  rate  of  grade  under  the  head  and  rear  of  the  train  shall  not  exceed 
the  grade  of  repose  of  the  last  car, 

A  rate  of  change  per  station  (100  feet)  of  .025  will  most  completely 
25 


386       CHAP.   IX,— RISE  AND  FALL— VERTICAL   CURVES. 


fulfil  this  condition  with  all  kinds  of  trains,  including  those  with  a  great 
deal  of  slack  in  the  couplings,  like  coal  trains  ;  but  .05  per  station  will 
obviate  all  the  more  serious  effects,  especially  if  the  speed  be  high  or  the 
train  short,  or  both.  After  the  introduction  of  improved  freight  couplers 
.05  per  station  will  be  ample. 

Both  of  these  rates  give  a  longer  curve  than  is  usual ;  but  more  change 


Fig.  87.  Fig.  88. 

per  station  than  that  last  specified  should  never  be  used  in  sags  (Fig. 
87),  unless  for  high  speed  and  very  short  trains.  On  summit  curves 
(Fig.  88)  shorter  curves  are  admissible  ;  but  these  also  should  not  be 
shorter  than  o.i  per  station — if  for  no  other  reason,  because  it  is  needless 
to  make  them  so. 

470.  The  angle  between  grade-lines,  a.  Figs.  87,  88,  is  considered  to 
be  the  sum  or  difference  in  the  rate  per  cent  of  the  grades,  or  their 
deflection  from  each  other.     In  Fig.  87,  a  =  1.4;  in  Fig.  88,  a  —  i.o,  etc. 

If  we  let  r  =r  the  change  of  rate  per  station  which  is  considered  admis- 
sible, =  0.0.25  to  o.io  according  to  circumstances,  then  the  aggregate 
length  of  any  curve  is  at  once  given  by  the  equation 

r 

If  the  angle  between  grade-lines  be  i.o  per  cent,  this  gives  a  vertical 
curve  10,  20,  or  40  stations  long,  according  as  the  assumed  value  of  r  is 
0.1,  0.05,  or  0.025. 

The  condition  that  the  change  in  rate  of  grade  shall  be  uniform  per 

T 


Fig.  89. 
(In  this  cut,  which  is  rather  poorly  executed, 
.1,  2,  3,  4,  5  are  successive  stations  of  100  feet 
from  the  tangent  point  T,  but  the  "curve"  as  drawn  is 
supposed  to  consist  merely  of  a  series  of  straight  lines, 
ad,   be,  cd,  etc.,    tangent  to  the  curve  at  these  stations, 
these  tangents,  as  prolonged  by  the  dotted  lines,  being  supposed 
to  differ  from  each  other  in  rate  of  grade  by  a  constant  change 
of  rate,  r.) 

Station  or  other  unit  results  in  the  generation  of  a  curve  such  as  that  out- 
lined in  Fig.  89,  which  is,  mathematically,  a  parabola. 


CHAP.    IX.— RISE  AND  FA LL^ VERTICAL   CURVES.        387 


471.  It  is  to  be  remembered  that  all  geometrical  diagrams  connected 
with  railway  location  are  greatly  exaggerated  or  distorted,  so  that  the 
succession  of  chords  outlined  in  Fig.  89  are  in  fact  practically  coincident 
with  the  curve.  Fig.  90  gives  to  correct  scale  the  intersection  of  a  4 
per  cent  (211  feet  per  mile)  grade  with  a  level,  which  is  perhaps  twice  as 
large  an  intersection  angle  as  actually  occurs  on  any  located  line  in  the 
United  States,  even  on  the  engineer's  profile,  and  four  or  five  times  as 
much  as  is  usual ;  topographical  reasons  generally  requiring  one  or  more 
intermediate  grades  in  cases  of  such  abrupt  change. 

Fig.  90  will  also  make  it  clear  that  in  the  two  sketches  of  vertical 


Jjeuet  —  • 


■^  »«>/*  c»nf  _ 


^      '   ■  ■         

Fig.  90. 

curves  shown  in  Figs.  91  and  92  the  tangents,  the  chord  My  and  the 
curves  themselves  are  sensibly  of  the  same  absolute  length,  independent 
of  the  fact  that,  all  distances  being  measured  horizontally,  they  are  neces- 
sarily equal  as  measured  in  the  field. 

472.  From  the  law  of  the  parabola  it  results  that  in  any  vertical 
curve,  Fig.  91  or  92,  the 
curve  bisects  the  middle 
ordinate  IM  in  c,  and 
from  elementary  geomet- 
rical relations  we  have  for 

the   distance    Ic  =  c,    by  Fig.  91. 

which  the  curve  departs  vertically  from  the  intersection  of  tangents  : 
I    '  a       la 


2^4 


'/z^ 


or,  as  /=  —  (par.  470), 


Fig.  92 


473.  From  this  formula  we  can  compute  the  following  Table  125,  giv- 
ing the  first  detail  which  it  is  desirable  to  know  in  laying  out  a  vertical 
curve,  viz.  :  How  much  vertical  change  it  will  produce  in  the  position  of 
the  grade-line,  which  is  greatest  at  the  middle  of  the  curve  and  thence 
rapidly  diminishes  in  each  direction,  being  only  one  fourth  as  much  at 
the  "  quarter-points"  of  the  curve  or  at  the  middle  of  each  tangent. 

474.  Having  determined  from  Table  125,  or  otherwise,  what  rate  of 
per  station  will  be  necessary  or  feasible  :  To  LAY  OUT  A  VERTICAL  CURVE, 

HAVING  GIVEN  THE  RATE  OF   THE   TWO    GRADIENTS    AND    THEIR   ANGLE 


388        CHAP.    IX.— RISE  AND  FALL— VERTICAL    CURVES. 


Table  125. 

Vertical  Change  in  the  Position  of  the  Grade-Line  at  Intersection 
OF  Gradients  resulting  from  Vertical  Curves  of  Various  Rates  r 
AND  WITH  Various  Grade-Angles  a. 

(Computed  by  formula  of  par,  472.) 


Grade-Angle 

a. 

Figs.  91,  q2. 

Vertical  Distance  of  Curve  from  Intersection  of 

Gradients  =  /<r,  Figs.  91  and  92,  for  Change  of  Rate 

OF  Grade  per  Station,  =  r  of — 

0.2 

0.1 

0.05 

0.025 

O.I 

0.2 

0.3 
0.4 

0.5 
0.6 

0.7 
0.8 
0.9 

1.0 

I.I 

1.2 

1-3 

1.4 

1-5 
1.6 

1-7 
1.8 
1.9 
2.0 

Feet. 

.006 

.025 

.061 

.100 

.156 

.225 

.306 

.400 

.501 

.625 

.756 

.900 

1.056 

1.225 

1.406 

1.600 

1.806 

2.025 

2.256 

2.500 

Feet. 
.01 
.05 
.11 
.2 
.31 
•45 
.61 
.8 

1. 01 

1-25 

I-5I 
1.8 
2. II 

2-45 

2.81 

3^2 

3-6i 

4-05 

4-51 

5-0 

Feet. 
.025 

.225 

•4 
.625 

•9 
1.225 
1.6 
2.025 
2^5 
3-025 
3.6 
4-225 

4.9 

5-625 

6.4 

7.225 

8.1 
9-025 
10. 0 

Feet. 
•05 
.2 

•45 
.8 
1.25 
1.8 
2-45 
3-2 
4.05 
5-0 
6.05 

7-2 

8.45 
9.8 
11.25 
12.8 

14-45 
16.2 
18.05 
20.0 

The  vertical  change  in  the  position  of  the  grade-line  at  the  "quarter-points"  of  the 
curve,  or  at  the  middle  of  the  tangents,  is  in  each  case  one  fourth  of  the  above. 

a  grade-angle 


The  whole  length  of  the  curve  (both  tangents) 


change  of  grade  per  station' 


OF  INTERSECTION  a,  THE  RATE  PER  STATION  r,  AND  THE  STATION  OF 
THE  INTERSECTION  OF  GRADIENTS  : 

a 
I.  The   total   length  of  the  curve   in   stations  is  —  (which    let  =  n 

stations),  one  half  of  which  is  the  length  of  each  tangent,  whence  the 
station  of  the  tangent-point  can  be  determined  and  the  elevation  of  the 
grade  at  that  point. 


CHAP.   IX.— RISE  AND  FALL— VERTICAL    CURVES. 


389 


2.  Having  given  the  station  and  elevation  on  either  grade,  and  the 
rate  (which  let  =  R)  of  the  grade  in  which  it  lies,  write  successively 
R  —  \r,  R—  \\r,  R  —  i^r,  etc.,  adding  or  substracting  r  from  each 
(as  the  case  may  require)  until  n  quantities  have  been  written  down, 
paying  strict  attention  to  the  algebraic  signs,  as  below  specified. 

The  ;zth  quantity  thus  determined  will  differ  from  the  rate  R'  of  the 
other  tangent  by  \r,  and  the  addition  of  the  several  quantities  thus  de- 
termined to  the  elevation  of  the  first  tangent-point  will  give  the  elevation 
of  each  station  of  the  curve,  to  and  including  the  other  tangent-point, 
where  the  elevation  will  check  upon  that  independently  fixed  by  the 
tangent  grade-line  for  the  second  tangent,  if  the  work  has  been  correctly 
done. 

When  the  angle  between  the  grade-lines  is  upward,  or  on  a  summit, 
the  successive  additions  of  r  are  — ,  or  subtractions;  when  the  angle  of 
the  grades  is  downward,  the  additions  are  positive. 

Examples. — Curves  to  connect  the  gradients  shown  in  Figs.  93,  94,  95,  each 
with  the  intersections  of  gradients  at  station  100  and  elevation  loo. 


iBe.2)  „    ^  ^.     (56.9> 


(100.9) 


Fig. 


Rate  ,0.f 

6  StaHons 

Fig.  94. 


Fig.  93. 

Angle  between  grade-lines 1.6 

Rate  of  change  of  grade  per  station.  0.2 

Total  length  of  curve 8  si 

Station  of  tangent-points i    ^ 

Elevations  of  grade  at  do.  (computed).    \  ^^'^ 


Additions. 

F.C. 

i? -in........  0.7 

J^  —  lin 0.5 

J?  —  2^r..   .....  0.3 

R  —  3i^ O- 1 

Etc. —  0,1 

-  0.3 

—  0.5 
F.T —0.7 


98.1 
97.6 
96.9 


Eleva-     Stations. 

TIONS. 

969 
97.6 
98.1 
98.4 
98.5 


96 

97 
98 

99 
100 

lOI 

102 
103 
104 


Addi- 


-0.75 
-0.45 
-0.55 
—  0.65 

-0.75 
-0.85 


Elevations.        Sta- 


100  go 
100.55 
100.10 

99-55 
98.90 
98.15 
97-30 


97 
98 

99 
100 

lOI 

102 
103 


390 


CHAP.   IX.— RISE  AND  FALL— VERTICAL   CURVES. 


ZO  stafions  ^        ""i?^ 

Fig.  95. 

Angle  between  grade-lines „ i.o. 

Rate  of  change  of  grade  per  station 0.05 

Total  length  of  curve  20  stations. 

Station  of  tangent-points j  ^^ 

Elevation  of  grade  at  tangent-points -j  jq2  o 

Additions.  Elevations.  Stations. 

RC.  108.0  90 

^R  -    \r  —  .775  107.225  91 

R  —  lir  —  .725  106.5  92 

R  -  2ir-  .675  105.825  93 

R-~3ir—  .625  105.2  94 

etc.,         -  .575  104.625  95 

—  .525  104- 1  96 

—  .475  103.625  97 

—  .425  103.2  98 

—  .375  102.825  99 

—  .325  102.5  100 

—  .275  102.225  lOI 

—  .225  102.0  102 

—  .175  101.825  103 

—  .125  101.7  104 

—  .075  101.625  105 

—  .025  101.6  106 
+  .025  101.625  107 
-j-  .075  101.7  108 
+  .125  101.825  109 

P.  T.       +.175  102.0  no 

This  method  is  practically  much  the  most  convenient  when  the  curve 
begins  and  ends  at  a  full  station,  or  can  be  assumed  to  do  so  by  comput- 
ing grades  for  half  stations  or  otherwise.  In  other  cases  the  following 
may  be  used  :       ' ' 

475.  By  the  property  of  the  parabola,  Fig.  96,  offsets  to  it  from  its 
tangents  parallel  to  the  "  diameter,"  O,  vary  as  the  square  of  the  distance 
from  the  tangent-point.  Therefore :  Having  given  O  and  TV,  Fig.  96, 
TO  determine  offsets  to  the  curve,  0,  0',  0"  at  distances  n,  n',  n"^ 
from  the  P.  C. 


CHAP.    IX.^RISE  AND  FALL— VERTICAL    CURVES.        39 1 


Letting  ^V^  the  length  of  one  tangent  we  have,  for  any  offset  0  what- 
ever at  a  distance  n  from  the  P.  C, 


0_ 


=  — „-,  whence  0  =  0-^j-, 

71^  N' 


Thus,  if  we  divide  the  tangent  N  into  five  parts  the  first  offset,  0,  will  be 


(9x 


.2  Q 

or—-,  and  the  succeeding  ones  will  be  4,  9,  16  times  the  first. 


5         25- 
By  this  formula  we  may  compute  the  elevation  of  any  two  points  100 


Fig.  96. 
feet  apart  on  any  vertical  curve  (presumably  at  full  stations)  and  deter- 
mine the  rate  of  grade  between  them  ;  whence,  knowing  the  change  per 
station  in  rate  of  grade,  all  remaining  stations  are  determined  by  succes- 
sive additions  as  above.  To  avoid  cumulative  error,  the  computation 
should  be  carried  out  to  more  decimals  than  it  is  expected  to  use. 

The  entire  curve  may  likewise  be  computed  by  determining  the  off- 
sets 0,  o',  o",  which  ordinarily  involves  little  labor. 


PART  III. 


LIMITING  GRADIENTS  AND  CURVATURE. 


**  The  crime  which  bankrupts  men  and  states  is,  job-work; — declining 
from  your  main  design  to  serve  a  turn  here  and  there." 

— R.  W.  Emerson,  Essay  on  '•^  Wealth.^'' 


PART   III. 
LIMITING  GRADIENTS  AND  CURVATURE. 


CHAPTER   X. 

THE    RELATIVE    IMPORTANCE    OF    GRADIENTS. 

• 

476.  To  summarize  the  conclusions  we  have  reachea  in  the 
preceding  four  chapters  as  to  why  the  minor  details  of  align- 
ment are  properly  so  called,  both  separately  and  collectively: 
Let  us  assume  that  we  have  a  line  over  which  an  estimated 
traffic  of  ID  trains  per  day  each  way  will  pass, — a  very  fair  traffic, 
— and  that  we  have  two  alternate  lines  for  it,  one  of  which  (A) 
is  200  miles  long,  while  the  other  (B)  is  210.  Let  line  A  have 
the  favorable  alignment  of  the  Illinois  Central,  which  (Table  102) 
has  only  8°  of  curvature  per  mile,  and  line  B  the  very  crooked 
alignment  of  the  Lehigh  Valley,  which  has  100°  per  mile,  giving 
1600°  in  all  on  line  A  against  21,000°  in  all  on  line  B.  Let  the 
rise  and  fall  on  A  average  only  10  feet  per  mile,  or  2000  feet  in 
all,  instead  of  20  feet  per  mile  on  B,  or  4200  feet  in  all ;  always 
assuming,  however,  that  the  ruling  gradients  and  length  of  trains 
are  the  same  on  each.  Then  the  entire  value  of  these  very 
marked  and  very  improbably  great  differences  in  minor  details 
will  be  as  follows: 


396      CHAP.   X.— RELATIVE  IMPORTANCE  OF  GRADIENTS. 

Estimated  Cost  Per  Year. 
Differences  against  Line  B.  Per  Daily        For  10  Daily 

Train.  Trains. 

10  miles  excess  of  distance,  which  we  will  assume 

will  not  affect  train-wages,  as  that  is  the  more 

probable,  and  which  may  have  a  credit  side  as 

large  as  the  debit,  but  which  we  will  assume  has 

no  credit  side  (see  par.  196  and  Table  89),  .  .  $266  50  $2,665  00 
19,400°  excess  of  curvature  (Table  115),  at  43.3  cts. 

per° 8,400  00      84,000  00 

2200  ft.  excess  of  rise  and  fall,  assumed  to  be  all  of 

^        ,  \  1000  ft.  on  minor  grades,  .     .     2,670  00      26,700  00 

Class  C,  and,  sav,  \  t  i-  j 

'    {  1200  ft.  on  ruling  grades,  .     .     4,200  00      42,000  00 

(See  par.  000,  and  Table  124.) 

Total  difference  in  yearly  expenses  against  line  B,  $15,536  50  $155,365  00 

Capitalizing  this  sum  at  7  per  cent,  which  is  lower  interest 
than  most  new  lines  ought  to  require  before  increasing  expendi- 
tures, this  represents  a  capital  valuation  of  $2,219,500  or  $11,097 
per  mile,  as  the  difference  due  to  the  most  extreme  differences  in 
all  minor  details  at  once. 

477.  On  the  other  hand,  the  total  operating  expenses  of  lifie 
A,  at  $1.00  per  train-mile  (on  which  cost  the  above  valuations  are 
based),  would  be  $1,460,000  per  year,  and  we  are  about  to  see 
that  something  like  half  of  that  great  sum — sometimes  more, 
sometimes  less — will  vary  directly  with  the  number  of  trains  re- 
quired to  transact  its  business.  If  therefore  we  adopt  grades 
which  will  cut  down  trains  to  something  less  than  half  what 
they  might  have  been, — which  is  an  easy  thing  indeed  to  do  by 
probable  errors  of  location, — we  shall  increase  its  operating  ex- 
penses by  something  like  $365,000  per  year  against  only  $155,365 
from  excessive  and  entirely  improbable  differences  in  each  and 
all  of  the  minor  details  of  alignment,  against  the  same  line  : 
differences  which  might  lead  to  most  unfavorable  conclusions  of 
what  was  really  the  best  line,  by  one  carelessly  inspecting  it; 
whereas  difference  in  ruling  grade  of  no  greater  comparative 
importance  might  well  attract  little  attention,  since  it  would  in- 
volve only  a  moderate  difference  in  ruling  grade. 

478.  Again,  the  gross  revenue  of  such  a  line  would  probably 


CHAP.   X.— RELATIVE  IMPORTANCE   OF  GRADIENTS.      397 

be  something  like  one  and  a  half  times  its  operating  expenses, 
or  $2,190,000  per  year.  Probable  differences  of  location  will,  in 
almost  every  case,  cause  the  loss  or  gain  of  as  much  as  10  per 
cent  of  this,  and  in  very  many  instances  may  be  readily  shown 
to  have  had  (probably)  two  or  three  or  five  times  that  effect. 
Ten  per  cent  extra  revenue,  as  we  have  seen  (par.  40),  may  in  a 
rude  way  be  taken  as  almost  so  much  pure  gain,  although  of 
course  there  always  is  a  debit  side  to  even  so  small  a  difference 
of  revenue,  possibly  as  much  as  25  per  cent.  Even  then  a  net 
difference  to  revenue  of  as  much  as  $164,000  per  year  not  only 
may,  but  probably  will,  hang  on  decisions  reached  in  location^ 
which  may  be  capitalized  at  7  per  cent,  as  equal  to  a  valuation 
of  $2,343,000,  or  nearly  $12,000  per  mile  added  to  or  taken  from 
the  value  of  the  property.  This  moderate  difference  in  revenue 
thus  suffices  to  overbalance  all  the  disadvantages  of  the  assumed 
differences  in  minor  details,  which  go  far  beyond  any  that  ever 
existed,  probably,  in  any  two  alternate  lines  between  the  same 
termini, 

_,  Granting  that  questions  of  revenue  cannot  be  reduced  to  pre- 
cise figures,  and  may  be  beyond  the  engineer's  control  (although 
correct  action  in  respect  to  them  v/ill  largely  depend  upon  him 
and  affect  his  other  work),  the  question  of  what  ruling  gradients 
to  adopt  can  be  reduced  to  tolerably  precise  figures,  and  will 
rest  exclusively  in  his  hands;  and  of  the  questions  which  so  rest, 
we  have  now  seen  the  reasons  why  it  may  almost  be  called  the 
question  before  him,  to  the  exclusion  of  all  others.  It  must 
therefore  be  studied  with  some  care. 

479.  We  have  seen  in  the  opening  to  Chap.  IX.  that  the  ex- 
pense of  gradients  arises  from  two  causes,  which  are  totally  dis- 
tinct and  must  be  kept  so  to  form  any  correct  idea  of  their  cost 
or  proper  adjustment ;  the  one  being  the  direct  or  inherent 
effect  of  all  rise  and  fall  or  curvature  to  increase  wear  and  tear 
and  expenses  per  train-mile  (considered  in  the  preceding  chap- 
ters), and  the  other  the  effect  of  the  heaviest  grade  or  sharpest 
curve  to  limit  the  weight  and  length  of  train,  and  thus  cause  an 
additional  expense  which  does  not  appear  at  all  in  the  expenses 


398      CHAP.  X.— RELATIVE  IMPORTANCE   OF  GRADIENTS. 

per  train-mile,  but  simply  in  the  number  of  trains  required  to 
handle  the  traffic.  The  distinction  between  these  diverse  sources 
of  expense  was  so  fully  drawn  in  Chap.  IX.  that  it  need  not  be  re- 
peated, but  it  should  be  always  borne  in  mind.  For  the  present 
we  assume  the  gradients  to  be  the  limiting  cause,  as  is  nearly 
always  the  case,  although  it  may  be  curvature  or — conceivably — 
any  other  cause,  like  the  strength  of  couplings. 

480.  To  be  prepared  to  deal  intelligently  with  questions  of 
gradients  we  must  begin  from  the  foundation  and  consider,  in 
some  detail,  what  we  may  call  the  physiology  as  distinguished 
from  the  anatomy  of  the  locomotive  engine,  especially  as  re- 
spects the  running  gear.  The  general  question  of  limiting  gra- 
dients will  then  divide  itself  naturally  into  the  following  different 
heads  : 

First.  Ruling  gradients  proper,  and  their  effects  on  train- 
loads  and  operating  expenses  (Chaps.  XIV.,  XV.). 

Secondly.  The  use  of  concentrated  or  "  bunched  "  grades  on 
high  rates,  operated  by  assistant  engines  or  "pushers,"  with 
lower  grades  elsewhere,  as  against  uniform  gradients  (Chap. 
XVI.). 

Thirdly.  The  proper  balance  of  grades  from  excess  of  traffic 
in  one  direction  (Chap.  XVII.). 

Fourthly.  Limiting  curvature,  which  may  intervene  in  ad- 
vance of  gradients  to  limit  the  length  of  trains  (Chaps.  XVIII. , 
XIX.). 

Fifthly.  The  choice  of  gradients  and  devices  for  reducing 
them  (Chap.  XX.). 

All  of  these  problems  come  up,  potentially  at  least,  in  the 
location  of  every  line.  Before  attempting  to  solve  them  we  will 
lay  the  necessary  basis  therefor  in  the  three  following  chapters  on 
the  Locomotive  Engine,  RoUing-Stock,  and  Train  Resistance. 


CHAP.   XI  — THE  LOCOMOTIVE  ENGINE.  399 


CHAPTER  XI. 

THE    LOCOMOTIVE    ENGINE.* 

481.  The  locomotive  engine  is,  so  far  as  the  skill  and  foresight  of  the 
designers  can  make  it,  and  practical  considerations  permit,  a  delicately- 
balanced  machine,  having  these  three  forces  in  equilibrium  for  the  par- 
ticular service  required  of  it : 

1.  The  steam-producing  or  boiler  power:  the  boiler,  fire-box, 
and  attached  parts. 

2.  The  mechanical  or  transmitting  power  :  developed  through 
the  cylinder  and  attached  parts,  and  transmitted  to  the  driving-wheels. 

3.  The  tractive  power  or  adhesion  for  exerting  or  transmitting 
the  energy  produced ;  developed  through  the  frictional  resistance  to 
sliding  of  the  drivers  on  the  rail. 

482.  The  amount  available  of  each  of  these  forces  is  : 
Boiler  power. — Li7nited  by  the  quantity  of  steam  which  can  be  pro- 
duced in  a  boiler  of  admissible  weight  and  size. 

Cylinder  power. — hidefaiitely  great.  The  cylinder  is  a  mere  trans- 
mitting machine  for  the  transformation  of  one  form  of  energy  into  an- 
other, and  can  be  adapted  (within  wide  limits)  to  the  transmission  of  any 
amount  of  power  (ft. -lbs.)  in  any  desired  ratio  of  speed  (ft.)  to  force 
(lbs.)  by  mere  variation  of  proportions. 

Tractive  power. — Limited  by  the  total  weight  of  the  machine  and 
the  proportion  thereof  which  can  be  placed  on  the  coupled  driving-wheels. 

483.  Thus  it  is  seen  that  the  limit  to  the  work  which  can  be  done  by 
any  well-designed  engine  lies  either  in  the  boiler  power  or  in  the  adhe- 
sion, and  never  in  the  cylinder,  which  latter  always  has,  or  should  have 

*  The  writer  had  gone  more  fully  into  the  theory  of  the  locomotive  than  was 
absolutely  essential,  and  he  finally  concluded,  more  fully  than  was  wise,  in  the 
belief  that  a  broader  general  knowledge  of  the  locomotive  by  civil  engineers 
would  in  many  ways  conduce  to  good  practice;  but  in  order  to  keep  the  volume 
within  reasonable  size  he  finally  concluded  to  abbreviate  this  chapter  very  ma- 
terially from  his  original  draft.  Much  of  the  data  thus  prepared  was  thought 
to  be  entirely  new,  and  still  more  of  it  has  not  been  systematically  presented  in 
treatises  on  the  locomotive,  but  it  must  be  given  in  another  form,  if  at  all. 


40C 


CHAP.   XL— THE  LOCOMOTIVE  ENGINE. 


(in  any  engine  of  ordinary  type),  power  in  excess  of  either  what  can  be 
transmitted  by  the  adhesion  or  developed  through  the  boiler,  or  both. 
That  the  cylinder  power  should  be  in  excess  of  one  or  the  other  of  the 
other  two,  under  all  ordinary  circumstances,  as  it  is,  is  plain.  The  ulti- 
mate power  of  the  engine  is  fixed  by  the  weakest  one  of  these  three 
forces.  Two  of  them  can  only  be  increased  by  radical  modifications  of 
the  machine,  while  the  other  can  be  made  as  great  as  desired  (within 
wide  limits)  by  trifling  modifications  of  detail,  affecting  cost  and  weight 
but  very  slightly.  Therefore,  it  is  plain,  it  would  be  inexcusable  neglect 
not  to  make  the  link  in  the  chain  whose  strength  we  can  control  strong 
enough  to  certainly  utilize  the  full  strength  of  the  other  two,  which  we 
cannot  control,  without  a  radical  change  in  the  machine ;  so  that  the 
ultimate  power  of  the  machine  as  a  whole  should  never,  at  any  time  or 
under  any  circumstances,  fall  by  mere  negligence  in  design  below  the 
limits  fixed  by  natural  causes. 

484.  That  the  comparative  conditions  stated  in  regard  to  the  possi- 
bility of  increasing  these  three  forces  do  in  fact  prevail,  is  evident  from 
the  data  as  to  comparative  weights  of  the  various  parts  of  a  locomotive 
engine  given  in  Table  126:  To  increase  the  boiler  power  OF  these 
ENGINES  10  PER  CENT  (assuming  it  to  be  possible  at  all  without  exceed- 
ing the  admissible  load  per  wheel  or  the  limits  of  physical  possibility) 
means  an  increase  of  nearly  10  per  cent  in  the  weight  of  the  boiler  and 
at  least  5  per  cent  in  the  weight  of  the  rest  of  the  engine.  As  this  would 
increase  the  available  adhesion  it  v/ould  naturally  lead  to  increasing  the 


Table  126. 

Comparative  Weight  in  Lbs.  of  the  Various   Parts  of  a  Locomotive 

Engine. 


" 

Total 

Weight  in 

Service. 

Lbs. 

Boiler  and  At- 
tached Parts 
varying  there- 
with. 

Cylinders, 
Valve-gear, 

and 

Connecting 

Rods. 

Running 
Gear. 

Frame. 

Cab, 
Smoke-box, 

Lagging-, 
and  Miscel. 

Water. 

Metal. 

Trimmings. 

Light  American 

Consolidation,  Penn.. 
ClassI 

Per  cent .  - 

60,807 
100. 0 

91,640 
100. 0 

6,000 
9.9 

9,543 
10.4 

15,989 
26.3 

24,262 
26.5 

10,032 
16.5 

15,397 
16.8 

16,663 

27.4 

26,119 
28. s 

5,121 
8.4 

7,500 
8.2 

7,002 
ir-5 

8,819 
9.6 

The  light  American  engine  is  that  given  in  detail  in  Table  133  ;  the  ConsoHdation  is 
given  in  detail  in  Tables  129  and  132.  The  singular  constancy  of  ratio  in  the  weights  of 
these  widely  different  locomotives  is  notable. 


CHAP.    XL— THE  LOCOMOTIVE  ENGLNE,  40I 

cylinders  correspondingly,  but  even  without  doing  so  we  have  an  increase 
of  about  7  per  cent  in  the  weight  of  the  machine. 

485.  To  INCREASE  THE  CYLINDER   POWER  lO  PER  CENT  we  havC  Only 

to  decrease  the  size  of  the  drivers,  effecting  an  actual  decrease  in  the 
weight  of  the  machine.  For,  since  the  cylinder  pressure  (which  let  =  C), 
whatever  it  be,  acts  with  a  leverage  of  half  the  stroke  (=  s)  against  a  lev- 
erage of  half  the  diameter  of  the  driver  (=  R),  we  have,  for  the  tractive 
force  exerted  by  the  cylinders, 

sC       ^  ^      TR 
T  =  —^  and  C  =  — . 
R  s 

To  increase  T  by  any  amount  without  changing  either  the  stroke  (s) 
or  the  diameter  of  the  cylinder  (C)  we  have  only  to  decrease  R.  This, 
however,  is  at  the  expense  of  increasing  the  piston  speed,  because,  as  the 
driver  is  made  smaller,  it  must  turn  so  much  oftener  per  mile. 

486.  To  increase  the  cylinder  power  10  per  cent  without  increasing 
the  piston  speed,  however,  nothing  more  is  required  than  the  addition  of 
from  2  to  8  per  cent  to  the  weight  of  the  cylinders  and  attached  parts 
alone,  the  remainder  of  the  machine  remaining  unaffected  except  in  a 
few  trifling  details.  Whether  the  increase  be  2  or  8  per  cent  depends 
chiefly  on  how  it  is  effected — whether  it  be  by  merely  lengthening  the 
cylinder  or  by  increasing  its  diameter;  but  in  either  case  the  total  addi- 
tion to  the  weight  and  cost  of  the  machine  is  trifling.  Assuming  8  per 
cent  added  to  the  weight  of  the  cylinders,  it  amounts  (see  Table  126)  to 
but  a  little  over  one  per  cent  of  the  whole  weight  of  the  engine. 

487.  Cylinder  power  may  also  be  increased  after  the  machine  is  com- 
pleted by  the  simple,  but  ordinarily  not  permissible  or  wise,  expedient 
of  increasing  the  boiler  pressure.  It  has  also  been  not  unfrequently  de- 
creased in  the  same  way,  so  as  to  be  smaller  than  either  the  boiler  power 
or  traction,  with  unfortunate  results  upon  the  efficiency  of  the  engine. 

488.  To   INCREASE  THE  TRACTIVE   POWER    lO   PER  CENT,    Or   by  any 

other  amount,  we  must  either  increase  the  load  per  drivers  or  the  num- 
ber of  drivers,  or  both.  The  possibility  of  increasing  the  load  per  wheel 
is  strictly  limited  by  that  which  the  permanent  way  and  structure  will 
sustain.  The  load  per  wheel  is  in  practice,  and  for  certain  reasons  may 
properly  be  in  theory,  greatest  with  those  engines  (fast  passenger  engines) 
which  have  and  require  the  least  amount  of  total  tractive  power.  To  in- 
crease the  number  of  drivers  we  must  take  a  new  type  of  engine,  and 
here,  too,  the  range  is  strictly  limited.  A  few  special  engines  excepted, 
the  largest  number  of  drivers  now  in  practical  use  on  a  large  scale  is 
eight  (Consolidation  and  Mastodon  types),  and  the  least,  four  (American 
type),  with  a  few  extra  fast  but  very  heavy  engines  having  only  a  single 
26 


402  CHAP.    XL— THE  LOCOMOTIVE  ENGLNE. 

driving-axle.  In  any  case,  to  increase  tractive  power  lo  per  cent  we 
must  increase  the  load  on  drivers  by  some  40  per  cent,  which  means  in- 
creasing the  total  weight  of  the  machine  by  from  50  to  60  per  cent.  We 
have,  therefore,  as  the  addition  to  weight  of  engine  : 

To  increase  boiler  power  10  per  cent.     .   .     7  to    8  per  cent. 
To  increase  cylinder  power  10  per  cent.    .     i  to    i|-     " 
To  increase  tractive  power  10  per  cent.  .  .  50  to  60      " 

Proving  the  statement  made,  that  cylinder  power  is  a  mere  matter  of  ad- 
justment, readily  capable  of  indefinite  increase,  and  hence  should  always 
be,  as  it  generally  is,  in  excess  of  the  other  two. 

489.  For  the  very  reason  that  the  amount  of  cylinder  power  is  a  mere  detail 
of  mechanical  design,  having  no  natural  limit  in  either  direction,  it  furnishes  a 
convenient  measure  of  relative  capacity  and  power  for  comparing  one  engine  with 
another.  In  other  words,  cylinders  of  the  same  size  can  be  said  with  far  more 
exactness  to  give  engines  of  always  equal  power  than  a  similar  identity  in  any 
other  one  detail  of  the  locomotive.  A  "17  X  24"  engine,  which  is  now  looked 
on  as  the  standard  or  unit  type,  may  be  either  a  fast  passenger  or  a  slow 
freight  engine,  but  it  will  always  be,  roughly  speaking,  of  about  the  same 
weight  and  cost,  and  will  ordinarily  exert  and  be  capable  of  exerting  about  the 
same  amount  of  power  (foot-pounds)  in  the  same  time. 

490.  This  is  therefore  a  very  common  and  often  all-sufficient  description  of 
an  engine,  when  it  is  desired  to  give  a  general  idea  in  a  few  words  of  its  charac- 
ter; but  this  should  not  lead  to  the  mistaken  conclusion  (as  it  sometimes  does) 
that  the  cylinder  is  an  important  element  of  design  in  a  locomotive  in  the  sense 
of  being  a  governing  element  by  which  its  power  in  service  is  limited.  On  the 
contrary,  the  logical  order  of  design  (but  not  necessarily  for  that  reason  the 
order  that  a  practised  designer  will  follow)  is — 

First,  to  fix  the  total  admissible  or  desired  weight  of  the  machine. 

Secondly,  (in  a  freight  engine)  the  proportion  of  this  weight  which  can  be 
utilized  for  adhesion,  or  (in  a  passenger  engine)  the  largest  boiler  power  which 
can  be  gotten  without  exceeding  that  weight. 

Thirdly,  to  adapt  the  boiler  power  and  adhesion  to  each  other;  and, 

Fourthly,  to  fix  the  size  of  the  cylinders  to  correspond,  making  sure  to  have 
them  large  enough. 

There  is  a  serious  disadvantage  in  having  cylinders  unnecessarily  large  for 
the  work  to  be  done,  due  to  external  and  internal  radiation,  which  limits  some- 
what the  wide  discretion  specified,  but  not  so  greatly  as  to  affect  the  substance 
of  what  has  been  said. 

491.  The  boiler  power  of  a  locomotive,  like  that  of  any  other  source 
of  energy  or  dynamic  force,  is  ultimately  measurable  in  foot-pounds  per 


CHAP.    XI.— THE  LOCOMOTIVE  ENGINE. 


403 


Jiour,  or  other  unit  of  time.  So  far  as  boiler  power  is  concerned,  there- 
fore, a  locomotive  is  capable  of  hauling  any  load  whatever  if  the  speed 
be  made  low  enough,  or  of  attaining  any  speed  whatever  at  the  expense 
of  the  load  hauled. 

Horse-powers  or  other  equivalent  units  are  merely  certain  multiples 
of  foot-pounds.  Whatever  the  name  of  the  unit  for  the  measurement  of 
energy,  it  is  always  made  up  of  the  three  elements  of  lifting  a  certain 
weight  through  a  certain  distance  m  a.  certain  tz'me  against  the  natural 
force  of  gravity,  gravity  being  the  only  constant  and  ever-present  force 
with  which  we  are  familiar,  and  hence  a  natural  unit  for  comparison. 

492.  The  tractive  power  is  measurable  only  in  pounds,  being  a  mere 
static  or  dead  force,  serving  for  the  transmission  of  energy,  like  a  belt  or  a 
shaft,  but  not  alTecting  its  amount.  The  tractive  power  is — with  impor- 
tant limitations  to  be  considered — an  approximately  constant  quantity  at 
all  speeds  and  under  all  circumstances. 

493.  Therefore,  remembering  (i)  that  the  cylinder  power  is  not  an 
element  in  fixing  the  working  power  of  an  engine,  and  (2)  that  speed 
includes  the  two  elements  of  time  and  space,  which,  with  the  third  ele- 


cjjmbinina-fhefwD elements  oFK'^'F^'^^  \^^^d 
\fT.orMiiesj  \l 


Time. 


Fig.  97.— Indicating  the  Manner  of  adapting  the  same  Boiler  Power  to  Passenger  or 

Freight  Service. 


ment,  weight  or  force,  make  up  the  three  which  are  necessary  for  the 
exact  description  of  the  amount  of  any  kind  of  power,  we  may  express 


404  CHAP,   XL— THE  LOCOMOTIVE  ENGINE. 

graphically  the  variations  which  can  be  made  in  the  manner  of  utilizing 
or  distributing  the  power  of  an  engine  as  follows  (Fig.  97)  : 

494.  On  a  pair  of  co-ordinate  axes  intersecting  at  O,  Fig.  97,  let  dis- 
tances on  the  vertical  axis  OA  represent  pounds  of  tractive  power,  and 
distances  on  the  horizontal  axis  OC  represent  the  compound  unit  speed, 
including  the  two  primary  units,  distance  and  time. 

Then  the  capacity  of  any  given  boiler,  which  is  measurable  only  by  a 
product  of  the  three  units,  lbs.  x  ft.  x  time,  may  be  represented  on  such 
a  diagram  by  a  rectangle  of  a  given  fixed  area  iOABC,  OA'B'C, 
OA"B"C")  which  may  be  proportioned  in  any  ratio  of  height  to 
length  desired,  provided  the  total  area  included  within  it  be  not  exceeded. 
The  number  of  such  possible  rectangles,  as  will  be  apparent  from  the 
figure,  is  infinite. 

As  a  matter  of  mere  mathematical  curiosity,  of  no  immediate  practical 
moment,  it  may  be  noted  that  if  an  hyperbola  be  drawn  passing  through  the 
point  B,  with  the  axes  OA,  OC,  as  asymptotes,  any  point  B'  on  it  will  be  the 
apex  of  a  rectangle  of  always  equal  area. 

495.  Each  one  of  these  rectangles  will  represent  a  possible  locomotive, 
each  different  from  the  other,  which  may  be  designed  to  fit  the  same 
boiler, — with  this  sole  limitation  :  The  tractive  power  in  pounds  of  ordi- 
nary forms  of  locomotives  is  a  limited  quantity,  which  cannot  be  indefi- 
nitely increased  ;  and  consequently  at  a  certain  point  on  the  diagram  A' 
we  reach  a  vertical  limit,  beyond  which  it  is  not  possible,  by  any  ordinary 
device,  to  increase  the  tractive  power.  It  follows  directly  from  this  fact 
that  we  have  a  certain  minimum  of  speed  OC,  below  which  it  is  not  pos- 
sible to  decrease  the  speed  and  still  utilize  the  full  power  of  the  boiler  by 
increasing  the  load  hauled.  As  might  naturally  be  expected,  this  limita- 
tion is  at  times  very  inconvenient,  when  it  is  desired  to  obtain  the  maxi- 
mum hauling  capacity  regardless  of  speed,  as  in  engines  for  yard  service 
or  for  working  on  heavy  grades.  It  is,  in  fact,  practically,  the  most 
serious  theoretical  defect  of  the  locomotive.  Various  exceptional  de- 
vices are  employed  to  evade  it  in  part,  the  simplest  and  most  common  of 
which  is  to  carry  the  water  supply,  and  sometimes  the  fuel  also,  upon  the 
driving  wheel-base.  A  still  more  radical  remedy  is  mentioned  in  par. 
511,  and  yet  another  device  is  the  so-called  traction-INCREASER,  throw- 
ing a  part  of  the  weight  of  the  tender  on  the  drivers  for  the  time  being  by 
cylinders  attached  to  the  piston,  or  by  various  combinations  of  levers. 
Finally,  the  device  of  a  rack  between  the  rails,  or  of  a  central  rail  which 
the  driving-wheels  grip  by  spring  power  or  other  pressure,  enables  the 
gravity  of  the  engine  to  be  wholly  dispensed  with  for  furnishing  the  trac- 


CHAP.    XI.— THE  LOCOMOTIVE  ENGINE.  405 

tive  force,  by  substituting  for  it  frictional  adhesion,  and  thus  removes  all 
limit  whatever  to  the  load  that  a  given  boiler  can  move,  provided  the 
speed  be  made  slow  enough. 

496.  When  this  is  done,  all  limits  to  the  diagram  in  Fig.  97  are  like- 
wise removed  :  so  that  it  then  becomes  literally  true  that,  so  far  as  boiler- 
power  is  concerned,  there  is  no  limit  whatever  to  either  the  speed  of  a 
locomotive  or  to  the  load  it  can  haul,  provided  one  decreases  as  the 
other  increases ;  but  since  the  load  to  be  hauled  can  in  no  case  be  de- 
creased below  the  weight  of  the  engine  itself,  a  limit  of  possible  speed  is 
soon  reached  as  well  as  of  tractive  force,  and  the  limit  of  expediency  in 
each  direction  is  much  narrower  than  that  of  possibility. 

A  very  interesting  and  instructive  study  of  the  differences  of  designs  in 
locomotives  and  of  the  causes  therefor,  which  the  writer  feels  compelled  to 
omit,  may  be  made  by  constructing  diagrams  similar  to  Fig.  89  for  various 
actual  locomotives;  laying  off  the  load  on  drivers  on  the  vertical  axis  ;  taking 
the  boiler  power  as  proportional  to  the  heating  surface,  and  adding  various  de- 
tails of  grate-area,  etc. 

497.  It  will  be  sufficiently  clear  from  what  has  preceded,  that  in  the 
practical  working  of  engines  a  deficiency  in  any  one  of  the  three  co-ordi- 
nate forces  which  when  combined  m.ake  the  complete  machine  will  be 
shown  in  the  following  ways: 

1.  If  adhesion  or  tractive  power  be  the  smallest  of  the  three,  the  en- 
gine will  slip  her  drivers. 

2.  If  boiler  power  be  the  S7nallest,  the  boiler  pressure  as  indicated  by 
the  steam-gauge  will  fall,  and  the  engine  will  from  this  fall  of  pressure 
be  unable  to  turn  the  wheels. 

3.  If  cylinder  or  engine  power  be  the  smallest,  the  engine  will.be  stalled 
while  utilizing  to  the  utmost  a  full  pressure  of  steam  and  while  yet  un- 
able to  slip  its  drivers. 

498.  The  last  is  either  an  evidence  that  the  engine  is  out  of  the  ser- 
vice for  which  it  was  designed,— as  for  instance  a  fast  passenger  engine 
hauling  freight  trains, — or  it  is  an  evidence  of  bad  design.  It' is  one  of 
the  most  discreditable  faults  an  engine  can  have,  for  the  reason  that  it 
is  an  entirely  unnecessary  sacrifice  of  a  portion  of  its  capacity  for  work, 
and  it  is,  naturally,  a  fault  of  rare  occurrence.  It  has  occurred  in  in- 
stances on  a  considerable  scale,  however,  as  an  effect  of  cutting  down 
the  permitted  boiler  pressure  to  120  lbs,  after  copying  the  general  pro- 
portions of  engines  designed  to  carry  130  or  140  lbs.  The  effect  of  such 
action  on  the  pounds  of  tension  which  can  be  exerted  is  the  same,  and 


406  CHAP.    XI.— THE  LOCOMOTIVE  ENGINE. 

as  injurious,  as  if  the  boiler  power  itself  had  been  reduced,  which  latter^ 
however,  does  not  at  all  follow  from  the  reduction  of  pressure  (par.  552). 

499.  The  indication  of  deficient  hauling  power  first  above  specified,, 
slipping  of  drivers,  is  that  which  should  first  occur  in  all  well-designed 
freight  engines ;  for,  since  hauling-power  and  not  speed  is  the  desidera- 
tum in  such  engines,  the  boiler-power,  however  small  (within  limits),  can 
be  made  to  exert  an  indefinitely  great  force  in  pounds  at  the  expense  of 
speed,  by  proper  design  of  the  engine;  which  can  hence  be  so  designed 
that  the  boiler  shall  be  able  to  exert  continuously  a  force  always  in  ex- 
cess of  the  tractive  power  when  at  its  maximum  (as  when  using  sand) 
by  a  little  at  least,  in  order  that  the  full  measure  of  the  latter  may  in  all 
cases  be  utilized. 

500.  This  theoretical  principle  is  limited  in  part  by  this  fact:  Convenient 
operation,  requires  that  it  should  not  be  too  easy  to  slip  the  drivers  under  ordi- 
nary conditions  but  should  require  nearly  a  full  head  of  steam  to  do  so,  or  the 
difficulty  of  throttling  the  pressure  just  right  (par.  527)  will  lead  to  too  frequent 
slipping.  Hence  it  is  desirable  that  the  cylinder  power  should  be  only  a  little 
in  excess  of  the  adhesion,  and  from  this  it  may  result  that  the  ultimate  maxi- 
mum of  adhesion,  when  using  sand  on  a  dry  rail  with  boiler  pressure  perhaps  a 
little  low,  cannot  be  advantageously  realized.  There  are  also  certain  disad- 
vantages in  an  over-large  cylinder,  from  greater  loss  by  radiation,  condensa- 
tion, etc.,  as  well  as  some  advantages.     See  also  foot  of  page  408. 

501.  But  it  is  probable  that  all  these  disadvantages  have  been  over-esti- 
mated, or  the  whole  question  inadequately  considered,  in  designing  many  of 
the  engines  now  running,  a  considerable  minority  of  which  cannot  utilize  the 
full  ultimate  adhesion,  and  are  in  consequence  compelled  to  haul  smaller  loads 
than  they  otherwise  might ;  although  most  freight  engines  can  slip  their  drivers 
in  ordinary  working,  when  starting  or  running  very  slowly,  and  do  so  liberally. 
No  well-designed  engine  will  slip  its  drivers  when  running  at  speed,  undess  the 
rails  are  in  bad  order,  as  the  average  cylinder  pressure  is  then  much  lower  than 
in  starting  (par.  594).  Over-frequent  slipping  of  drivers  is  an  evidence  of 
want  of  skill  or  care  in  the  engineman.  He  can  with  ease  slip  the  drivers  with 
the  lightest  train  or  with  no  train  at  all,  and  in  fact  must  use  care  not  to,  unless 
the  cylinders  are  too  small  for  the  engine,  because  only  an  infinite  force  can 
set  in  motion  the  lightest  body  instantly. 

502.  The  second  indication  of  deficient  hauling  capacity  above  speci- 
fied, deficiency  of  boiler  power,  is  the  only  one,  in  theory,  by  which  a 
passenger  engine  should  ever  fail ;  since  a  fraction  only  of  its  weight,  if 
on  the  drivers,  will  give  a  hanling  power  in  pounds  far  in  excess  of  the 
2.V2^\\2i}c>\^  foot-pounds  of  boiler  power  at  a  high  speed  in  feet  per  minute. 
Neither  do  passenger  engines  often  fail,  in  fact,  for  any  other  cause,  be- 
tween stations,  on  moderate  grades.  The  necessity  of  starting  heavy  trains 


CHAP.  XI.— THE  LOCOMOTIVE  ENGINE. 


407 


quickly,  however,  and  of  maintaining  a  high  rate  of  speed  even  on  long, 
heavy  grades,  makes  the  demand  for  adhesion  on  passenger  engines  very 
unequal,  and  at  times  very  great,  so  that  it  is  often  in  practice  the  actual 
limiting  cause  which  it  is  desirable  to  increase.  It  is  not  essential  to  do 
this  permanently.  Any  device  which  increases  the  load  on  the  drivers 
temporarily,  especially  for  stopping  or  starting,  answers  every  purpose, 
and  a  better  purpose  in  fact  than  a  permanent  increase.  Such  attach- 
ments are  now  in  use  on  extra-fast  engines  and  to  a  limited  extent  on 
others,  and  it  is  probable  that  their  use,  or  that  of  some  equivalent,  might 
be  greatly  extended,  for  both  passenger  and  freight  engines,  without  any 
disadvantage  at  all  comparable  to  the  gain. 

503.  But  however  well  an  engine  may  have  been  designed  for  the 
average  contingencies  of  ordinary  service,  when  the  engine  is  once  in 
service  there  are  limitations  to  or  variations  in  the  efficiency  of  each  of 
its  three  primary  forces  which  have  an  important  effect  upon  the  load  it 
can  haul,  and  which  we  need  to  consider. 

In  the  following  Tables  127  to  137  are  given  a  variety  of  data  as  to 
the  dimensions,  weight,  cost,  and  life  of  locomotives  which  we  shall  have 
occasion  to  use  or  refer  to,  which  are  here  grouped  together  for  conven- 
ience of  reference. 

Table   127, 
Comparative  Dimensions  of  Engines  of  the  American  Type. 


Weight  on  drivers. . 

Weight  on  truck 

Weight,  total  (lbs.). 


Grate  surface. 


Fire-box 
Tubes... 
Total . . . 


Heat'g  surf  ce 
Barrel  of  boiler 

Diameter  of  drivers 

Tender : 

^^^-      iTotal 

capacity -j  (.Q^j  (lbs.).... 

Wheel-base  : 

Driving 

Total  engine 

Tender 

Engine  and  tender 


Cylinders. 


Mason. 
1873. 


40,000 
22,000 
62,000 

sq.  ft. 

16.38 

105 

906 

lOII 

46" 
66" 


2,250 


No. 
Pac. 

1884. 


54,350 
19.450 
83,800 

sq.  ft. 
16. 

1335 

51" 

62" 


27,900 

29,438 

57,338 

2,800 

6,105 

8'  6" 

^3'  zVa" 


^H" 


Brooks. 
1884. 


48,000 
26,000 
74,000* 

sq.  ft. 
16.45 

^103 

E990 

1093 

48' 

67' 


2,640 


22   7 
42'  6' 


C,  B. 

&Q. 


53,600 
27,600 
81,200 

sq.  ft. 
17.6 
98. 
I  968. 
1066. 
49^" 
69" 


24,^S3 
37,467 
61,650 
2,750 
14,550 

8'  6" 
22'  6H" 
14'  11" 
44'  9" 


24  Cylinders. 


C,  B. 
&Q. 


54-500 
28,300 
82,800 

sq,  ft. 

17.7 

T02. 

1 958. 

1060. 

J  69"  p. 
165"  ft. 


24,183 
37,467 
61,650 
2,750 
14,550 


6" 
6W 


Mason 
1884. 


00,000 
32,000 

TOC,000 

sq.  ft. 

18. c 

^    145- 

E 1230. 

1375- 

54" 

68" 


3,600 


West  Shore. 


A. 

64,000 
32,000 
96,000 

sq.  ft. 

34- 

128. 

E  1084. 


B. 

62,500 

32.000 

94-500 

sq.  ft. 

17- 

128. 

E1084. 


1212.         1212 

55" 
68" 


34,000 
30,000 
64,000 
3,000 
10  000 


15'    8" 
47'   4V8' 


*  Weight,  empty,  66,000  lbs.,  leaving  8000  1 


nrenisof  boiler  and  fire-box,  and  two  men. 


408 


CHAP.  XI.— THE  LOCOMOTIVE  ENGINE. 


Table  128. 
Comparative  Dimensions  of  Mogul  and  Ten-wheel  Engines. 


Moguls. 

1 

Ten-wheel. 

Baldwin 
18x24. 
1873. 

Brooks 
18x24. 
1883. 

N.S. 
B.  &  0.       Wales. 
19x24.     (Baldwin) 
1883.           18x26 

1884. 

i 
Baldwin 
18x26. 
1873. 

1 

Brooks 
19  X  24. 
1883. 

66,000 
11,000 
77,000 

sq.  ft. 
16. 

948. 
105 1. 
50" 
52" 

72,500 
13,500 
86,000* 

sq.  ft. 

17- 
114. 
1141. 
1255- 
52" 
55%" 

58,000 
20,000 
78,000 

sq.  ft. 
14.4 
94. 

1014. 

1 108. 
50" 
54" 

73iioo 
21,400 
94,50ot 

sq.  ft. 
22  6 

Weight  on  truck 

17,000 
96,000 

sq.  ft- 
•  17 

1 1066: 
1189. 

&' 

31^500 
41,200 
72,700 
3,600 
10,000 

15'  0" 
23'  2" 
14'  6" 

46'    2>^" 

Weight   total  (lbs)     

Grate  surface      .            ... 

(  Fire-box 

128.4 
1422.4 
15  "JO  8 

1  Total 



52" 
55%" 

60" 

Tender : 

Wf'^ht'^  Load     ■■■■.■'■;■.■■.■.■ 

1*^^-  1  Total.'.........::::: 

Canacirvi  Water  (galls.) 

Capacity -j  ^^^^  ]y^^^  .   ..   . 

2,200 

2,880 

2,200 

2,880 

_  Wheel-base  : 
Driving                    

15' 
22'  8" 

is'  6" 
23'  0" 

%  .■ 

14'  0" 
25'  3" 

Tender                   

Engine  and  tender 

45'  7" 

*  Weight,  empty,  78,000  lbs.,  leaving  8000  lbs.  for  contents  of  boiler  and  fire-box. 
t  Weight,  empty,  84,300  lbs.,  leaving  10,200  lbs.  for  contents  of  boiler  and  fire-box. 

The  Baltimore  &  Ohio  Mogul  carries  140  lbs.  of  boiler  pressure,  affording  a  maximum 
average  cylinder  pressure  of  some  119  lbs,  (85  per  cent  of  boiler  pressure).  At  this  rate 
the  cylinder  tractive  force  is  17,184  lbs.,  or  about  J  weight  on  drivers.  In  most  American 
engines  it  is  about  J,  and  in  some  as  low  as  0.30. 

The  tendency  in  recent  years  has  been  strongly  toward  increase  of 
weight  and  boiler  power  with  the  same-sized  cylinders,  as  Tables  127  to 
130  and  Table  142  bring  out  very  clearly.  Three  concurrent  causes  have 
brought  this  about :  (i)  The  material  increase  in  steam  pressure,  which 
makes  a  smaller  C5dinder  do  much  more  work  ;  (2)  the  higher  average 
speed  of  trains,  which  necessitates  larger  boiler  power  to  maintain  it ;  and 
(3)  the  fact  that  the  more  perfect  track  has  justified  and  the  lower  rates 
required  loading  engines  up  to  the  last  limit  of  their  tractive  power,  and 
it  was  necessary  to  have  as  much  as  possible  under  all  conditions  of  rail 
and  weather. 


CHAP.  XI.— THE  LOCOMOTIVE  ENGINE. 


409 


Table  129. 

Comparative  Dimensions  of  the  Original  and  Present  Standard  Con- 
solidation Locomotive  of  the  Pennsylvania  Railroad,  and  of  the 
West  Shore  Standard  Consolidation. 


Size  of  cylinders 

Weight  on  drivers 

'■        "    truck 

Total  wheel-base 

Driving-wheel  base 

Diameter  of  drivers 

Working  pressure 

Boiler: 

Inside  diam.  smallest  boiler-ring 

T  K^^  ]  No.  and  size  (outside) 

luDes^  Length 

I  Length 

Fire-box-' Width 

^  Depth 

Grate  surface 

(  Fire-box . . 

Heating  surface^  Tubes 

(  Total 

Smallest  inside  diameter  chimney. . . 
Height  top  of  rails  to  top  of  chimney 

Tender : 

(  Empty 

Weight  -<  Load 

(Total 

c-p-»y]S".:  .•.•.•.•.:•.•.•.■.■.■.■.::::: 

Wheel-base 

Engine  and  Tender  : 

Total  wheel-base = . . . 

Length  over  all 


Class  I. 

1876. 


20  X  24" 

79,400  lbs. 

12,240  lbs. 

21'  6" 

13'  8" 

50" 
125  lbs. 

53%" 
138,  23^" 
12'  11" 

96" 

34J^" 
42  to  61" 

23  sq.  ft. 

92  "    " 

E  1,166  "   " 

1,2^8  "   " 


22,770  lbs. 
33,000    " 
55,770    " 
3,000  galls. 
8,000  lbs. 


47    l, 
56'  9% 


Class  R. 


Increase. 


20  X  24" 

100,600  lbs. 

14,025  " 

21'  9" 

13'  10" 

50" 
140  lbs. 


59" 

183,  2^" 

13'    III" 

107" 

42" 

57  to  591^" 
31.2  sq.  ft. 

167  "    " 
E  1,564  "  " 
1,731  "  '■ 
18" 
15'  o" 

23,800  lbs. 
33,000  " 
56,800  " 
3,000  galls. 
8,000  lbs. 
15'  4" 


48'  9'' 
58'  sJ^' 


None. 
27  p.  c. 
14.6    " 


None. 
12  p.  c. 


10.5  p.  c. 

32.6  " 


II. 5  p.  c. 


35-6  p.  c. 
81.5     " 
34-2 

t" 


4-5  P-  C. 

None. 
1.8  p.  c. 

None. 


I'  2" 
2' 3%' 


West  Shore. 


20  X  24" 

88,000  lbs. 

16,000    " 
21'  7" 
14'  o" 
50" 

140  lbs.  (?) 


55" 
169,  2I4" 
13'  4%" 

95%" 

343^" 

23  sq.  ft. 


120 
Ei,34o  "    " 
1,460  "    " 

'is'  6#" 


29,000  lbs. 
35,000    '• 
64,000    " 
3,000  galls. 
10,000  lbs. 
15'  8" 


47'  7' 
56'  8H 


The  following  are  some  further  details  in  respect  to  the  changes  in  the  latest  Pennsyl- 
vania Consolidation  from  the  earlier  design  : 

Cylinders. — Unchanged :  diameter  of  piston-rod,  size  of  ports,  trav-el  and  outside 
lap  of  valves,  size  of  slide-blocks.  Piston-head,  i  in.  thicker ;  cylinders,  2  in.  farther 
apart  (7  ft.  2  in.)  ;  inside  lap,  none  (in  place  of  ^  in.)  ;  lead,  ^  for  |  in.;  steam-pipe,  19.6 
for  18  sq.  in.;  each  blast-nozzle,  13.8  for  11. 2  sq.  in. 

Journal. — All  increased  materially.  Driving-axles,  from  6^  X  7J  to  7  X  8| ;  truck- 
axles,  from  4I  X  7^  to  5X89  ;  crank-pin,  from  41  and  5  to  5  and  6  in.  Coupling-rod 
and  journals  unchanged.,  3^-  in. 

Boiler. — Unchanged :  material  (steel;  wrought-iron  tubes),  distance  between  centres 
of  tubes  (3I  in.);  thickness  fire-box  plates  (|  in.  outside  ;  y%  in.  inside),  tube-plates  (i  in.). 
Barrel-plates,  \  and  1  in,  for  |  in.;  butt-joints,  welted  inside,  for  lap.  Water  grate  for 
shaking  grate. 

Tender. —  Unchanged :  tank,  19  ft.  x  43  in.  high. 

The  West  Shore  Consolidation  was  designed  by  the  late  Howard  Fry,  one  of  the  most 
eminent  of  American  mechanical  engineers,  and  was  designed  to  include  all  the  latest 
improvements  up  to  its  date. 


4IO 


CHAP.  XI.— THE  LOCOMOTIVE  ENGINE. 


Table  130. 

Comparative  Dimensions   of   Engines  more  Powerful  than  the  Con- 
solidation Type. 


Size  of  cylinders 

Weight  on  drivers 

"        "    truck  ... 

Total  wheel-base 

Driving  wheel-base 

Diameter  of  drivers 

Working  pressure 

Boiler  : 
Inside  diam.  smallest  boiler-ring. , 


Tubes 


No.  and  size  (outside). 
1  Length. 


(  Length. 
Fire-box -(  Width.. 


Mastodon  Type. 
(8  drivers  ;  4  truck-wheels.) 


Central 
Pacific. 


I  Depth 

Grate  surface 

I  Fire-box 

Heating  surfaced  Tubes 

\  Total 

Smallest  inside  diameter  chimney. . . 
Height  top  of  rails  to  top  of  chimney 

Tender : 

(  Empty 

Weights  Load 

(Total 

capacity^Sf.-.-.-.v.-.v;::::;:::::; 


Wheel-base 

Engine  and  Tender  ; 

Total  wheel-base 

Length  over  all 


19  X  30" 
106,050  lbs. 

16,950   " 

24'   T-T-V^' 
15'    9'/ 

135  lbs. 


54      , 
166,  2I4" 
12' 

13'  aV^' 

39)4  to  58^" 

25.74  sq.  ft. 

182  "    'I 

I   1,076  "    " 

1,258  "    " 

20" 
15'  6^" 


26,000  lbs. 
37,000 
63,000    " 
3,000  galls. 
12,000  lbs. 
15'  oH" 


53'   i^" 
64'  o" 


Lehigh 
Valley. 


20  X  26" 

82,432  lbs. 

19,264    " 

23'  2" 

13'  °%" 

48" 
125  lbs. 


SI 
199,  z" 

10'  iiy2" 

11'  6" 

34" 

435^  to  521^" 

32  sq.  ft. 

179  "    '' 

I  995     ^     ^ 

1,174  ' 

17" 

14'  7" 

23,400  lbs. 

30,418    " 
53,818    " 
2,575  galls. 
8,960  lbs. 


55  4 


"  El  Guber- 

nador" 

(Cent.  Pac). 

(10  drivers; 

4  truck- wh' Is) 


21  X  36" 
121,600  lbs. 

32,400  " 
28'  11" 
19'  j" 

57" 
140  lbs.  (?) 


178,  2^'' 


50,650  lbs. 
35,000    " 
85,650    " 
3,000  galls. 
10,000  lbs. 


65'  5' 


Decapod 

(Baldwin). 

(10  drivers; 

2  truck- wh'ls) 


22  X  26" 

128,000  lbs. 

16,000    " 

24'  4" 


45' 


64" 

268,  2" 

12'  g%'> 

10'  x" 

39^" 


80,000  lbs. 
3,500  galls. 


These  four  engines  are  as  yet  the  most  powerful  in  the  world.  A  Fairlie  engine 
weighing  about  85  gross  tons  and  having  two  six-wheel  driving-trucks,  each  with  17X  22 
cylinders,  with  two  Bissell  (pony)  trucks  at  each  end,  is  running  on  the  Iquique  Railway, 
in  Peru.     Other  heavy  locomotives  are  given  in  Table  137. 

The  Central  Pacific  Mastodon  (the  original  of  the  type)  has  hauled  20  loaded  cars,, 
weighing  422  tons,  up  a  long  grade  of  116  ft.  per  mile.  By  Table  170  it  should  haul  421 
tons.  At  8  miles  per  hour  it  is  reported  to  have  shown  an  average  pressure  of  124  lbs. 
per  square  inch  in  the  cylinders.  "  El  Gubernador,"  cutting  off  at  five-sixths  stroke,  at  a 
speed  of  6^  miles  per  hour,  showed  an  average  of  115  lbs.  with  130  lbs.  boiler  pressure, 
or  88  per  cent,  which  is  much  nearer  to  boiler  pressure  than  is  often  possible,  and  de- 
velops the  enormous  tractive  power  of  32,039  lbs. ,  or  just  39  lbs.  more  than  one  fourth 
the  weight  on  drivers.  As  this  is  about  the  very  utmost  the  cylinders  can  do,  it  indicates 
that  the  cylinders,  large  as  they  are,  might  with  advantage  be  larger,  or  the  boiler  pres- 
sure higher. 


CHAP.  XI.— THE  LOCOMOTIVE  ENGINE. 


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413 


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CHAP.  XL— THE  LOCOMOTIVE  ENGLNE, 


Table  133. 

Weights  in   Detail  of  an  Old   Illinois   Central    Passenger    Engine, 
i6  X  22  Cylinders. 

[Abstracted  from  a  record  taken  by  Mr.  M.  N.  Forney.] 


Weights— Lbs. 


Brass. 


Wrought 
Iron. 


Cast 
Iron. 


Wood,  etc. 


Total. 


Boiler  sheets,  rivets  and  stay-bolts 

Braces,  crown-bars,  etc 

Tubes  and  copper  thimbles  .   .    .. 
Ring  for  dry-pipe, furn'e-door,etc. 

Dome   

Dry-pipes 

Throttle-valve,  etc   

Steam  and  exhaust  pipes 

Petticoat-pipe 

Blower 

Smoke-box  door 

Smokestack 

Grate  

Ash-pan 


Total  Boiler 


Frames 

Boiler-braces. 
Bed-casting  . 


Total  Frames. 


Cylinders 

Steam-chest 

Valves 

Pistons ,. . 

Cross-head  guides 

Connecting-rods 

Crank-pins 

Driving-wheel  boxes. 

Valve-gear 

Reverse-lever 

Pumps 

Pump-check  valves. . . 

Total  Machinery. 


Driving-wheel  centres..   . 

"      tires 

"     axles 

Truck- wheels 

"      axles 

"      frames,  boxes,  etc 

"      check-chains 

Driver  springs,  steel 

"      attachments 

Truck  springs 


Total  Running  Gear. 


no 
36 


117 
112 


436 

39 


6,299 

1,635 

3,034 

90 

24 

103 

no 

II 

52 

38 

45 

452 

175 

314 


17 
845 

93 
193 
377 


336 

200 

1,333 


12,382 


3,552 
628 


912 


609 
166 
6 
740 
221 
253 


3,360 
1,033 

604 
1,181 

131 
416 
506 
337 


7,568 


2,795 
805 
132 
262 
240 
42 

430 

984 

19 

163 


5,324 


107 
,884 


1,058 


136 


136 


640 


6,299 

1,635 

3,034 

147 

944 

246 

316 

398 

52 

54 

390 

652 

1,508 


15,989 


3,552 
628 


5,121 


650 


3,106 
921 
232 
389 
933 
768 
166 
548 

1,724 
242 
852 
151 


10,032 


5,964 

3,360 

1,140 

1,884 

604 

2,311 

131 

416 

516 

337 


16,663 


CHAP.  XL— THE  LOCOMOTIVE  ENGINE. 


415 


Table  133. — Continued. 


Summary. 


Weights— Lbs. 

Brass. 

Wrought 
Iron. 

Cast 
Iron. 

Wood,  etc. 

Total. 

Safety-valve      .  .         

53 
73 
10 
66 

68 

60 

139 

4 

15 
114 

26 
26 
57 
21 
144 
9 

ID 

44 

lOI 

337 

56s 

757 

II 

329 

7 

12 
50 
283 

52 

120 

446 

77 

68 



334 

1,083 
320 

49 
874 

86 

Steam  grauEres  and  cocks     

99 

Cylinder  cocks  and  fittings 

79 

Sand-box                

472 

Bell  and  clapper         . 

89 

Hand-rail          

107 

596 
2,098 

Cab  and  foot-board    

Pilot 

Head-light  bracket 

1,154 
143 

Lagging  and  sundries  . 

1,317 

Total  Fittings 

790 

2,437 

1,115 

2,660 

7,002 

Tender  tank  

19 
■■■'64 

3,515 

37 

1,124 

1,272 

29 

880 

1,330 

143 

103 

722 

3,952 

'"536 
32 

1,596 
46 

3 
2,327 

12 

670 
106 

3,515 
162 
4,173 
3.952 
1,272 
536 

880 

Fittings  for  ditto 

Truck-wheels 

Axles  and  collars 

Bearintjs  and  fittings  for  ditto 

Springs                                   .... 

3,596 
295 

Brakes  "         

Total  Tender 

83 

8,330 

6,987 

3,118 

18,518 

Boiler  

201 

■"882 

72 

790 

12,382 
4,209 
3,042 
7,568 
2,437 

3,394 
912 
5,972 
8,373 
x,ii5 

12 

■••136 

650 

2,660 

15,989 
5,121 
10,032 
16  66- 

Frame                

Machinery  . 

Running  gear 

F"ittings               

7,002 

Total  Engine    

1,945 

29,638 

19,766 

3,458 

54,807 

Tender 

83 

8,330 

6,987 

3,118 

18,518 

Total  Engine  and  Tender. . . . 

2,028 

37,968 

26,753 

6,576 

73,325 

To  which  is  to  be  added,  for  weight  of  engine  in  working  order,  for  contents  of 

boiler,  fire-box,  and  two  men  in  cab,  about 

And  for  contents  of  tender,  coal 8,000  lbs. 

water  (1600  galls.) 13,500    " 


Giving  for  total  weight  of  engine  in  service . 
And  for  total  weight  of  tender 


60,807 
40,018 


Approximate  total  engine  and  tender  in  service 100,825 

No.  0/  separate  pieces,  large  and  small  (not  j  i^  f  °fi°5 '"^°A 

including  nails).....   ^  __   -^  In  tender 1,366      ■ 

'     Total 6,270 

The  proportion  0/ brass  is  now,  in  general  practice,  much  less  than  in  the  above  engine. 


4i6 


CHAP.  XL— THE  LOCOMOTIVE  ENGLNE. 


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f ) 

0 

CJ 

'U 

2^ 

a:  o 
-a  S 
0  ^ 


O! 


<u 


<u    o 

So  _cn 

^    n 

^'% 
o 


c   c 
H  .2 

H     O 


4i8 


CHAP.  XI.— THE  LOCOMOTIVE  ENGINE. 


Table  135. 

Length  of  Service,  Mileage,  and  Life  of  Locomotives  on  Pennsylvania 

Railroad  (P.  R.  R.  Division)  to  January  i,  1S85. 

Fassenzer  Locomotives. 


Years 

Number  of  Locomotives. 

Total  Mileage  (i  =  looo  miles). 

Average 

IN 

Service. 

Total. 

In  Ser- 
vice. 

Con- 
demned. 

Highest. 

Lowest. 

Average 
per  Loco. 

Miles  per 

Loco,  per 

Year. 

8 

9 

10 

II 

12 

13 

14 

15 

16 

17 

18 

2 

7 
3 
8 
6 

3 
II 

7 
9 

5 
4 

2 

7 

I 

7 
3 

I 

9 

7 
8 

4 
3 

0 
0 

2 

I 

3 
2 
2 
0 

I 
I 
I 

382 
345 
294 
389 
563 
428 
613 
589 
780 
688 
637 

344 
248 
264 

247 
307 
319 
286 

397 
351 
431 

488 

363 
302 
282 
316 
391 
369 
401 
483 
491 
536 
559 

45,372 
33  566 
28. 165 
28.702 
32-573 
28.349 
28,657 
32,204 
30,689 

31.519 
31,067 

13 

65 

52 

13    . 

780 

247 

412 

31,707 

Freight  Loco?notives. 


5- 
6. 

7. 
8. 

9- 
10. 
II. 
12. 

13. 
14. 

15. 
16. 

17. 
18. 
19. 
20. 
21. 
22. 

I3i 


33 

33 

0 

23 

23 

0 

10 

10 

0 

13 

13 

0 

27 

24 

3 

15 

II 

4 

12 

7 

5 

43 

29 

14 

44 

32 

12 

36 

15 

21 

26 

14 

12 

21 

12 

9 

16 

8 

8 

17 

12 

5 

2 

0 

2 

4 

I 

3 

3 

I 

2 

4 

0 

4 

349 

245 

104 

197 

220 

279 
289 
314 
317 

416 
454 
440 
426 
561 
532 
485 
430 
400 
519 
464 
431 


561 


130 

147 
192 
240 
225 
201 
202 
206 

235 
244 
271 
271 

324 

30S 

351 
378 
354 
387 


130 


161 
176 
250 
262 

273 
260 
287 
302 
318 
339 
378 
392 
397 
371 
375 
438 
393 
411 


301 


32,263 
29,391 
35,705 
32,715 
30,349 
25.973 
26,063 
25,172 
24,425 
24.215 
25.204 
24.529 

23.337 
20.620 
19.758 
21,905 

18,733 
18,684 


22,331 


The  above  locomotives  were  intended  to  give  a  fair  average  of  engines  of  all  ages  and 
classes  of  service,  and  cover  about  60  per  cent  of  the  whole  number  in  service.  The  loco- 
motives having  the  highest  mileage  (780,182  miles,  passenger;   561,139  miles,  freight) 


CHAP.  XI.— THE  LOCOMOTIVE  ENGINE. 


419 


were  both  still  running;  and  in  good  order.  In  the  original  abstract  the  miles  run  were 
given  to  units,  but  have  been  abbreviated  to  the  nearest  thousand. 

Running  of  engines  first  in  first  out  was  first  introduced  in  1878,  six  years  before  date 
of  table,  and  abnormally  increases  the  average  mileage  of  the  younger  engines  relatively 
to  the  older.  Allowing  for  this,  there  is  Httle  evidence  of  diminution  of  yearly  mileage 
with  age. 

Special  Performances. — Engine  273,  479,248  miles  in  ten  years  ;  $8336.42  for 
repairs,  or  1.74  cents  per  mile  run  ;  251,552  miles  before  being  off  its  wheels  for  general 
repairs.  Engine  274,  504,301  miles  in  ten  years  ;  $6534.45  for  repairs,  or  1.29  cents  per 
mile  run  ;  243,476  miles  before  being  off  its  wheels,  except  once  as  the  result  of  an  acci- 
dent.    Engine  1047,  41,510  miles  in  three  months,  or  4.61  miles  per  day. 


Average  mileage  of  72  passsenger  engines,  1S82, 
"  "  175  freight  engines,  1882, 


Highest.  Lowest.  Average. 
79,258  30,039  45,936 
58,711         30,000         36,584 


About  80  or  90  per  cent  of  the  breakages  of  the  working  parts  of  engines  on  the  Penn- 
sylvania Railroad  occur  immediately  on  starting  from  a  stop. 

A  paper  before  the  German  Society  of  Mechanical  Engineers  showed  that  out  of  39 
engines  (presumably  a  fair  average) — 

10  of  shortest  life  were  broken  up  after 6.5  years. 

10  of  longest  life  were  broken  up  after 28. 5     " 

15  were  in  use  less  than  20  years,  and  average  of  all  was  .         .         .         .         .  20.2     " 

The  average  mileage  of  German  locomotives  (Table  69)  is  11,870  miles  per  year,  indi- 
cating a  very  short  locomotive  life  in  miles. 

Table  136. 
Approximate  Life  of  Various  Parts  of  the  Locomotive. 


Part. 


Authority. 

Life  in 
Years. 

Life  in 
Miles. 

M.  M.,L.  S.  &M.  S.  Ry. 

22  to  24 

700,000 

j-R.  P.Williams 

20 

■ 

450,000 

to   500,000 

L.  S.  &  M.  S.  Reports.... 

10 

800,000 

M.  M.  Association..  

7 

250,000 

L.  S.&M.  S.  Reports.... 

... 

] 

800,000 

to    1,000.000 

McDonnell,  M.  Inst.  C.E. 

10  to  14 

] 

320,000 

to    350,000 

M.  M.,  L.  S.  &  M.  S 

15 

450,000 

■ 

300.000 

to  350,000 

M.  M.,  L.  S.  &M.  S 

6 

180,000 

M.  M.,  Ph.  &  Reading... 

..». 

120,000 

M.  M.  Association 

10  + 

300,000 

M.  M.  Association 

8  + 

250,000 

Locomotines  as  a  luhole,  American 

"             "        "       English  (and  Eu- 
rope generally) 

Tenders,  Tanks 

"        Frames,  wood 

Boilers,  as  a  whole  {ex  partial  renewals) 

"        English  (prob.  an  av.  of  all  parts) 

U.  S.  "        "        "        " 

"  "    (bad  water) 

Fire-box    steel,     bituminous    coal     fuel 
(wood,  two  thirds  greater) 

Fire-box  steel,   anthracite  coal  (iron    or 
copper  fire-box,  about  one  third  only).. 

Fire-box    steel    {anthracite    fuel,     50,000 
miles  less,  passenger) 

Fire-box    steel    {a?ttkracite    fuel,    50,000 
miles  less,  freight) 


420 


CHAP.  XI.— THE  LOCOMOTIVE  ENGINE. 


Bad  water  estimated  to  reduce  these  last  averages  about  100,000  miles,  and  increase  cost 
of  maintenance  $750  per  year,  or  2J  to  3  cents  per  mile  run,  in  extreme  cases.  The  L.  S. 
&  M.  S.  is  an  unfavorable  road  in  this  respect.  Fractures  of  fire-box  sheets,  range  as 
an  average  of  3  years  (M.  M,  Ass'n  Reports)  over  xooo  engines  per  annum,  about  one 
sheet  for  10  engines  per  year  on  roads  with  bad  water,  and  thence  down  to  none  with 
pure  water.  Lowest  mileage  of  fractured  plates,  75,000;  highest,  150,000.  Occurs  only 
after  deposit  of  scale.  Nearly  all  fractures  (about  seven  eighths)  are  in  side  sheets,  vertical^ 
starting  just  above  fire. 

Washing  out  boilers. — Good  water,  England,  every  three  weeks.  U.  S.  average, 
about  one  month,  but  much  oftener  with  bad  water.  Thickness  of  steely  almost  univers- 
ally :  tube-sheet,  Tstoi^";  sides,  back,  and  crown,  jV';  barrel,  |". 


Fire-boxes  copper.— Gt.  No.  and  L.,  S.  C. 
&  D.  Rys.,  English  (pass,  and  freight).. 

Tubes.,  iron,  various  English  railways 

"  "       entirely  new  sets 


McDonnell 

McDonnell 

ioyrs.,L.S.&  M.S.  Reps. 


Mileage  Life. 


74,ooO' 

to    161,000 

120,000 

to   167,000 


360,000 


Ordinarily  taken  for  entirely  new  sets  at  half  the  life  of  the  engine,  with  one  or  morf^ 
piecings  at  ei\d  in  addition,  and  removal  once  in  i  to  if  to  2i  -f  years,  according  to  water, 
for  removing  scale.  On  Boston  &  Albany,  with  very  good  water,  tubes  are  never  re- 
moved nor  boilers  blown  out  except  for  repairs.     Other  lines,  once  in  6  to  8  years.    Brass 

tubes  not  essentially  different ;  require  cleaning  less  frequently. 

Mileage 
Tubes,  <5raw.— Average  of  English  returns,  passenger,  fair  water  (freight  Life. 

about  one  half  only) 200,000 

Maximum  reported  (McDonnell,  average  of  10  years) \  ^^  437,'ooa 

Axles,  iron  {drivers).—!..  S.  &  M.  S.  and  J.,  M.  &  L  (max.  before  removal)..  300,000 

"         "     (....^).-Enghsh -j  ,,  Jg;°- 

"  "      truck.— L.  S.  &  M.  S 100,00a 

Bearings  (<frzV'i?rj).— Various  railways,  per  te"  wear -J  ^^     56^ 

Highest  report,  D.,  L.  &  W.,  89.000  ;  lowest,  Philadelphia  &  Reading,  14,000. 

Tires,  steel. — 5'  6"  average  of  U.  S. ;  65,000  per  turning  ;  3  turnings 200,000 

In  heavy  service,  with  small  drivers,  near  about  half  this,  or 100,000 

(  6'  6" 196,600 

English  reports  very  nearly  the  same,  viz.  <    ,  ^„  S  106,000 

[^         {  to   150.000 

Driving-wheel  centres.— L.  S.  &  M.  S.  Reports 1,000,600 

Cylinders. — Same  as  engine. 

Frame.—"  A  question  of  accident"  (M.  M.  Assoc). 

Truck-wheels.- (About  av.  of  U.  S.,  28"  to  30"  wheels).    M.  M.,  Ph.  &  Rdg.  34,000 

Tender-wheels.— (About  average  of  U.  S.,  33"  wheels) 50,000  -|- 

Valves. — Common  slide-valve  between  facings  (M.  M.  Assoc.) 30,00a 

"        —Good  balanced,  several  patterns,  between  facings  (M.  M.  Ass'n) ^.^   100000 

Scrap  Value,  old  English  locomotives  (copper  fire-box,  brass  tubes),  about 
10  p.  c.  of  original  cost  of  materials. 

The  locomotives  of  the  Pennsylvania  Railroad  go  into  shop  for  general  repairs  once  in. 

18  to  20  months. 


CHAP.  XL— LOCOMOTIVE  RUNNLNG   GEAR. 


421 


Table  137. 

Miscellaneous   Extra   Heavy   Locomotives. 
(A  list  published  in  the  National  Car-Builder.) 


Road, 

Kind. 

Weight. 

Driv- 
ers. 

Cylin- 

Total. 

On  Drivers. 

ders. 

Passenge? 

'  Locomotives. 

96,200  lbs. 
92,700    " 
85,000    " 
80,000    " 
§  120,400    " 

102,000    " 

101,000    " 

%  1x5,000    " 

*  64,250  lbs. 

*  65,300    " 

t  35  to  45,000  lbs. 
t  56,000  lbs. 

68  in. 
78   ^' 
78   " 
6^   " 
60   " 

50  " 
46   ■' 
48   " 
48   " 

Pennsylvania 

Baldwin  Loc.  W'ks. 

Class  K... 

18x24  '• 
18x24  " 

18  X  22    " 

Boston  &  Albany. . . 
Pennsylvania 

Freight 
Reading 

u 

Tank  locomotive 

Locomotive. 

Consolidation 

Twelve  wheels  coupled 
Consolidation,  tank.... 

17X24    " 
20X24    " 

88,500  lbs. 
101,000   " 
X  100,000  " 
88,000   " 

A.,  T.  &  Santa  F^.. 
Central  Pacific 

17X24    " 
16X24    " 

*  On  four  wheels.        t  On  two  wheels,        %  Estimated.    §  Reported  weight. 


THE   RUNNING   GEAR. 

504.  The  distinctive  peculiarities  of  the  running  gear  of  American 
locomotives,  as  compared  with  foreign,  are  two:  the  swivelling  TRUCK 
in  front  (in  England  called  "  bogie"),  and  the  equalizing  levers  by 
which  the  load  is  kept  uniformly  distributed  on  the  four  or  more  drivers, 
and  the  effect  of  any  chance  irregularities  in  the  track  reduced  to  a 
minimum.  The  first  was  invented  by  John  B.  Jervis  in  1834,  before  the 
trial  of  the  Rocket  had  taken  place  ;  the  second  was  invented  by  Ross  M. 
Winans,  who  also  invented  the  double-truck  railway  car  which  has  be- 
come all  but  universal  in  this  country,  only  a  few  years  later.f 

505.  Both  of  these  inventions,  with  much  else  that  was  novel  and 
meritorious,  had  their  origin  in  the  necessities  of  the  earlier  years  of 
American  railways,  which  required  that  the  locomotives  should  be 
adapted  to  ready  passage  over  sharp  curves  and  imperfectly  surfaced 
track  and  road-bed.     Both  of  them  are  now  gradually  making  their  way 

II  A  crude  form  of  double-truck  car  was  shown  to  have  been  used  in  Quincy, 
Mass.,  before  Winans  invented  it,  so  that  Winans  was  unable  to  support  his 
-claim  for  patent;  but  he  reinvented  it  independently,  and  really  deserves  the 
credit  for  conceiving  of  and  introducing  it  as  the  normal  type  of  car. 


422  CHAP.  XI.— LOCOMOTIVE  RUNNING   GEAR. 

into  England  and  throughout  the  world  ;  and  both  of  them,  beyond 
doubt,  will  eventually  become  universal,  since  they  are  almost  equally 
advantageous  on  good  roads  and  on  poor  roads,  the  only  difference  being 
that  on  poor  track  they  are  absolutely  indispensable,  while  on  good  track 
they  are  not  indispensable,  but  merely  advantageous.  In  great  part,  we 
owe  to  them  two  advantages  which  experience  appears  to  indicate  that 
the  American  locomotive  possesses :  It  can  (at  least  it  unquestionably 
does)  haul  greater  loads  in  proportion  to  weight  on  drivers,  and  it  is  less 
readily  disorganized,  so  that  it  can  run  in  practice  (at  least  it  does)  a 
great  many  more  miles  in  a  day  and  a  year  (see  Tables  68,  69). 

The  extent  of  this  advantage  should  not  be  exaggerated.  It  does  not 
clearly  appear  that  on  first-class  track  (on  which  alone  English  locomo- 
tives can  be  run  at  all  to  any  advantage)  the  cost  of  locomotive  repairs 
per  mile  run  is  noticeably  different  for  either  type,  although  the  cost  per 
ton  hauled  is  enormously  in  favor  of  American  engines.  Nevertheless  it 
still  remains  true,  that  wherever  American  locomotives  have  fairly  come 
in  competition  with  those  without  their  distinctive  features,  as  m  Canada, 
Mexico,  South  America,  and  the  Australasian  colonies  (in  nearly  all  of 
which  the  right  of  decision  has  rested  in  English  officials),  they  have  in- 
variably obtained  the  preference,  with  exceptions  that  prove  the  rule. 

506.  The  original  type  of  American  locomotive,  still  distinctively 
known  as  the  "American"  type,  has  two  drivers  coupled,  spaced  8  ft.  to  S 
ft.  6  in.  apart  so  as  to  include  the  fire-box  between  them,  with  a  four-wheel 
truck  in  front.  Until  about  twenty  years  ago  this  type  was  all  but  uni- 
versal in  both  passenger  and  freight  service,  but  the  name  is  now  rapidly 
losing  its  appropriateness.* 

507.  At  the  present  time  there  are  the  following  types  in  common  use 
in  America. 

1.  American  (Table  127),  4  drivers,  4  truck  wheels  ;  stillapproved 
for  light  service,  but  passing  out  of  use  for  ordinary  freight  and  heavy 
passenger  service. 

2.  Mogul  (Table  128),  6  drivers,  2  truck  wheels  (pony  truck);  one  of 

*  Complete  illustrations  of  every  detail  of  the  ordinary  form  of  "  American"' 
engine,  with  outline  drawings  of  others,  may  be  found  in  the  "Catechism  of 
the  Locomotive,"  by  M.  N.  Forney,  and  drawings  and  descriptions  of  many 
examples  of  all  the  types  of  locomotives  here  named  in  "  Recent  Locomotives," 
both  published  by  the  Railroad  Gazette  of  New  York.  The  catalogues  of  the 
Baldwin  and  the  Rogers  Locomotive  Works  also  contain  views  and  many  of 
the  details  of  all  ordinary  types  of  locomotives,  with  much  other  interesting 
matter.     All  the  above  works  are  valuable  ones  for  the  engineer  to  own. 


CHAP.  XI— LOCOMOTIVE  RUNNING   GEAR.  423 

the  earliest  modifications  of  the  "  American"  locomotive  and  largely  used, 
but  in  rather  less  favor  than  formerly. 

3.  Ten-wheel  (Table  128),  6  drivers,  4  truck  wheels;  generally  pre- 
ferred to  the  Mogul,  and  at  one  time  bidding  fair  to  become  the  standard 
type  for  heavy  freight  service,  but  now  hardly  tending  to  multiply,  except 
as  a  substitute  for  the  American  for  heavy  passenger  service. 

4.  Consolidation  (Table  129),  8  drivers,  2  truck  wheels  ;  a  compara- 
tively recent  innovation,  invented  by  Alex.  Mitchell,  superintendent  of 
the  Lehigh  Valley  Railroad,  in  1872.  It  has  very  rapidly  won  its  way 
into  public  favor,  and  is  now,  it  is  hardly  too  much  to  say,  the  standard 
American  locomotive  for  heavy  freight  service,  and  is  fast  coming  into  use 
for  all  but  the  lightest  service. 

507.  These  are  the  only  types  which  can  be  said  to  be  in  general  use 
for  road  service,  but  in  addition  there  are  the  following  in  approved  but 
more  limited  use  : 

5.  Mastodon  (Table  130),  eight  drivers,  four  truck  wheels  a  very 
recent  design  introduced  by  Mr.  A.  J.  Stevens,  of  the  Central  Pacific 
Railroad,  in  1881,  and  said  to  be  rendering  most  excellent  service.  Some 
have  been  built  for  the  Lehigh  Valley.  It  has  not  as  yet  (1886)  been  in- 
troduced to  any  extent  on  other  roads,  but  it  is  exceedingly  probable 
that  it  will  be.  While  not  very  largely  increasing  the  load  on  the 
drivers,  which  is  not  feasible,  the  four-wheel  truck  and  greater  load 
thereon  not  only  makes  the  engine  run  better,  but  enables  the  boiler  to 
be  enlarged. 

6.  Forney,  a  type  invented  by  Mr.  M.  N.  Forney  some  twenty  years 
ago,  having  the  tender  and  engine  combined  on  one  frame,  the  tender 
running  in  front  and  its  truck  serving  in  lieu  of  an  engine  truck,  so  that 
the  weight  of  the  engine  itself  is  carried  wholly  on  the  drivers. 

508.  The  advantage  of  the  Forney  type  is  that  it  gives  more  tractive  power 
(adhesion)  for  the  same  size  of  engine,  by  placing  the  entire  weight  of  the  latter 
on  the  drivers.  Its  disadvantage  is  that  the  boiler  of  no  locomotive  engine 
can  generate  steam  enough  to  utilize  its  whole  weight  for  adhesion,  unless  at 
slower  than  ordinary  freight  speeds,  or  in  service  requiring  very  frequent 
stops,  as  will  be  seen  from  par.  551.  For  such  service  only  is  the  engine  well 
adapted,  and  for  such  service  only  has  it  come  into  use.  As  this  service  is 
the  exception,  the  quite  extensive  use  which  the  type  has  recently  been  given 
still  leaves  it  an  exceptional  type.  It  has  been  urged  for  use  in  general  ser- 
vice, but  is  not  well  adapted  for  it  in  the  respect  mentioned. 

509.  Other  types  of  engines  are  : 

7.  Double-Ender,  with  two  "pony"  trucks,  one   at   each   end,  or 


424  CHAP.  XI.— LOCOMOTIVE  RUNNING  GEAR. 

sometimes  with  one  "  pony"  and  one  four-wheel  truck ;  used  chiefly  for 
short-run  local  service. 

8.  Tank  Engines  ;  a  type  not  confined  to  any  especial  form  of  run- 
ning gear,  but  available  for  any  locomotive,  whenever  it  is  desirable  to 
have  very  great  adhesion  for  short  runs.  As  this  adhesion  can  only  be 
utilized  at  very  slow  speeds,  without  exceeding  the  boiler  power,  there  is 
no  economy  or  advantage  in  placing  a  tank  on  the  engine,  except  as  a 
temporary  resource,  unless  for  very  slow  speeds ;  and  hence,  naturally, 
very  small  drivers,  carrying  nearly  the  whole  weight  of  the  engine,  are 
usual  with  tank  engines. 

510.  This  type,  carried  one  step  further,  resuks  in — 

9.  Fairlie  Engine  ;  two  boilers  placed  back  to  back  with  a  single 
frame,  and  carrying  on  their  back,  the  entire  supply  of  both  fuel  and 
water.  The  two  "  trucks"  on  which  the  whole  is  carried  are  driving- 
wheel  bases,  each  carrying  their  own  cylinders,  which  are  supplied  with 
steam  through  a  swivelling  joint.  It  is  still  less  possible  for  engines  of 
this  type  than  for  tank  engines  to  utilize  their  great  adhesion  without 
exceeding  their  boiler  power,  except  at  the  slowest  speeds.  Consequently 
they  have  only  found  acceptance  for  work  on  very  heavy  grades  where 
great  tractive  power  is  necessary  and  slow  speed  no  objection,  and  for 
such  service  only  are*  they  suitable.  The  type  is  the  invention  of  the 
late  Robert  F.  Fairlie,  the  "apostle"  of  the  now  moribund  narrow-gauge 
movement,  and  was  pushed  by  him  energetically  for  many  years,  but 
without  success,  except  as  respects  localities  such  as  described  (as 
for  example  the  Mexican  Railway  described  in  Appendix  C),  where  the 
type  has  done  and  is  doing  good  service,  although  very  costl37to  mamtain. 

511.  Finally,  in  certain  extreme  cases,  where  still  greater  adhesion  is 
necessary  and  still  less  speed  desired,  there  is  a  device,  already  referred  to 
(par.  495),  by  which  the  paying  load  is  carried  on  a  platform  slung  be- 
tween two  tank  engines,  and  so  utilized  for  adhesion,  and  when  even 
these  devices  have  not  sufficed  to  give  necessary  adhesion  on  very  heavy 
grades,  reliance  upon  insistant  weight  to  give  necessary  adhesion  has 
been  abandoned  altogether,  except  as  an  auxiliary  resource,  and  recourse 
had  to  other  devices  noted  in  par.  495. 

512.  In  addition  to  the  previous  types  mentioned,  there  are  for  yard  use 
only — 

10.  Four-wheel  Switching  Engines. 

11.  Six-WHEEL  Switching  Engines. 

Both  of  these  are  made  either  tank  or  with  tender,  usually  the  latter.  They 
are  admirably  adapted  by  their   great  tractive   power  for  yard  work,  which 


CHAP.  XI.— LOCOMOTIVE  RUNNING   GEAR.  425 

demands  great  power  even  for  short  trains,  in  order  to  get  them  under  way 
easily,  and  they  are  only  used  for  such  service.  Neither  their  boiler  power 
nor  running  gear  is  adequate  for  high  speed,  and  in  fact  engines  with  trucks 
are,  as  a  rule,  preferred  even  for  yard  service. 

513.  In  all  these  various  types  the  load  on  the  drivers  is  equalized  by 
side  levers  connecting  the  springs,  whereas  in  foreign  locomotives  it  is 
not  customary  to  do  more  than  give  a  separate  spring  for  each  wheel. 
The  effect  of  this  equalizing  is  that  in  all  engines  of  the  "  American"  type, 
and  less  perfectly  in  the  other  American  types  of  engines,  the  loco- 
motive is  carried  in  effect  upon  three  points,  the  centre  of  the  truck  and 
the  centre  of  the  equalizing  system  on  each  side  of  the  boiler,  in  three- 
legged-stool  fashion,  which  ensures  perfect  contact  of  wheel  and  rail, 
and  uniform  distribution  of  pressure,  on  all  inequalities  of  track.  For  the 
same  reason  that  a  three-legged  stool  always  stands  solidly  on  any  surface 
however  rough,  while  one  with  four  or  more  legs  will  only  stand  solid 
on  a  plane  surface,  the  total  weight  is  always  evenly  and  fairly  distributed 
between  the  wheels,  however  rough  the  track. 

In  foreign  engines,  on  the  contrary,  which  are  not  equalized,  the  con- 
sequence of  this  or  some  other  and  unexplained  difference  of  detail  or 
of  administration  is  that  there  is  very  great  irregularity  in  the  pressure 
of  the  wheels  on  the  track.  The  exhaustive  experiments  01  the  late 
Baron  von  Weber  on  maintenance  of  way  showed  the  pressure  on  the 
rail  varying  all  the  way  from  zero  to  twice  the  average  load.  That  the 
elimination  of  this  irregularity  of  load  by  adding  equalizers  should  have 
a  certain  effect  to  increase  the  tractive  power  seems  reasonable,  and  that 
or  other  cause  (perhaps  only  greater  effort  to  utilize  to  the  utmost  the 
power  of  the  locomotive)  has  had  that  effect. 

514.  All  the  diverse  types  of  engines  for  road  service,  both  American 
and  foreign,  while  differing  in  almost  every  other  detail  of  their  running 
gear,  agree  in  this— that  in  every  case  (except  four-  and  six-v/heel  switch- 
ing engines)  there  is  either  a  truck  or  some  substitute  therefor  to  per- 
form the  office  of  pilot  for  the  driving-wheel  base.  Experience  has 
abundantly  shown  that  such  a  pilot  is  necessary  for  safety  at  high  speeds, 
or  on  rough  track,  and  advantageous  at  all  times.  The  different  methods 
for  accomplishing  this  end,  in  the  order  of  their  introduction,  are  as 
follows : 

1.  A  fixed  axle,  parallel  with  the  drivmg- wheel  axle,  but  carrying  a 
lighter  load  ;  the  normal  foreign  type. 

2.  The  ordinary  Ajnerican  four-wheel  truck,  consisting  of  four  wheels 
on  two  parallel  axles,  the  whole  swivelling  on  a  centre-pin  O,  Fig.  92. 


426 


CHAP.  XI.— LOCOMOTIVE  RUNNING   GEAR. 


3.  The  same  truck  with  a  swing  motion,  the  mechanical  details  of 
which  are  in  substance  similar  to  Figs.  loi,  103,  permitting  the  truck  to 
deviate  somewhat,  laterally,  from  the  axis  of  the  driving-wheel  base,  as 
Oa,  Fig.  100. 

4.  The  "pony'  or  Bissell  truck  (so  named  from  its  inventor),  consist- 
ing of  only  a  single  pair  of  wheels  on  a  single  axle,  but  with  its  axle 

attached  to  a  radius  bar  (constructed  in  prac- 
tice as  a  double  V-shaped  bar,  as  shown  by 
the  solid  lines)  so  that  the  pair  of  wheels 
■""  swivel  around  a  point  O,  Fig.  98,  6  to  8  feet 
in  the  rear,  thus  having  the  effect  to  compel 
the  single  axle  to  always  remain  parallel  with 
the  driving-axles  on  tangents,  while  permitting 
it  to  assume  a  radial  position  on  curves. 

I;  515.    All   these  four    plans    have    approxi- 

i  mately  the  same  object,  to  relieve  the  driving- 

i*^     '  wheel  flanges  of  the  task  of  guiding  the  driv- 

ing-wheel base  on  curves,  and  to  leave  them 
only  the  simpler  duty  of  holding  them  on  the 
rails  against  the  effect  of  chance  irregularities 
of  motion.  To  do  this,  if  it  be  effectually 
done,  it  is  plain  that  a  heavier  duty  must  be 
thrown  upon  the  flanges  of  the  forward  wheels 
than  properly  appertains  to  the  load  carried  on 
them,  and  apparently  these  diverse  plans  will 
accomplish  the  end  with  very  unequal  degrees 
of  efiiciency,  and  cause  very  unequal  derailing  moments  in  the  forward 
wheels.  Nevertheless,  each  and  all  of  them  have  been  approved  by 
experience  as  adequate  for  the  end  in  view,  nor  has  experience  shown  anv 
very  great  difference  in  the  coefficient  of  safety  of  each.  By  investigat- 
ing tlieoretically  the  mechanics  of  the  locomotive-wheel  base,  we  shall 
see  why  this  should  be  so,  and  at  the  same  time  gain  an  important  insight 
into  the  feasibility  of  using  various  types  and  sizes  of  locomotives  on 
different  alignments.  The  result  of  such  an  analysis,  which  follows  below, 
is  presented  in  Fig.  107,  page  433. 

516.  The  work  to  be  done  by  the  pilot-wheels  is  in  all  cases  the  same — to 
prevent  the  front  outer  driving-wheel  flange  from  grinding  against  the  rail  and 
compel  it  to  stand  away  from  the  rail,  or  at  least  relieve  its  pressure.  To  do 
this,  force  or  pressure  must  be  applied  at  some  point  on  the  axis  of  the  driving- 
wheel  base  sufficient  to  cause  it,  in  effect,  to  continuously   rotate;  because  it 


CHAP.  XI.— LOCOMOTIVE  RUNNING   GEAR. 


427 


compels  the  wheel-base  to  change  its  direction  to  follow  the  curve  sooner  than 
it  naturally  tends  to  do  so. 

The  force  (pressure)  in  pounds  necessary  to  cause  this  rotation  is  the  same, 
however  fast  or  slow  the  motion  of  rotation  takes  place  (the  work  done  in  foot- 
pounds per  second  only  varying),  and  varies  only  with  (i)  the  load  on  drivers, 
(2)  the  coefficient  of  friction,  which,  for  reasons  we  shall  shortly  see,  we  will 
take  at  one  third,  and  (3)  the  length  of  the  wheel-base.  The  rotation  may  take 
place  either  by  throwing  the  front  axle  inward  or  the  rear  axle  outward,  or 
both;  but  without  going  into  unnecessary  and  doubtful  details  as  to  which  is 
most  probable,  which  would  but  little  affect  the  final  result,  the  resisting  mo- 
ment of  the  driving-wheel  base  to  rotation  may  be  estimated  as  follows: 

Two-axle  driving-wheel  base,  of  length  =  /  and  total  ^  load  =  W\  letting 
r=  diagonal  distance  from  centre  of  wheel-base  to  each  wheel: 

Resisting  moment  M  =  Wr  X  coefficient  of  friction  (say  ^). 
Three-axle  wheel-base,  of  length  =  /  and  total  load  =  W  : 

Resisting  moment  J/=  {^Wr-\-^W7')  X  coefficient  of  friction. 
Four-axle  wheel-base  : 

Resisting  moment  AI  =z^W  {r-\- r)  X  coefficient  of  friction. 
The  values  of  rand  ?'  are  readily  computed  from  the  gauge 
and  the  length  of  wheel-base. 

This  resisting  moment  is  overcome  in  any  form  of  loco- 
motive-wheel-base by  a  force  applied  at  some  point  O,  Figs. 
98,  100,  acting  Avith  a  leverage,  which  let  =  L,  varying  with  the 
pattern  of  engine;  and  the  amount  of  this  force,  O,  is  readily 
determined  by  the  formula 

L 

517.  This  statement  of  the  action  of 
these  forces  is  incomplete  in  this,  that  a 
motion  of  rotation  of  the  driving-wheel 
base  can  only  be  produced  by  the  action 
of  a  COUPLE,  and  not  by  any  single  force. 
Actually,  therefore,  it  is  essential  that 
one  or  the  other  wheels  should  serve  as 
a  fulcrum,  to  enable  the  force  O,  Fig.  99, 
by  which  the  truck  causes  the  driving- 
wheel  base  to  rotate,  to  act  ;  but  which 
wheel  it  would  be,  or  whether  it  would 
be  any  one  single  wheel  for  more  than 
a  few  instants  at  once,  we  cannot  assert  with  certainty,  nor  would  the  action  or 


Fig.  99. 


Fig.  100. 


428  CHAP.  XI.— LOCOMOTIVE  RUNNING  GEAR. 

amount  of  the  force  0  be  very  greatly  affected  by  any  possible  differences  in 
this  respect. 

In  the  English  type  of  wheel-base,  three  parallel  axles,  the  two  rear  being 
driving  axles,  this  force  0  is  of  necessity  all  supplied  by  the  flange  of  the  outer 
leading-wheel.  In  the  American  type  of  wheel-base,  Figs.  99,  100,  it  is  of  neces- 
sity all  supplied  by  the  centre-pin  of  the  truck  ;  but  it  is  to  be  remembered,  as 
respects  the  wheel-bases  with  more  driving-axles,  like  Fig.  98,  that  it  is  not 
essential  that  the  driving-wheel  flanges  should  be  wholly  relieved  of  all  work  in 
guiding  the  wheel-base,  but  only  that  they  should  be  so  greatly  relieved  that 
such  flange  pressure  as  remains  to  them  shall  not  be  injurious. 

518.  The  lateral  force  at  O,  Figs.  98,  100,  being  given,  the  more  important 
question  remains— the  amount  of  additional  lateral  strain  thrown  by  it  on  the 
leading  wheel  a,  Fig.  99.  In  every  locomotive,  as  they  are  actually  constructed, 
this  wheel  is  in  most  danger  of  mounting  the  outside  rail  on  curves.  The  flange 
pressure  of  this  wheel  may  be  determined  as  follows  : 

In  the  American  type,  Figs.  99,  100,  the  action  of  the  forces  on  the  leading 
truck  is  as  follows  : 

As  a  result  of  guiding  the  truck  itself,  considered  as  a  separate  vehicle,  the 
reaction  of  the  rail  against  the  front  outer  flange  a  must  be  enough,  as  we  have 
seen  (par.  302),  to  cause  three  of  the  wheels,  a,  b,  c.  Fig.  99,  to  rotate  around 
d SLS  a.  centre;  or,  calling  the  load  on  each  truck- wheel  w,  and  the  coefficient  of 
friction  i  (instead  of  ^,  as  for  the  driving-wheel  base,  on  account  of  the  lighter 
load),  we  have  for  the  force  /,  Fig.  99, 

The  wheel  c  normally  stands  away  from  the  rail,  as  shown  in  Figs.  99  and 
20,  and  resists  being  crowded  up  against  the  outside  rail  with  a  force  =/= 
enough  to  slide  the  three  wheels  d,  c,  d. 

519.  The  force  O  is  equally  divided  between  the  two  axles  ab  and  cd.  Fig. 
99,  so  that  we  have,  in  any  engine  truck  of  an  American  engine  : 

Pressure  of  leading  wheel  a.  Fig.  99,  against  outside  rail  =  \  force  C-j- force/. 
Pressure  of  rear  wheel  c  against  outside  rail  =  \  force  O  —  force/. 

The  latter  is  true  because  the  force /on  the  rear  axle  is  a  negative  or  resist- 
ing force.  If  \0  be  greater  than  /  the  wheel  will  be  crowded  up  against  the 
rail,  but  there  will  always  be  a  force  = /tending  to  cause  it  to  leave  the  rail,  so 
that  the  net  pressure  against  the  rail  will  be  only  the  difference  between  the 
two  forces. 

520t  When  the  truck  is  a  swing-motion  truck  the  distribution  of  the  forces 
is  in  no  way  affected.  A  certain  amount  of  lateral  motion  takes  place  first — 
that  is  all — sufficient  to  bring  about  the  equilibrium  of  forces  sketched  in  Fig. 
loi,  as  one  might  take  out  the  slack  of  a  chain  before  it  comes  to  a  bearing, 
and  then  the  force  O  acts  as  before. 

Right  here  we  touch  upon  the  leading   theoretical,  and  in  fact  practical. 


CHAP.  XI.— LOCOMOTIVE  RUNNING   GEAR. 


429 


objection  to  the  swing-motion  truck,  although  its  true  cause  is  not  always  ap- 
preciated. We  have  seen  (par.  516)  that  the  force  O  is  a  constant,  regardless 
of  the  radius  of  curvature.  Consequently,  whenever  this  force  is  called  into 
action  at  all,  the  same  amount  of  lateral  deflection,  Oa,  Figs.  100,  loi,  102,  will 
take  place,  or  tend  to  take  place,  unless  stopped  by  the  driving-wheel  flange 
coming  in  contact  with  the  rail,  which  it  is  the  object  of  the  truck  to  prevent. 


Fig.  ioi. 


Fig. 


521.  This  is  not  at  all  what  is  desired,  since  it  correctly  adapts  the  wheel- 
base  to  motion  on  only  one  curve,  that,  namely,  on  which  the  distance  Oa,  Fig. 
102,  =  the  offset  to  the  curve  at  0  from  a  tangent  to  the  curve  at  c.  This  must  be 
on  a  comparatively  sharp  curve  if  the  very  object  of  the  swing-motion  (to  enable 
the  locomotive  to  pass  sharp  curves  easily)  is  to  be  attained.  On  easier  curves 
the  amount  of  deviation  which  the  swing-motion  permits  is  as  much  too  great 
as  that  of  the  fixed  centre-pin  is  too  small.  On  all  easier  curves  the  wheel-base 
will  tend  to  assume  a  position  something  like  Fig.  102,  which  is  still  less  favor- 
able  than  the  normal  position  of  an  American  engine  wheel-base,  without  the 
swing-motion,  outlined  in  Fig.  100.  It  is  true  that,  owing  to  the  splay  given  to 
the  links  of  the  swing-motion,  there  is  a  certain  amount  of  resistance  to  any 
lateral  motion,  however  slight;  but  this  is  not  sufficient  to  restrain  the  tendency 
to  assume  the  position  shown  in  Fig.  loi,  and  hence  has  little  remedial  effect. 


430 


CHAP.  XI.— LOCOMOTIVE  RUNNING   GEAR. 


522i  For  these  reasons  the  swing-motion,  although  very  largely  used,  has 
never  shown  the  advantage  over  the  fixed  centre  which  it  probably  would  if  the 
lateral  deviation  were  in  fact  proportioned  to  radius 
of  curvature,  as  it  is  often  assumed  to  be.  As  orig- 
inally designed  by  Mr.  Bissell  (for  "pony"  trucks) 
it  was  not  open  to  this  objection;  two  inclined 
planes  being  used,  in  the  manner  shown  in  principle 
in  Fig.  103,  which  offered  the  same  lateral  resist- 
ance however  much  or  little  motion  took  place. 
But  for  practical  reasons  (rapid  deterioration  of 
bearing  surfaces  and  impact  when  bearings  return 
to  the  centre)  this  form  has  passed  out  of  use.,  per- 
haps in  part  for  lack  of  giving  due  weight  to  the 
theoretical  advantages  which  it  undoubtedly  pos- 
sesses. 

523.  The   manner  in  which  the   two-wheeled 
Bissell  or  "  pony"  truck  (Figs.  104,  105)  relieves  the 
Fig.  103.  driving-wheel  base  of  lateral  strain  is  quite  differ- 

ent, and  much  less  clear.  Apparently  it  ought  not  to  assist  at  all,  except  to 
the  very  slight  extent  (especially  on  easy  curves)  by  which  the  resistance  of  the 
swing-motion  (Fig.  loi),  which  is  directly  over  the  axle,  resists  lateral  motion; 

for  it  is  free  to  swivel  around 
its  bearing  at  O  (Figs.  104  and 
98),  regardless  of  the  remain- 
der of  the  wheel-base.  It  is 
known  to  have  in  fact,  how- 
ever, a  very  material  effect 
upon  the  motion  of  the  wheel- 
base,  and  theory  very  readily 
indicates  to  us  why  this  should 
be. 

The    "pony"   truck    natu- 
rally tends  to  roll  forward  in 
Fig.  105.  ^  x\^\i\.  line,  parallel  to  itself, 

as  in  Fig.  104.  The  rigid  driving-wheel  base  behind,  and  not  its  own  flange  or 
its  coning,  as  we  shall  see,  compels  it  to  move  in  a  curve,  to  do  which  the 
driving-wheel  base  must  exert  a  stress,  (9,  Fig.  104,  in  the  opposite  direction 
to  the  arrow,  of  sufficient  magnitude  to  produce  motion  in  the  direction  ak. 
Fig.  105,  and  thus  slide  one  or  the  other  of  the  wheels  continuously  on  the  rail, 
compelling  the  leading  axle  to  move  in  a  curved  path  instead  of  a  straight  one. 
The  resistance  of  the  wheels  to  this  sliding  creates  one  or  the  other  (not  both) 


CHAP.  XL— LOCOMOTIVE  RUNNING  GEAR. 


431 


of  the  two  forces  represented  by  the  longitudinal  arrows  in  Fig.  104,  and  for 
the  force  0,  resulting  therefrom,  we  have 

(Fig.  104) 


O  =  (load  on  one  wheel  X  coef.  frict.)  X 


/  (Fig.  I04)' 


524.  Lest  the  wheels  should  run  toward  the  outside  rail,  and  from  coning  or 
otherwise  adapt  their  diameters  to  naturally  travel  in  a  curve,  we  have  this 
further  precaution: 

To  enable  both  the  pony  truck  and  the  transverse  axis  of  the  driving-wheel 
base  to  assume  radial  positions,  the  radius-bar  of 
the  pony  truck  should,  from  well  known  properties 
of  the  circle,  pivot  at  the  point  O  (Fig.  106),  mid- 
way between  c  and  the  ' '  pony"  axle.  If  shorter  than 
this,  as  at  0,  Fig.  106  (as  it  always  is),  the  driving- 
wheel-base  will  throw  the  rear  end  of  the  radius- 
bar  over  through  a  certain  distance  {ak.  Fig.  105) 
toward  the  outsidq  rail,  and  thus  create  in  it  a 
tendency  to  run  toward  the  inside  rail  and  away 
from  the  outside  rail.  This  tendency  is  increased 
by  the  fact  that  it  is  the  rear  and  not  the  centre  of 
the  driving-wheel  base  which  tends  (par.  294  and 
Fig.  20)  to  assume  a  radial  position,  the  front 
outer  driving-wheel  tending  of  itself  to  crowd 
hard  against  the  outer  rail. 

525.  These  two  causes  together  ensure  that 
the  pony  axle  shall  always  have  a  continuous  ten- 
dency to  run  toward  the  inside  rail  and  away  from 
the  outside,  and  if  the  radius-bar  be  made  too 
short  this  tendency  becomes  so  decided  that  inju- 
rious wear  results.     Thus,  in  a  Consolidation  en-  Fig.  106. 

gine  of  the  Norfolk  &  Western  Railroad  the  radius-bar  was  originally  only 
4  ft.  2  in.  long,  and  created  so  strong  a  tendency  to  run  to  the  inside  rail  that  it 
was  lengthened  to  5  ft.  6  in.  long,  with  very  beneficial  results.  Even  then  the 
point  O  was  some  9  ft.  ahead  of  the  centre  of  the  wheel-base,  c.  Fig.  106,  so  that 
it  was  still  much  shorter  than  was  apparently  required  to  enable  the  wheel-base 
to  adapt  itself  most  perfectly  to  the  curve. 

No  very  strong  tendency  in  the  pony  axle  to  run  toward  the  inside  rail 
is  necessary,  but  only  just  enough  to  ensure  the  driving-wheel  bas^  shall  in 
fact  modify  its  natural  path  in  the  way  outHned,  by  however  little,  since  if  any 
force  whatever  {0,  Fig.  104)  needs  to  be  applied  to  cause  the  pony  axle  to 
roll  in  the  curve  it  must  necessarily  be  adequate  to  slip  the  wheels  on  the 
rails :  the  stress  necessary  to  slip  them  a  little  is  as  great  as  to  slip  them  a 
good  deal. 


432  CHAP.  XI,— LOCOMOTIVE  RUNNING  GEAR. 

From  this  it  will  be  seen  that  \il^=  g  (Fig.  104)  the  lateral  force  at  0  neces- 
sary to  alter  the  path  of  the  leading  wheels  is  just  half  2,^  great  as  if  these  were 
a  fixed  axle  at  0,  in  the  English  style  (because  there  is  only  one  wheel  to  slide 
instead  of  two),  with  the  added  advantage  that  the  pony  axle  is  approximately 
radial  and  guided  by  the  wheel-base  behind,  so  as  to  relieve  the  pony  flanges 
of  strain,  and  thus  add  greatly  to  safety. 

In  addition  to  the  force  6>,  Fig.  104,  the  swing-motion  of  the  pony  truck  sup- 
plies any  desired  amount  of  additional  lateral  force,  directly,  whenever  the 
engine  is  running  on  curves  sharp  enough  to  develop  it  fully. 

526.  For  the  forces  acting  on  the  leading  outer  wheel  of  any  locomo- 
tive wheel-base,  then,  if  it  is  in  fact  to  perform  the  office  of  guiding  the 
complete  wheel-base  on  curves,  we  have  these  conditions  :  There  is  a 
vertical  component  equal  to  the  load  on  the  wheel,  and  there  is  a  hori- 
zontal component  equal  to  the  forces  determined  for  all  the  various  types 
in  pars.  516  to  525.  These  forces,  as  computed  for  a  great  variety  of  light 
and  heavy  engines  of  all  types,  have  been  plotted  in  Fig.  107,  which  rep- 
resents graphically  the  comparative  degree  of  safety  of  various  types  of 
locomotives  for  passing  curves;  and  the  surprising  degree  of  uniformity 
which  they  show  in  a  measure  tends  to  confirm  the  correctness  of  our 
conclusions,  since  experience  has  shown  that  there  is  in  fact  no  marked 
difference  in  safety  between  the  engines  themselves. 

Note  to  Fig.  107. — The  diagram  show§  in  magnitude  and  direction  the  resultant  of 
the  horizontal  and  vertical  forces  acting  on  the  front  outer  truck-wheel  of  locomotive 
wheel-bases  of  all  common  types  on  curves  of  any  radius  (the  same  being,  except  for 
unknown  variations  in  the  coefficient  of  friction,  uniform  for  all  radii). 

The  comparative  safety  may  be  considered  as  var}-ing — 

First.  With  the  direction  of  the  resultant,  as  being  more  or  less  inclined  to  the 
horizontal ;  those  most  inclined  being  the  safest,  other  things  being  equal,  since  the  re- 
sistance to  the  flange  mounting  the  rails  is  then  greatest. 

Secondly,  and  chiefly.  With  the  magnitude  of  the  resultant,  or  total  pressure  of  the 
wheel  against  the  rail. 

All  American  engines,  embracing  a  great  variety  of  designs  and  weights,  will  be  seen 
to  lie  within  the  small  quadrilateral  marked  out  by  the  points  i,  3,  10,  15.  The  more  com- 
mon English  types  cause  a  far  greater  pressure  against  the  rails,  but  as  a  compensating 
advantage  have  more  nearly  vertical  resultants. 

Details  as  to  all  the  locomotives  shown  may  be  found  either  in  "  Recent  Locomotives," 
Forney's  "Catechism  of  the  Locomotive"  (Railroad  Gazette),  or  Barry's  "  Railway  Ap- 
pliances" (Spon). 

Manner  of  Constructing  the  Diagram. 

The  vertical  ordinates  represent  the  load  in  pounds  on  the  front  outer  wheel. 

The  horizontal  abscissas  represent  the  lateral  stress  in  pounds  acting  on  the  wheel, 
which  consists  of  (a),  with  four-wheel  trucks  only,  the  flange  pressure  necessary  to  cause 
rotation  in  the  truck,  and  {b)  half  the  force  (9,  Figs.  99  and  104,  required  to  be  applied  at 


CHAP.  XI.— LOCOMOTIVE  RUNNING   GEAR. 


433 


434 


CHAP.  XI.— LOCOMOTIVE    TRACTIVE  POWER. 


the  centre-pin  of  the  truck  (or  all  of  it  in  the  case  of  two-wheel  "pony"  trucks)  to  produce 
rotation  of  the  driving-wheel  base. 

The  various  types  of  locomotives  shown  are : 


Mastodon. 
(4- wheel  truck.) 

Consolidation. 
(Pony  truck.) 

Ten-wheel. 
(4- wheel  truck.) 

Mogul. 
(Pony  truck.) 


I — Central  Pacific. 
2 — Lehigh  Valley. 

3 — Baldwin. 

4 — Pennsylv'a  (Class  I). 

5 — Baldwin. 

6 — Pennsylvania. 

7 — Baldwin. 

II — Heavy  Mogul. 


American. 
(4- wheel  truck.) 


English. 
(No  truck,  lead 
ing  axle.) 


9— Baldwin. 
10 — :Pennsylvania. 
12 — Enghsh  fast  passenger 
14 — Pennsylvania  fast  pas- 
senger. 
15— Old   (light)   fast  pas- 
l  senger. 

8 — Freight  type. 
Passenger  type. 


-1» 


TRACTIVE    POWER. 

527.  The  friction  between  the  driving-wheels  and  rails  which  prevents 
them  from  slipping  and  enables  them  to  propel  the  train  is  a  STATIC  or 
merely  resisting  friction,  as  distinguished  from  dynamic  friction,  or  that 
in  which  motion  takes  place  between  the  surfaces  in  contact,  with  result- 
ing destruction  of  energy.  Its  cause,  beyond  all  question,  is  an  absolute 
interlocking  of  the  roughnesses  or  projecting  fibres  of  the  surfaces  in 
contact,  as  cogs  might  interlock.  That  this  is  essentially  true  of  all 
friction  between  metallic  surfaces,  under  the  most  favorable  circumstances, 
was  curiously  shown  by  experiments  of  Mr.  Beauchamp  Tower  *  on  the 
most  finely  polished  and  completely  lubricated  journals:  a  mere  change  in 
the  direction  of  revolution  resulted  in  a  noticeable  but  temporary  increase 
in  the  coefficient  of  friction,  for  which  so  careful  and  competent  an  ob- 
server could  ascribe  no  other  cause  than  that  the  fibres  were  stroked  one 
way  by  continuous  revolution,  as  fur  might  be,  and  that  on  motion  being 
reversed  the  fibres  opposed  each  other. 

528.  Our  best  existing  evidence,  by  far,  of  the  general  laws  which 
govern  static  friction  between  rail  and  wheel  is  contained  in  two  papers 
by  Capt.  Douglas  Galton,  giving  the  results  of  experiments  on  brake 
efficiency  conducted  by  him  and  by  Mr.  Geo.  Westinghouse  in  1876. 
These  experiments  are  quite  unique  in  the  completeness  and  accuracy  of 
the  apparatus  used,  and  (what 'is  still  more  important)  in  the  thorough- 
ness and  technical  knowledge  with  which  the  records  were  analyzed,  and 
they  positively  contradict  the  assumption   sometimes   made,  that  the 


*  Trans.  Inst.  Mech.  Engrs. ,  1885.     See  Appendix  B. 


CHAP.  XI.— LOCOMOTIVE    TRACTIVE  POWER.  435 

coefficient  of  friction  between  rail  and  wheel  is  greater  at  low  speeds 
"on  account  of  less  time  for  new  surfaces  to  interlock."  * 

An  impression  that  the  adhesion  is  less  at  speed  has  been  derived,  in 
some  instances,  from  dynamometer  records,  which  shows  far  less  tractive 
pull  between  stations  than  in  starting.  This,  however,  results  merely 
from  the  fact  that  the  cylinders  are  not  able  to  exert  their  full  power  at 
speed,  and  has  no  real  connection  with  the  adhesion. 

No  error  of  moment  can  arise,  therefore,  from  assuming  that  the 
resistance  of  the  wheels  to  slipping  is  sensibly  constant  at  all  speeds.  It 
is  only  at  slow  speeds  that  the  precise  amount  of  adhesion  becomes 
important.! 

That  the  coefficient  of  adhesion  is  the  same  at  all  train-speeds  has  not  been 
experimentally  proven;  but  however  fast  the  motion  of  the  locomotive,  so  long 
as  the  drivers  do  not  slip,  the  adhesion  is  equally  static;  and  the  only  reason 
why  the  adhesion  should  be  less  at  high  speeds  is  that  the  fibres  are  afforded 
less  time  to  completely  engage  with  each  other.  That  this  difference  may  have 
some  slight  effect  is  possible,  but  as  the  available  cylinder  power  falls  far  more 
rapidly  with  increase  of  speed,  it  is  a  fact  which  is  not  important,  even  if  true. 

529.  When  slipping  has  once  begun,  however,  the  conditions  are 
very  different.  Chiefly  from  the  Galton-Westinghouse  experiments 
before  referred  to,  which  are  confirmed  from  other  sources  and  by  uni- 
versal experience,  we  may  derive  the  following  conclusions  as  to  the  gen- 
eral laws  which  govern  friction  between  rail  and  wheel ;  all  of  which  cor- 
respond closely  with  the  results  of  modern  investigations  of  other  kinds 
of  friction. 

*  "The  Pennsylvania  Railroad  Company,"  by  James  Dredge:  Appendix  on 
Brake  Trials.     The  exact  language  of  Capt.  Galton  on  this  point  is: 

"  The  amount  of  frictlonal  resistance  which  determines  the  point  at  which 
the  rotation  of  wheels  is  checked  varies,  it  is  true,  in  the  different  experiments. 
The  ratio  which  it  bears  to  the  weight  upon  the  braked  wheels"  varies  from  .29 
to  .35,  averaging  .25.  "But  it  [the  variations]clearly  represents  simply  the 
adhesion  between  the  wheel  and  the  rail,  and  varies  only  with  this,  and  not 
with  the  speed. 

"Thus  at  60  miles  per  hour  the  amount  of  frictional  resistance  which 
checked  the  rotation  of  the  wheels  was  about  2000  lbs,  exhibiting  an  adhesion 
of  about  .191  per  cent;  at  15  miles  per  hour,  2160  lbs.  or  .196  per  cent.  As 
these  two  values  are  so  nearly  equivalent,  it  would  appear  that  the  effort  is 
much  the  same  at  all  speeds." 

f  D.  K.  Clark,  a  usually  careful  authority,  states  (p.  724,  "Man.  Mech. 
Engr."),  "  As  the  speed  is  increased  the  adhesion  is  reduced,"  as  a  result  of  his 
own  tests  of  locomotives.  The  author  cannot  but  believe,  however,  that  this 
is  an  over-hasty  conclusion  by  that  able  and  usually  trustworthy  writer. 


436  CHAP.  XI.— LOCOMOTIVE    TRACTIVE  POWER. 

1.  The  coefficient  of  static  friction  between  rail  and  wheel  is  not  sen- 
sibly affected  by  the  velocity  of  motion  (as  above). 

2.  It  is  very  greatly  affected  by  the  insistent  weight,  increasing  rapidly 
therewith. 

3.  It  is  very  greatly  affected  by  the  condition  of  the  surfaces  as  re- 
spects moisture  or  other  equivalent  for  a  lubricant,  even  when  the  eye 
can  detect  no  difference,  and  is  very  considerably  affected  by  unknown 
causes,  so  that  it  can  rarely  be  determined  twice  alike. 

4.  It  is  greatest  when  the  rails  are  very  dry  or  (probably  for  the  rea- 
son that  the  minute  mineral  and  metallic  particles  which  act  as  rollers  are 
washed  away)  very  wet,  moisture  or  frost  having  the  most  injurious  effect. 

5.  The  coefficient  of  dynamic  or  sliding  friction  is  very  greatly  less 
than  static  friction,  and  very  greatly  affected  by  velocity,  in  inverse 
ratio  thereto.  At  the  instant  when  slipping  begins,  the  velocity  of  the 
rubbing  surfaces  being  very  small,  it  is  sensibly  the  same  as  static  friction, 
but  as  the  velocity  becomes  greater  it  falls  very  rapidly,  until  it  is  hardly 
one  third  or  one  fourth  as  great  as  the  static  friction. 

Tables  112,  113,  page  290,  show  the  general  results  of  these  tests,  and 
the  evidence  on  which  the  above  conclusions  are  based,  more  clearly 
than  words. 

From  these  laws  it  necessarily  results  that  when  slipping  of  the 
drivers  once  begins  the  resistance  to  further  slipping  (coefficient  of  fric- 
tion) should  almost  instantly  fall,  and  hence  that  the  wheels  should 
almost  instantly  begin  to  "spin;"  i.e.,  the  surplus  energy  of  the  drivers, 
no  longer  required  to  turn  the  wheels  against  a  great  resistance,  but 
only  against  a  small  resistance,  must  necessarily  go  somewhere,  and  is 
stored  in  the  wheels  in  the  form  of  velocity,  sometimes  making  them 
"spin"  so  violently  (when  steam  is  not  shut  off  soon  enough)  as  to  wear 
holes  in  the  rails  one-eighth  to  one-half  inch  deep.  This  spinning  is  not 
an  evidence  of  overloading,  since  (par.  483)  in  any  well-designed  engine 
letting  in  the  full  powder  of  the  cylinders  will  in  any  case  give  a  greater 
tractive  energy  than  the  wheels  can  transmit.  The  proper  course  when 
it  occurs  is  to  shut  off  steam,  let  the  drivers  come  to  rest,  and  start  more 
gradually.  If  engines  are  to  be  loaded  up  to  their  full  capacity,  only  the 
greatest  care  can  prevent  this  phenomenon  occasionally  occurring,  and 
it  does  occur  constantly  in  practice,  in  starting  trains,  although  rarely 
when  in  motion,  except  when  the  train  is  almost  at  a  stand-still. 

530.  A  long  list  of  actual  performances  of  locomotives  in  ser- 
vice is  given  in  Table  138,  and  from  this  and  the  further  data 


QHAF.  XI.— LOCOMOTIVE    TRACTIVE  POWER.  437 

below  it  is  clear  that  the  following  average  coefficients  of  adhe- 
sion may  be  assumed  with  sufficient  exactness  as  corresponding 
closely  to  the  results  of  American  practice.  European  practice 
(par.  537  and  Table  139)  shows  much  lower  ratios  of  adhesion  : 

Min.  (load  on 
drivers  =  i.oo). 

1.  Ultimate  limit  of  adhesion  in  practice,  under  con- 

ditions   in    all    respects    favorable,  and    with 

loads  per  wheel  exceeding  10,000  lbs.,    .     .     .  0.35  to  0.37 

2.  Working  limit  of  adhesion  when  sand  is  used,      .  (^)  0.33 

3.  Working  limit  of  adhesion   in  ordinary  summer 

weather,  and  maximum   limit  with  loads   of 

less  than  10,000  lbs.  per  wheel, (;^)  0.25 

4.  Working  limit  of  adhesion  on  slightly  moist  or 

frosty  rail,  being  the  apparent  average  of  ad- 
hesion which  limits  the  weight  of  trains  in 
winter  (as  to  which  see  par.  632), (-J^)  0.20 

5.  After  the  wheels  have  once   slipped,  the  co- 

efficient rapidly  falls  (see  Table  112)  to  less 

than {^-^  o.io 

531.  The  first  of  these  limits  was  realized  by  Zerah  Colburn 
as  early  as  1853,  and  with  light  locomotives  (10,000  lbs.  per 
driver),  in  his  still  famous  tests  on  the  Erie  Railway,  and  re- 
peatedly since.  In  a  large  number  of  recorded  instances  trains 
have  been  hauled  in  regular  service  which  demanded  nearly  or 
quite  one  third  adhesion,  but  only  as  exceptional  performances. 
A  long  list  of  notes  as  to  such  trains  might  be  given, 

532.  The  second  limit  (when  sand  is  used)  is  less  fully  deter- 
mined, but  various  dynamometer  records  of  the  effect  of  sand  to 
increase  tractive  power  indicate  that  it  increases  the  working 
limit  of  coefficient  to  about  \  under  all  conditions  of  track  or 
weather;  that  is  to  say,  it  makes  the  adhesion  on  a  bad  rail  as 
high  as  on  a  good  one.  On  a  good  rail  it  does  not  appear 
that  the  coefficient  of  adhesion  is  appreciably  increased,  but 
what  is  gained  by  the  sand  is  to  retard  the  tendency  to  slip. 
Direct  evidence  on  the  subject  is  scarce,  and  there  is  no  doubt  a 


438 


CHAP.  XI.— LOCOMOTIVE   TRACTIVE  POWER. 


Table 

Performance  of  American 
(Including  all  the  Records  of  Performance  given 

AMERICAN" 


No.  of 
Record. 


Cylin- 
ders. 
Inches. 


Weight  of  Engine. 
[All  Tons,  2000  lbs.] 

En- 
gine. 

Ten- 
der. 

On 
Drivers 

28.0 

24.0 

17-5 

29.5 

24-5 

19.0 

31.0 

25.0 

20.0 

33-0 

25.0 

21-5 

35 -o 

25^.0 

23.0 

37 -o 

26.0 

24 -S 

Tractive 

Power, 

atM 

Adhesion. 

Lbs. 


Character  of 
Performance. 


Grade, 
Feet 
Per 

Mile.* 


13  X  22 

14  X  22 

15  X  22 

16  X  24 


18x24 


b,750 
9.500 
10,000 
10,750 


Single  performance 

"  "  "engineers  say. 

Regular  (?) 

Single  perf.  "  with  ease.". 
Regular  service 


Second  trip 

Regular ;. . 

"  Frequently." 

Regular';?)   

"  No  difficulty." 

"  Can't  exceed  10  m.  p.  h. 


72 -f  2 

52.8 
71.0 
237.0. 

42.0 

65.0 

47-7 
70.0 
40  o 
63.9  +  2 
160.0 


*  The  additions  to  the  grade  in  this  column  are  an  allowance  for 

Ten-wheel 


23- 


16x24 

36 .  15 

26.0 

27.1 

17  X  24 

38.0 

26.0 

28.5 

18x24 

40.0 

26.0 

30-5 

(I 

19  X  24 

42.0 

26.0 

32.0 

13,550 
14,250 
15,250 


16,000 


"Have  taken." 

Pass,  exceed  20  m.  per  hour 
Single  trip 


Maximum  load 

Regular        "     

*'  Daily  and  easily.' 


Maximum  Load 

Usual  load 

"  Have  pulled. " 


48  +  8 
53  +  5 
77  +  3 
150  +  la 
79+3 

62  +  4. 

21  +  5 
126 
76 

126 

76 

76  +  6 


Mogul 


16x24 

35-5 

25-5 

30.0 

17x24 

37-5 

25-5 

31-5 

j; 

i( 

(( 

<; 

(' 

" 

" 

" 

18  x  24 

39 -o 

26.0 

i5i7So 


16,500 


"  Equiv't  work  every  day." 

do.    (gained  speed  in  test) 

Regular  trains 

Irregular    "     

"  Have  hauled." 


Largest  regular  load 

Comparative  test 

"  Equal  serv.  every  day."., 
Intended  as  daily  duty.    . . 


Momentum  grades,  reg.  ser, 


83  +  : 

40.5 
53- 

44  ± 


70  +  6 
85  +  10 

53 

60 

70 

53-21 


CHAP.  XI,— LOCOMOTIVE    TRACTIVE  POWER. 


439 


138. 

Locomotives  in  Practice. 

in  the  Catalogue  of  Baldwin  Locomotive  Works.) 

Engines. 


No.  of 
Record 


3 
4 
5 
6 

7 
8 
9 

lO 

II 

12 

13 


Resist- 
ance. 
Lbs. 
Per 
Ton. 


36.03 


34-9 
97.8 

23.91 

32.62 

26.0 

34-52 

23-15 

33-0 

68.6 


Train-Load. 


Actual, 


No.  Kind  of       Tot.Td, 

Cars.  Load.  inc.en 


Loaded  flats. 
15 

15     !  Loads 

18      Green  wood 
3      Passeng^er... 


23-5 

16 

41 
20 

33-4 


17.9  tons. ..  < 

Loads 

!ii  tons 

'21%  tons 

iNot  ascert'd. 

Passenger... 


276 
330 
362 
422 

1X2 


to  5 

354 
847 
503 
662 


%\ 


143+ 
163+ 


Accord- 
ing- to 
Table 
170. 


339 
273 


330 
443 
333 
497 
350 
178 
178 


Excess  of  Actual 
Load  over  Table. 


Tons. 


33 
87 
23 
149 
10 

30 
to  66 

24 
404 
170 

165 
118 
-35 
-IS 


Per 

Cent. 


13 
35 

6 
54 

9 

6 
to  14 

7 
91 
51 
33 
33 
-19 


5^ 


Name  of  Road. 


Macon  ^Ga.)  &  B.. 

W.  Ala. 
Macon  &  Br. 
Sp.,U.&C.(S.Ca.X 

j-Atl.  &  W.  Pt. 

Atl.  &  Charlotte. 
Kansas  Pacific. 
Mo.,  K.  &  Tex. 
Long-  Island. 
Ate,  T.  &  S.  Fd. 
Cumb.  &  Penna. 


the  effect  of  curvature,  as  noted  below  this  table,  on  next  page. 
Engines. 


14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 

25 
26 
27 


29.21 

.. 

30.0 

34 

38.3 

14 

69-36 

39-15 

18 

" 

15 

33-0 

48 

17-85 

40 

55-73 

38.79 

55-73 

38.79 

39.06 

22 

43-23 

22 

Eng-.,  pass... 
Heavy  loads 

21  tons 

Empties 

Loads 

18  tons 


577-2 

462 

387.8 

450 

372 

372 

207.4 

205 

452 

389 

410 

389 

496-3 

463 

945.2 

855 

331-2 

274 

448.8 

393 

189  1 
to  292  f 

274 

315-5 

393 

472 

409 

472 

370 

"5 
-62) 


-77 
63 
102 


24 

Q^ 

■13 

1%) 

0 

I 

oi 

16 

ii 

5 

2% 

7 

2% 

10 

4% 

20 

8% 

14 

2% 

0 

19 

%fo 

i-^ 

3,% 

27 

8^ 

Del.,  L.  &  W'n. 

Norway. 
West.  Md. 
C.&Fogelsv.(Pa.) 
Youghiogheny. 

B.,  N.  Y.  &  Phlla. 

Lehigh  Valley. 


St.  L.  Sl  San  Fran. 


Engines. 


28. 
29. 
30- 
31- 
32- 

33- 

34- 
35- 
36- 
37- 
38- 

39- 


40.2 

45 

23-4 

28 

28.0 

21 

" 

25 

24.7 

28 

i( 

\    5 
(45 

36.8 

17 

44.0 

37 

28.08 

28 

28.1 

34-5 

20.12 

Uo 
(45 

Empties.  ...< 

Load  of  coal.. 
Loads 

Loaded  . . . .  ) 
Empties....  ) 

23  tons 

9.5  tons 

Loaded  

Loaded  . .  -1 


390-4 

395.8 

j-  373 -j 

573-3 

605 

481 

536 

561 

536 

679 

637 

665 

637 

452 

428 

418.5 

358 

709 

588 

66s 

587 

544-1 

479 

825  1 
910  i 

820 

17 
23 

• 

5- 

o± 

0 

-45 

-8. 

25 

4- 

42 

6. 

28 

4- 

24 

5- 

60 

16. 

121 

20. 

78 

13. 

bS 

13- 

o± 

0 

4^ 


Sharpsville. 

Western  Ala. 
T.  H.  &  Ind'olis. 


E.  T.,  Va.  &  Ga. 

E.  Kentucky. 

F.  &  Pere  Marq. 
Mo.,  K.  &  Tex. 

C.  &  Talc.  (Chili). 


440 


CHAP.  XL— LOCOMOTIVE    TRACTIVE  POWER. 


Table  138. — 
Consolidation 


No.  of 
Record 


40, 

41 
42 
43 
44 
45 
46 
47 
48 
49 
50 
51 
52 
53 
54 
55 
56 
57 
58 
59 
60 
61 
62 
63 
64 
65 


Cylin- 
ders, 
Inches. 


20x24 


Weight  of  Engine. 
Tons,  2000  lbs. 


En- 
gine. 


45-8 
51.0 


60.0 


Ten- 
der. 


26.2 
26.0 


On 
Drivers 


39-7 
44.0 


Tractive 
Power, 

Adhesion. 
Lbs. 


19,850 


25,000 


Character  of 
Performance. 


Regular  service . 


do.  (fair  average  work.) 


Regular  load 

Occasional  load 

Trial  trip 

Daily  service 

Using  sand 

Regular  service  (?). 

Maximum  load 

Usual  "     

Maximum    "     

Usual  "     

Maximum    "     

Usual  "     

Average  of  s  years. 


Daily  service . 


Maximum . 


Grade. 
Feet 
Per 

Mile. 


96 
145  -H  10 
116  +  10 

644-28 

96 -|-  ID 

45  +  3 
171 

23 
126 

96  -1-  10 

96 

130 

68.6 

67.6 

53  —  4 
105.6 
184.8 
316.8 


The  caboose  is  included  in  the  gross  loads  given  when  used  on  train,  although  not  in- 
cluded in  list  of  cars. 

The  assumed  ratio  of  adhesion  used  in  this  volume  (as  also  by  the  Baldwin  Locomo- 
tive Works)  is  34.  The  percentage  by  which  the  calculated  load  taken  from  Table  170 
exceeds  or  falls  below  the  computed  load  may  be  estimated  by  the  following : 


An  assumed  adhesion  of 


would  increase  the  calculated  load  33J  per  cent. 
"     decrease    "  "  "     20     "       " 


The  principal  cause  of  the  fluctuations  between  the  actual  and  computed  loads,  how- 
ever, lies  in  the  fact  that  the  reported  gradients  are  not  the  actual  defacto  gradients  for 
operating  purposes,  but  are  increased  in  effect,  in  some  instances,  by  uncompensated  curva- 
ture or  stopping-points  on  the  maximum  grade,  and  diminished  in  others  by  the  use  of 
momentum  to  assist  in  surmounting  them.  No.  8  (Kansas  Pacific)  and  No.  9  (M.,  K.  &  T.) 
are  conspicuous  instances  of  the  latter,  the  loads  reported  as  hauled  being  beyond  all 
probability  for  defacto  grades  of  the  given  rate.  Nos.  2,  4,  10,  11,  14,  and  27  are  prob- 
ably less  conspicuous  instances  of  the  same  use  of  momentum  to  practically  reduce  grades 
below  the  profile  rate.  In  Nos.  27,  39,  61  this  was  expressly  stated  to  be  the  case,  and 
(the  length  of  the  grade  being*given)  the  corresponding  defacto  grade  per  mile  was  com- 


CHAP.  XL— LOCOMOTIVE    TRACTIVE  POWER. 


441 


Continued. 

Engines, 


No.  of 
Record 


40 

41 
42 
43 
44 
45 
46 
47 
48 
49 
50 
51 
52. 
S3' 
54- 
55- 
56. 
57- 
58. 
59- 
60 
61. 
62. 
63- 
64. 
65. 


Resist- 
ance. 
Lbs. 
Per 
Ton. 


Train-Load. 


Actual. 


No 
Cars. 


Kind  of 
Load. 


Loaded  . . 
Empties. . 
Loaded  .. 


Tot.  I'd 
inc.eng 


26 
15 
40 
33 
35 
47 
32 

100 
35 
25 

140 

100 
40 
35 

100 
30 
29 
30 
40 


Empties. 


Load,  4-wh. . 
4-wh.,  coal... 

Empty  4-wh. 

Load,  4-wh.. 

Empty  4-wh. 
Load,  4-wh.. 
15-ton  load. . 


Loads. 


Loads . 


1720 
1886 

438.4 

298 

405 

478 

375 

393 
1 100 

264 

309 
1 144 

445 

340 

610, 

458 

498 

445 

457- 

392 

752 

776 
1005 

542.5 

318.5 

210.5 

254 


Accord 

ing  to 

Table 

170. 


1804 
496 
330 
394 
513 
456 
456 
840 
302 
.302 
1320 
394 
394 
600 
600 
487 
487 
496 
384 
644 

653 
828 
520 
320 
195 
195 


Excess  of  Actual 

Load  over  Table. 

Tons. 

Per 

Cent. 

o± 

0 

-S8 

-11.7^ 

-31 

-  9-45? 

9 

2.3^ 

-35 

-   (y.6% 

-80 

-17.4^ 

-62 

-13-7^ 

260 

31.0$^ 

-38 

-12.6^ 

7 

2.3^ 

-176 

—13-3^ 

52 

13.1^ 

-54 

-13-7^ 

10 

1.7^ 

-141 

-23.5^ 

II 

2.3^ 

-41 

-  8.4^ 

-38 

-   7-7^ 

9 

2.4^ 

108 

16.8^ 

123 

18.8^ 

177 

21.4^ 

22 

4.2^ 

-1-5 

0 

16 

8.2^ 

59 

30.3^ 

Name  of  Road, 


Ph.  &  Erie. 
Dom  Pedro  IL 
Tyrone  Br.,Penn. 

Lehig-h  &  Susq. 
Lehigh  Valley. 

Missouri  Pacific. 
Cumb.  &  Penna. 

Central  N.  J. 
Lehigh  Valley. 


Chic,  Burl.  &  Q. 
Ate,  T.  &  S.  F^. 


puted  and  used  in  computations,  the  reduction  being  indicated  by  a  —  sign  in  the  column 
of  grades. 

On  the  other  hand,  most  of  the  instances  in  which  the  reported  performance  is  less  than 
Table  170  calls  for  are  to  be  explained  by  high  speed  or  by  uncompensated  curvature, 
except  under  Consolidation  engines,  where  the  character  of  the  trains  (chiefly  4-wheel  coal 
cars)  had  no  doubt  equal  or  greater  effect  to  diminish  the  load. 

Curvature  was  assumed  to  add  only  1  ft.  per  mile  (0.38  lb.)  per 
degree  of  curvature  up  to  10°  curves,  and  2  ft.  per  mile  per  degree  for  sharper  curves,  when 
expressly  stated  to  constitute  an  addition  to  the  grade,  and  this  addition  is  indicated  by 
the  sign  -f  in  the  column  of  grades,  A  very  low  rate  was  assumed  in  order  that  the 
comparison  of  actual  and  theoretical  loads  might  be  more  certainly  trustworthy. 

From  the  above  table  we  may  conclude  that  if  the  given  grade  be  the 
de-facto  grade  for  operating  purposes,  with  all  effects  of  curvature  and  velocity  elim- 
inated,  an  assumed  adhesion  of  one  fourth  the  weight  on  drivers  and  a  rolling 
f7'iction  on  tangent,  at  15  miles  per  hour,  of  8  Ids.  per  ton  {the  latter  being  somewhat 
more  than  ample)  will  give  very  approximately  the  safe  operating  load  in  regu- 
lar  SERVICE, 

A  long  list  of  further  records  of  performance  the  writer  omits  to  save  space.  Quite  a 
number  of  them  show  more  than  J^  adhesion  realized  as  an  average  of  long  runs,  but 
not  as  every-day  performances. 


442  CHAP.  XL— LOCOMOTIVE    TRACTIVE  POWER, 

certain  deduction  to  be  made  from  the  apparent  gain  because  of 
the  increased  tractive  train  resistance  caused  by  the  sand  on  the 

rails. 

533.  The  third,  and  most  important  limit,  that  of  ordinary- 
working,  is  warranted  by  the  all  but  universal  evidence  of  mod- 
ern experience,  as  sufficiently  proved  by  Table  138,  which  gives  a 
loner  record  of  actual  performances  with  locomotives,  taken  chiefly 
from  the  very  abundant  data  given  in  the  catalogue  of  the  Bald- 
win Locomotive  Works,  and  including  all  the  records  therein. 
The  ratio  of  J  is  used  by  them  as  the  basis  for  computing  the 
table  of  capacity  on  various  grades  given  in  their  catalogue,  and 
thus  in  a  measure  guaranteed  by  them,  and  the  high  character 
and  great  experience  of  that  firm  entitles  this  fact  to  far  more 
than  the  usual  weight  which  would  be  accorded  to  manufac- 
turers' evidence. 

534.  Many  causes  combine  to  make  the  apparent  indications 
of  practice  very  variable.  One  of  the  most  important  is  that 
the  nominal  ruling  gradient  is  not  the  real  or  "virtual"  one, 
being  in  some  cases  higher  than  the  virtual  grade,  because  the 
ruling  grades  are  short  and  surmounted  in  part  by  momentum  ; 
and  in  others  (and  far  more  commonly)  lower  than  the  virtual 
grade,  because  of  the  necessity  of  stops  on  unreduced  gradients, 
or  of  unreduced  curvature  on  the  ruling  grade,  thus  materially 
increasing  the  nominal  maximum :  so  that  if  we  assume  the  grades 
of  the  profile  to  be  the  virtual  grades,  the  trains  hauled  will  ap- 
pear to  be  only  such  as  are  due  to  \  adhesion,  or  even  less. 

On  very  low  gradients  this  is  especially  true;  and,  moreover, 
another  cause  comes  in — the  difficulty  of  starting,  making  up, 
and  handling  very  long  trains.  From  this  it  results  that  we 
very  rarely  indeed  hear  of  trains  being  hauled  on  very  easy 
grades  such  as  are  beyond  all  question  within  the  power  of  the 
locom.otive  under  conditions  which  are  as  fair  actually  as  they 
are  nominally.  But  when  these  errors  are  eliminated  it  will  be 
found  that  in  all  cases,  in  good  American  practice,  the  actual 
ratio  of  adhesion  is  \,  whenever  it  is  attempted  to  load  the 
engines  to  their  full  capacity. 


CHAP.  XI.— LOCOMOTIVE    TRACTIVE  POWER. 


443 


535.  The  fifth  ratio  of  adhesion,  \^  apparently  applies  to 
winter  loads,  and  will  actually  give,  in  most  cases,  the  loads 
which  are  hauled  in  practice  in  winter.  It  is  usually  assumed 
that  this  difference  is  due  to  the  fact  that  the  ratio  of  adhesion 
is  less  in  winter  than  in  summer,  but  it  appears  probable  that  in 
reality,  as  we  shall  see  (par.  632),  it  is  due  to  an  increase  in  the 
rolling  friction,  both  because  of  greater  axle  friction  and  because 
of  the  poorer  condition  of  the  track. 

536.  In  the  former  edition  of  this  treatise  \  instead  of  \  was  as- 
sumed as  the  ordinary  working  ratio  of  adhesion.     This  was  deduced 

Table  139. 

Comparative  Ratios  of  Adhesion  of  American  and  Foreign 
Locomotives. 


Ratio  of  Adhesion. 


Conditions. 


Maximum  at  slow  speeds  and  under  favor- 
able conditions 


Working  maximum 

Ordinary  apparent  adhesion. 


Foreign  Engines. 


i  or  0.25 

1^  or  0.20  to 
ioro.17 

\  or  0.14 


American  Engines. 


i  or  0.33 
\  or  0.25 
1^  or  0.20 


Many  European  engineers  assume  7,  or  even  less  ;  but  many  American  engineers,  in 
like  manner,  assume  \. 

From  a  summary-  by  Mr.  O.  Chanute,  in  "  Haswell's  Pocket-Book,"  we  may  abstract 
the  following  data  as  to  early  and  European  tests  of  adhesion  : 

Ratio  of  Adhesion. 

Mr.  Wood   on  early  English  railways  (per- j  ^f^^''^^^  ^^^^l^"^  v,  • °-^4 

hapstheearHesTtests^nrecord).'...'...^^J,7/^,^-;?^^^^^^^^^^  0;o8 

B.  H.  Latrobe  on  B.  &  O.  R.  R.    1838 Safe  working  limit 0.13 

(Maximum 0.20 

Modern  European  practice <  Minimum o.  11 

(  Soemmering  line 0.16 

Italian    Alpine    road,    subject     to    frequent  j  Maximum  in  open  cuttings 0.12 

mists '(  Maximum  in  tunnels o.io 

'Dry  weather... ]    oi^o^f^-^SS 


French  experiments.  1862-67  by  Messrs.  Vuil- 


lemin,  Guebhard,  and  Dieudonne |  Wet  weather 


Damp  weather \    °- ^32 

0.139 


0.078 
.    0-164 

Light  rain .,. 0.09 

I  Rain  and  fog    0.14 

I.  Heavy  rain 0.16 


The  last  records  are  of  dubious  value.  Mr.  Chanute  gives  a  table  of  average  European 
and  American  practice,  which  differs  somewhat  from  the  above,  but  seems  open  to  ques- 
tion in  several  details.    , 


444  CHAP.  XI.— LOCOMOTIVE   TRACTIVE  POWER. 

by  comparison  of  the  actual  loads  hauled  on  various  nominal  grades  by 
the  same  engine.  Besides  the  causes  just  mentioned,  however,  which  tend 
to  make  this  process  inaccurate,  within  the  nine  years  from  1876  to  1885 
a  very  great  change  has  taken  place  in  the  average  train-loads  hauled  on 
American  railways,  as  shown  in  Tables  30  to  33,  and  others.  Much  of 
this  is  due  to  the  use  of  heavier  engines,  but  a  great  part  of  it  is  due  to 
greater  care  to  load  engines  to  their  full  capacity. 

537.  The  adhesion  of  English  and  other  foreign  locomotives  is  ordi- 
narily stated  at  less  than  of  American  by  a  considerable  percentage. 
Table  139  approximates  closely  to  the  difference  which  appears  to  exist. 
How  much  of  this  represents  an  actual  difference  of  capacity,  and  how 
much  is  due  merely  to  difference  of  administration,  it  would  be  impos- 
sible to  say ;  but  there  is  no  room  for  doubt  of  the  fact  that  foreign 
engines  haul  lighter  trains,  as  a  rule,  than  American  engines  of  the 
same  weight,  or  that  European  engineers  state  the  limit  of  their  ad- 
hesion at  less  than  that  given  by  American  engineers  for  American 
engines. 

538.  If  we  may  assume  that  the  loads  hauled  by  the  same  engine  on 
any  two  grades  are  affected  only  by  the  difference  in  the  grades  (which 
ordinarily  we  cannot,  except  very  approximately),  we  may  at  once  deter- 
mine from  the  records  of  these  loads  the  rolling  friction  and  ratio  of 
adhesion,  as  follows . 

Let  L  and  L'  —  the  gross  load  (including  its  own  weight)  hauled  by  the  same 
engine  on  any  two  grades,  g  and  g' . 

Let  X  =  the  total  resistance  per  ton  on  the  lowest  grade  g,  and  d  =  the  dif- 
ference in  resistance  per  ton  on  grades  g  and  g'  (being  that  due  to  gravity  only, 
and  equal  to  the  resistance  from  gravity  on  a  grade  of  ^'  —  g). 

Then  Zx  =  Z'  (x  -f-  d), 

I'd 
whence  x  =  — jk- 

Then  we  have 

Rolling  friction       =■  x  —  resistance  from  gravity  only  on  grade  g. 
Traction  of  engine  =  xL 

traction 


Ratio  of  adhesion    = 


wt.  on  drivers' 


But  while  these  formulae  are  theoretically  correct,  results  determined  by 
them  are  to  be  accepted  as  reliable  only  with  great  caution.  If  the  reported 
low-grade  loads  are  too  small,  as  they  usually  are,  the  effect  will  be  to  greatly 
increase  the  apparent  rolling  friction. 

539.  Owing  chiefly  to  some  misinterpreted  experiments  made   in  France 


CHAP,  XI.— LOCOMOTIVE    TRACTIVE  POWER.  445 

jome  years  ago  by  a  M,  Rabeauf,  a  chief  engineer  of  the  Corps  des  Ponts  et 
Chaussees,  there  has  for  some  time  been  some  available  authority  to  show  that 
there  may  be  such  a  thing  as  ''imperceptible"  or  continuous  slip  in  the 
driving-wheels  of  locomotives  in  motion.  Such  a  thing  is  really  impossible, 
but  the  impression  that  it  occurs  has  become  widespread,  and  mere  assertions 
in  support  of  it,  or  allusions  to  it  as  a  well-known  fact,  exist  without  number. 
The  experiments  referred  to,  from  which  this  whole  imaginary  discovery  seems 
to  have  originated,  were  described  in  a  paper  in  the  Annates  dii  Genie  Civil 
(1876),  in  which  the  record  was  given  of  tests  of  a  fast  passenger  engine  for  the 
Northern  Railroad  of  France,  having  four  coupled  drivers  6  ft.  10  in.  diameter, 
carrying  i(i\  tons  on  a  grade  of  0.5  per  cent  (26  ft.  per  mile),  with  good  rail  and 
weather,  and  121  lbs.  per  square  inch  boiler  pressure.     The  report  continues: 

"  Under  these  conditions  the  locomotive,  which  was  tested  alone  (hauling 
no  train  behind  it),  attained  a  speed  on  the  down  grade  of  74I-  miles  an  hour, 
corresponding  to  303  revolutions  of  the  drivers  per  minute.  Now,  the  regis- 
tered number  of  revolutions  was  360,  corresponding  to  88.8  miles  per  hour — a 
slip  of  ig  per  cent. 

•' Surprised  at  these  results,  the  writer  repeated  the  same  observations  on 
a  certain  number  of  locomotives  of  different  types,  comparing  the  speed 
with  the  revolutions  of  the  drivers.  It  was  generally  found  that  the  slip  was 
slight  on  an  up  grade,  but  very  apparent  on  a  down  grade,  ranging  from  13  to 
25  per  cent.     It  increased  rapidly  with  the  speed." 

This  evidence  appears  pretty  conclusive,  especially  as  other  articles  and 
paragraphs  to  the  same  effect  have  appeared  from  time  to  time,  accompanied 
by  various  reasons  why  the  centrifugal  force  of  the  counterweights,  and  what 
not.  must  have  the  effect  of  producing  it. 

540.  As  a  result  of  these  tests  it  was  concluded  that  "  common  locomotives" 
were  *' actually  unsuited  for  speeds  of  60  to  75  miles  per  hour,"  because  the 
slippage  was  as  much  as  20  per  cent.  In  a  specific  instance  (the  Uetliberg  road) 
referred  to  in  the  paper  it  was  said  that  on  grades  of  7  per  cent  (370  ft.  per 
mile;  less  by  i  per  cent  than  is  now  successfully  operated  in  Colorado,  and  less 
by  3  per  cent  than  was  successfully  operated  on  temporary  lines  by  the  late 
Benj.  H.  Latrobe)  "  the  slip  of  the  driving-wheels  was  found  so  considerable 
that  the  gear  system  was  found  more  economical,"  in  spite  of  the  slow  speed. 

541.  On  the  other  hand,  tests  of  various  American  passenger  locomotives  at 
speeds  at  from  75  miles  per  hour  down,  made  by  Prof.  Chas.  A.  Smith,  Mr. 
Albert  F.  Hill,  and  Messrs.  Henry  Abbey  and  Oscar  H.  Baldwin  (see  Engineer- 
ing, Aug.,  1885),  to  mention  no  others,  have  uniformly  indicated  that  no  such 
phenomenon  occurs  with  American  locomotives  under  any  circumstances. 

There  is  an  undoubted  possibility,  so  far  as  this  evidence  alone  is  concerned, 
that  the  phenomenon  might  not  occur  with  American  locomotives,  and  might 
occur  with  differently  constructed  foreign  locomotives;  but  in  addition  to  the 
grave  reasons  for  questioning  the  physical  possibility  of  the  assumed  phenom- 


44^  CHAP.  XI.— LOCOMOTIVE    TRACTIVE  POWER. 

enon,  as  being  contrary  to  what  is  known  in  other  ways  of  the  laws  of  friction, 
it  is  not  difficult  to  see  how  the  alleged  slipping  may  have  occurred  and  yet 
have  been  in  no  respect  "imperceptible"  slip,  nor  different  in  any  way  from 
ordinary  slipping,  which  is  perceptible  enough. 

542i  When  a  locomotive  is  only  moving  itself,  especially  if  running  down 
a  grade,  and  so  having  little  work  to  do,  and  when  all  possible  power  is  put  on 
to  run,  in  literal  truth  "  as  fast  as  the  wheels  can  turn,"  whether  the  wheels  are 
slipping  or  not  will  make  no  very  conspicuous  difference  in  their  speed  of  revo- 
lution; while,  on  the  other  hand,  the  work  required  of  the  locomotive,  simply 
to  keep  up  speed,  will  be  so  small  that,  when  the  wheels  once  begin  to  slip,  the 
loss  of  power  will  not  be  so  great  as  to  prevent  the  acquirement  and  mainte- 
nance of  very  high  speed,  although  they  will  continue  to  slip  indefinitely,  never- 
theless. On  the  other  hand,  with  a  train  of  even  one  car  behind  the  engine  no 
high  speed  could  probably  be  maintained  under  such  conditions,  for  the  mini- 
mum power  to  maintain  the  speed  would  then  be  so  great  that  the  speed  would 
be  immediately  checked,  and  make  it  clear  to  the  senses  that  the  wheels  were 
slipping.  Whenever  the  locomotive  was  running  up  any  considerable  grade  it 
would  be  still  less  possible;  and  the  cautious  statement  quoted  above,  that  it 
was  "generally  found"  that  "the  slip  was  slight"  on  an  up  grade,  probably 
means  that,  as  a  matter  of  fact,  no  absolute  evidence  of  any  slip  was  detected, 
or  the  figures  for  it  would  have  been  given. 

543.  To  make  the  true  explanation  of  the  phenomenon  clearer:  Suppose, 
when  the  wheels  of  a  freight  engine  were  slipping,  while  it  was  standing  still, 
that  the  engine  were  simply  uncoupled — instead  of  shutting  off  steam  in  the 
usual  fashion.  If  the  grades  were  not  too  unfavorable  the  engine  would  prob- 
ably start  ahead;  the  wheels  still  slipping;  and  if  all  the  steam  were  put  on,  on 
a  favorable  down  grade,  a  velocity  of  "  74^  miles  per  hour"  might  possibly  be 
obtained,  with  an  "imperceptible  slip"  of  20  per  cent.  These,  or  something 
like  these,  are  probably  the  conditions,  and  the  only  conditions,  under  which 
the  phenomenon  has  ever  been  observed,  and  they  correspond  to  nothing  in  the 
worst  extremes  of  practical  operation.  The  only  thing  really  proved  by  such 
"tests"  is  that  even  the  wheels  are  slipping  in  ordinary  fashion  they  will  kick 
hard  enough  against  the  rails  to  make  an  unloaded  engine  move  down  a  grade 
at  a  very  lively  pace;  which  illustrates  how  easy  it  is  to  draw  wrong  conclusions 
from  observed  facts. 

544.  The  ef[ect  of  the  CENTRIFUGAL  FORCE  OF  THE  COUNTERWEIGHTS 

of  the  locomotive  to  modify  the  pressure  of  the  wheels  on  the  rail  is  con- 
siderable, and  especially  on  bridges  very  important,  but  as  respects  its 
effect  on  the  adhesion  it  is  less  important,  if  indeed  it  can  be  said  to  be 
of  any  importance. 

The  counterweights  are  weights  added  to  balance  the  piston  and 
other  reciprocating  parts,  and  thus  prevent  serious  disturbance  of  the 


CHAP.  XI~LOCOMOTIVE    TRACTIVE  POWER, 


447 


Fig.  io8. 


motion  of  the  engine.  They  are  either  cast-iron  weights  between  the 
spokes  of  the  drivers  or  lead  poured  into  hollows  in  the  wheel-centre, 
and  have  the  effect  to  make  the  wheel  lop-sided.  When 
the  counterweights  are  in  the  position  a,  Fig.  io8,  their 
■centrifugal  force  will  be  so  much  added  to  the  weight  car- 
ried by  the  wheel,  and  increase  its  pressure  on  the  rail  by 
so  much.  When  they  are  in  the  position  a',  at  the  top  of 
the  wheel,  the  centrifugal  force  will  decrease  the  pressure 
on  the  rail.  When  they  are  in  the  position  b  and  b'  the 
■centrifugal  force  will  have  no  vertical  effect. 

As  respects  freight  engines,  especially  when  the  engine  is  working 
hard  enough  to  be  in  any  danger  of  slipping  the  wheels,  the  speed  is 
ordinarily  so  slow  that  the  centrifugal  force  of  the  counterweights  is  all 
but  imperceptible.  As  respects  passenger  engines,  the  counterweights 
can  at  worst  exert  no  appreciably  injurious  effect  upon  the  adhesion,  for 
the  reason  that  the  possible  boiler  tractive  power  decreases  with  speed 
very  much  faster  than  it  can  be  diminished  by  any  possible  effect  of  the 
counterweights. 

645.  But  while  this  phenomenon  has  no  measurable  effect  upon  the  adhe- 
sion, and  is  not  likely  to  have  a  very  serious  effect  upon  the  track,  it  may  and 
does  have  such  effect  on  bridges.  The  sharp  variation  which  takes  place  in 
the  load  on  the  rails  has  no  effect  on  the  riding  of  the  engine,  since  it  does  not 
act  through  the  springs.  But  it  does  give  to  the  rail  what  has  been  not  inaptly 
termed  a  "hammer-blow;"  and  its  effect  on  bridges  (especially  on  over-light 
bridges;  see  Chap.  XXIII.)  is  visi- 
ble in  the  striking  diagrams  repro- 
duced in  Figs.  101-108,  which  show 
how  very  greatly  the  oscillations 
of  bridges  are  increased  when  the 
period  of  revolution  of  the  drivers 
happens  to  coincide  with  the  period 
of  oscillation  of  the  bridge. 


BBfWWVVWWW  ^  ■ \r p      I 


Figs.  109-116  are  from  observations 
on  the  vibration  of  bridges  by  Prof.  S. 
W.  Robinson.  They  show  the  vertical 
and  lateral  vibrations  of  the  panel 
point  nearest  the  middle  of  its  lower 
chord  during  the  entire  passage  of  the 
train. 

The  upper  line,  AB,  shows  the  ver- 
tical movements,  and  the  lower  one, 
MJVy  the  lateral  movements.     The  lowest  one,  -STK,  is  a  line  of  reference. 


Figs.  log,  no.— Effect  of  Passage  of  Fast  Pas- 
senger Trains  (40.8  and  42.1  Miles  per  Hour) 
OVER  Through  Pratt  Truss,  148  Ft.  Span. 


As  a  train 


448 


CHAP.  XI.— LOCOMOTIVE    TRACTIVE  POWER, 


^yyain  Length—^ i(     'V  i-      -« 


Figs.  111-116. — Vibrations  Produced  in  the 
SAME  Bridge  by  the  Passage  of  Various 
Freight  Trains  at  Various  Speeds. 
Vertical  Scale  three  fourths  of  actual  move- 
ment. 

[Through  Pratt  Truss  Bridge,  New  York, 
Pennsylvania  &  Ohio  Railroad,  near  Leav- 
ittsburg,  O.,  141  feet  span,  24  feet  deep,  9 
panels,  15  feet  8  inches  each.  Kind  of  engine 
and  train  and  speed  given  in  each  diagram. 
The  scale  below  "  Length  of  Train"  shows 
the  revolutions  of  the  drivers.] 


jlp-fTfTUVWH 


iVWfm^A' 


Length  oF Train ^o     j  3  T. n 

lJj._L  J_l_Llji_Li_Ll_l_l-lii-  l_l_lJj._LJ.l.il.L' 


approached  the  indicator  was  started,  making  the  straight  lines  to  the  left  of  A,  M  and,  X. 
As  the  train  struck  the  bridge  lateral  motion  of  the  pencils  began,  and  it  will  be  seen  that 
in  all  cases  the  deflection  was  greatest  within  a  second  or  two  after  the  locomotive  had 
entered  upon  the  bridge,  or  about  when  the  whole  of  the  engine  and  tender  was  fairly  on 
the  bridge,  and  long  before  it  had  reached  even  the  middle  point  of  the  bridge. 

The  hollow  in  the  diagrams,  which  immediately  follows,  showing  a  reaction  fron> 


CHAP.  XI.— LOCOMOTIVE  BOILER. 


449 


this  extreme  depression,  indicates  clearly  that  the  latter  is  a  dynamic  effect,  the  sudden 
depression  caused  by  the  entrance  of  the  load  setting  the  bridge  in  motion  downward  so 
quickly  that  its  momentum  carries  it  down  far  below  what  even  much  greater  static  strains 
are  able  to  maintain.  It  is  probable  that  bridges  of  longer  span  and  greater  weight  would 
show  this  effect  much  less  markedly. 

The  length  of  train  and  also  a  scale  (on  the  right  line  between  A  and  B)  on  which  the 
revolutions  of  the  drivers  are  indicated  has  been  added  to  the  originals. 

It  will  be  seen  that  in  every  instance  the  vibrations  of  greatest  magnitude  are  almost 
exactly  synchronous  with  the  drivers'  revolutions,  but  as  the  vibrations  decreased  they  be- 
come less  so,  and  when  the  vibrations  become  a  mere  wavy  line  there  is  no  observable 
connection  whatever  with  the  drivers'  revolutions. 

The  difference  in  the  effect  of  passenger  and  freight  trains,  or  of  different  construc- 
tion and  speed,  as  shown  by  comparing  Figs.  1 15-16  with  Figs.  109-10,  is  very  noticeable 
and  curious. 


THE  LOCOMOTIVE   BOILER. 


546.  To  burn  more  than  80  lbs.  of  coal  per  square  foot  of  grate  per 
hour  is  sure  to  decrease  the  efficiency  of 
combustion,  although  as  much  as  100  lbs. 
may  be  burned  under  favorable  conditions, 
with  fair  economy.  When  combustion  is 
pushed  beyond  this,  as  it  not  unfrequently 
is,  sometimes  even  so  far  as  to  apparently 
double  it,  it  is  all  but  certain  that  a  large 
proportion  of  the  additional  coal  supply  will 
be  ejected  at  once  from  the  smoke-stack, 
unconsumed.  As  much  as  20  per  cent  of 
the  entire  coal  put  into  the  fire-box  has  fig, 
been  actually  caught  in  the  smoke-box,  and 
it  is  quite  certain  that  when  more  than  130 
to  150  lbs.  per  square  foot  are  "burned" 
nearly  the  whole  of  the  excess  of  supply  is 
thus  ejected  (see  Table  146).  Fig.  117,  with 
ts  accompanying  note,  gives  a  rather  exag- 
gerated instance  of  what  is  continually  tak- 
ing place.  The  minimum  waste  of  coal  in 
this  way  is  probably  5  per  cent. 

547.  The  ordinary  evaporation  of  water   Sen' moS'S^i^'carrird  "out'^by 
per  pound  of  coal  burned  is  hardlv  more   the  blast,  but  probably  broken  up 

^        ^  '  m  the  prooess.) 

than  6  lbs.  in  this  country,  and  sometimes 

only  5  lbs.,  or  even  less,  although  it  rises  to  8  or  9  lbs.  in   some  cases, 
29 


Lump   of   Unconsumed 
Anthracite  Coal,  Natural  Size, 

EJECTED    FROM   THE    SmOKE-STACK 

OF  AN  Express  Locomotive  with 
SUCH    Force     as     to    fall     in 
through  the  Open  Window  in 
the  Second  Car  in  the  Rear. 
(This  lump  was  picked  up  by  Mr. 
Geo.  W.  Parsons,  who  handed  it  to 
the  writer,  still  hot.    The  most  sali- 
ent angles  only  had  been  ignited, 
and  they  but  slightly.     No   larger 
lump,  perhaps,  could  be  found  with 
such    a    record,    but    innumerable 
smaller  ones.    The  lump  was  near- 
ly a  cube.     If  partially  ignited  its 
specific  gravity  would   have   been 


450 


CHAP.  XI.— LOCOMOTIVE  BOILER. 


and  very  frequently  if  not  usually  does  so  abroad,  where  the  evaporation 
is  more  economical  than  is  common  here,  owing  in  great  degree  to  the 
combustion  being  less  pushed  by  the  hauling  of  heavy  loads,  and  in  part, 
probably,  to  more  skilful  firing.  Theoretically,  a  fair  ordinary  coal  (of 
14,000  heat-units — not  by  any  means  the  best — see  Table  140)  ought  to 
evaporate  something  over  12  lbs.  from  water  at  60°  Fahr.  to  steam  at 
120  lbs.  pressure. 


Table  140. 
Heat-units  in  Various  Fuels. 


Pure  carbon 

Pennsylvania  anthracite — 
Pittsburg  bituminous 

Illinois  coal  (pure  quality) 


English  coal  (average)., 

English  coke  (average). 

Crude  petroleum 

Lignite 

Asphalt 

Dry  wood  (all  kinds) . . . 


Heat-units. 


a, 000  I 
10,000 ! 

14,858  i 
13,860  I 

14,150  i 
12,300 ' 


9,834  \ 
14,449  ) 


14,500 
14,500 
14,200 

9,000 

14,320 

13,550 
20,240 
11,678 
16,655 
7,792 


Evap.  Power  (lbs.  water) 
from  and  at  212°. 


14-34  1 
15-52$ 
14.64  I 
12.72  f 


10.18  I 
14.96 f 


15.02 
15-02 
14.69 

9.20 
14.82 
14.02  lbs. 
20.33  '* 
12.10  " 

17.24  " 
8.07  " 


The  heat  required  for  evaporation  "from  and  at  212°  (i.e.,  the  conversion  of  water  at 
212°  into  steam  at  212°  or  atmospheric  pressure)  being  i.oo,  the  heat  required  to  turn 
water  at  normal  feeding  temperatures  into  steam  of  usual  working  pressures  is  as  follows: 


Feed- 

Steam  Pressure  above  Atmosphere — Lbs. 

«  Fahr. 

20 

40 

60 

80 

100 

120 

140 

160 

4o» 

6o» 

8o"> 

lOO' 

I -193 
1.172 

1-151 
1. 131 

1.203 
1.182 
1.161 
1.141 

1.209 
1.188 
1.167 
1.147 

1. 214 
I -193 
1.172 
1.152 

1.219 
1. 198 
1. 177 
1-157 

1.223 
1.202 
1. 181 
1.161 

1.226 
I.  =05 
1.184 
1.164 

1.229 
1.208 
1.187 
1.167 

(Abstracted  from  a  large  table  in  "  Steam-Making,"  by  the  late  Prof.  Charles  A.  Smith.) 


The  lowest  rates  of  evaporation  occur  with  the  highest  rates  of 
combustion,  and  vice  versa  ;  and  ordinarily  it  is  not  possible  to  evaporate 
more  than  600  lbs.  of  water  per  square  foot  of  grate  per  hoar  (say  80  lbs. 
coal  X  7i  lbs.  evaporation  ratio,  or  100  lbs.  x  6)  for  any  length  of  time. 


CHAP.  XI.— LOCOMOTIVE  BOILER.  45 1 

More  may  be  done,  but  it  cannot  be  relied  on,  and  500  lbs.  of  water  per 
square  foot  of  grate  would  come  nearer  to  a  moderate  working  maximum. 

548.  The  ordinary  load  on  drivers  per  square  foot  of  grate  ranges 
from  2500  to  4000  for  ordinary  types,  as  shown  in  Tables  127-130  ;  3000 
lbs.  being  rather  low  for  passenger  engines  of  the  American  type  and 
for  Consolidation  engines,  and  4000  rather  low  for  Mogul  and  Ten-wheel 
engines.  The  larger  proportion  of  grate  surface  in  the  Consolidation 
type  may  be  considered  as  in  part  a  concession  to  the  difficulty  in  firing 
such  engines. 

549.  The  steam  used  in  the  every-day  working  of  locomotives  (in- 
cluding the  entrained  water  carried  along  with  the  steam  mechanically)  to 
do  33,000  ft.-lbs.  of  net  effective  work  is  somewhat  under  30  lbs.,  never, 
probably,  running  very  much  higher  than  that,  and  rarely  quite  as  low 
as  to  25  lbs.,  even  under  the  most  favorable  circumstances;  that  being 
the  lowest  fair  assumption  for  steam  used  at  slow  speeds  on  long  grades 
or  at  other  specially  favorable  points,  except  that  for  very  short  distances 
considerably  more  than  that  may  be  shown,  owing  in  part  to  drawing  on 
the  small  reserve  of  power  in  the  boiler  (par.  553  and  Table  144). 

550.  Then,  as  the  production  of  steam  is  600  lbs.  per  square  foot  of 
grate  per  hour,  and  the  consumption  per  horse-power  per  hour  is  rarely 
better  than  25  lbs.  and  often  much  worse,  we  have  ^^  =  24  horse-power 
as  the  maximum  ordinary  capacity  of  one  square  foot  of  grate  area. 
Tables  146  and  147  will  indicate  that  this  is,  on  the  whole,  a  rather 
favorable  showing  for  what  can  be  actually  realized.  But  to  determine 
the  very  highest  maximum  which  can  be  claimed  in  the  way  of  locomo- 
tive performance,  we  may  appropriately  refer  to  Mr.  Wm.  Stroudley's 
paper  on  the  locomotive  performance  of  the  London,  Brighton  &  South 
Coast  Railway  (Trans.  Inst.  C.  E.  1885),  where  we  find  that  an  average 
of  about  600  indicated  horse-power  was  maintained  for  6  or  8  miles  in 
succession  by  an  engine  with  17.04  square  feet  grate  area,  with  an  aver- 
age horse-power  for  the  whole  run  of  50  miles  of  528.5,  corresponding  to 


Indicated  H.  P.  per  sq.  ft.  grate  - 


600  T-  „ 

maximum  —  =  35.3  H.  r. 
17        ^^  ^ 

528.5 
j  average   - — -  =31.1      " 


Net  effective      "  "  "         (10  per  cent  less),  say,  32  and  28  H.  P. 

In  round  figures,  30  effective  horse-powers  per  square  foot  maybe  said 
to  be  the  ultimate  limit. 

551.  The  horse-power  which,  if  it  could  be  produced,  might  be  trans- 


452 


CHAP.  XI.— LOCOMOTIVE  BOILER. 


mined  through  the  drivers  for  propelling  the  train  is  very  much  greater 
than  this  except  at  the  slower  speeds,  so  that  at  the  slower  speeds  only 
is  it  possible  to  utilize  the  full  adhesion,  as  may  be  determined  thus  : 

Per  Square  Foot  of  Grate  Area. 

Usual  load  on  drivers,  as  per  Table  141,       3,000  to  4,000  lbs. 
Equivalent  tractive  power  for  J  adhesion,      750  to  1,000  lbs. 

Table  141. 

Load  on  Drivers   Per  Square   Foot  of  Grate  Area  for  the  Various 
Locomotives  given  in  Tables  127-130. 


Table  127.— American  Engines.        1 

Table  128,— Mogul  Engines. 

Date. 

Road  or  Maker, 
and  Cylinders. 

Lbs.  per 
sq.  ft. 

Date. 

Road  or  Maker, 
and  Cylinders. 

Lbs.  per 
sq.  ft. 

1873  -•• 
1884.... 
1884  ... 
1884.... 
1884.... 
1884.... 

Mason,  17  x  24 

2,440 

3o9o 

2,920 

3,050 

3^070 

3,590 

1,880* 

3,670 

1873-. • 
1883... 
1884... 

4,120 
4,270 

Brooks,  18  X  24 

Brooks   17  X  24 

Baldwin  (N.S.Wales),i8x26 

4,650 

r"            TS        Rr     C\           -rm   ^   n  . 

"        "       18x24     

Table  129. — Consolidation  Engines. 

20x24  cj'linders. 

A 

1875-6. 
1886... 
1883... 

Penna.  "  Class  I  " 

3,450 
3,210 
3,830 

1884.... 

West  Shore  ]g  

"       "  Class  R" 

West  Shore 

Table  128.— Ten-wheel  Engines. 

Table  130. — Mastodon  Engines. 

1873  •-• 
1883.... 

4,020 
3,230 

1882... 
1882... 

Central  Pac,  19x30 

Lehigh  V.,  20x26 

4,120 

2,570* 

*  These  engines  have  specially  large  grates  to  permit  of  slow  combustion. 


Then  the  horse-power  per  hour  per  square  foot  of  grate  area  which 
will  or  might  be  transmitted  through  the  drivers,  if  their  utmost  adhesion 
be  utilized,  will  be — 

Maximum  H.  P.  =  '°^d°ndrhgrs  ^  _5?8^  ^  speed  in  miles  p.  hour. 

coeff.  adhesion      33,000X00 

By  this  formula  Table  142  was  computed,  which  indicates  at  once  a 
truth  of  the  first  importance— that  it  is  absolutely  impossible  to  produce 
enough  power  in  the  boiler  to  utilize  more  than  a  small  fraction  of  the 
available  tractive  power  at  any  of  the  higher  speeds,  and  it  is  only  as  we 
fall  below  1 5  miles  per  hour  that  it  becomes  possible  for  even  freight 
engines  to  do  so. 


CHAP.  XI.— LOCOMOTIVE  BOILER. 


453 


Table  142. 

Horse-power  of  Net  Effective  Work  required  to  be  Continuously 
Generated  Per  Square  Foot  of  Grate  Area  to  FULLY  utilize 
THE  Entire  Tractive  Force  of  Various  Engines  at  Various  Ve- 
locities. 

Adhesion  assumed,  \.     Reduce  by  one-fifth  part  to  correspond  to  i  adhesion. 


Pounds  on  Drivers 
Per  Square  Foot  of 

Horse-power  to  be  supplied  Per  Square  Foot,  at 
Velocities  in  Miles  Per  Hour. 

Geate  Area. 

10 

15 

20 

30 

40 

50 

2,000    1               Minimum 
2,500    1-                    for 

13-33 
16.67 
20.00 

23-33 
26.67 
30.00 

20.0 

26  67 

40.0 

53-33 
66.67 
80.00 

93-33 
106.67 
120.00 

66.67 

25.0 
30.0 
35-0 

33-33 

:     50.0 

83.33 

3,500 

American  engines. 
Freight  types. 

40.00 
.       46.67 

60.0 
70.0 
80.0 
90.0 

100.00 
116.67 

4,000 

4.500    . 

40.0 
4S-0 

53-33 
60.00 

133-33 
150.00 

The  black  line  marks  the  Hmit  at  which  it  ceases  to  be  physically  possible,  under  the 
most  favorable  circumstances,  for  the  boiler  to  produce  sufficient  steam  to  utilize  the  full 
adhesion,  allowing  30  horse-power  per  hour  per  square  foot  of  grate  (an  ordinary  maximum 
being  24  horse-power)  and  for  \  adhesion.  To  add  a  similar  line  corresponding  to  \  ad- 
hesion, draw  the  line  at  37.5  horse-power  instead  of  30  horse-power,  as  indicated  by  dotted 
line,  making  little  change. 


552.  There  is,  however,  one  more  resource  for  eking  out  deficiency 
of  boiler  power — to  draw  upon  the  reserve  in  the  boiler  itself,  either  by 
pumping  in  no  feed-water  for  the  time  being,  or  by  allowing  the  pressure 
to  fall  somewhat  while  the  excessive  demand  continues,  or  both. 

Neither  of  these  resources  amounts  to  much,  although  both  assist  very 
slightly.  As  respects  variations  of  pressure  ;  as  the  pressure  of  steam  rises 
or  falls,  the  sensible  temperature  of  the  steam  rises  or  falls  very  rapidly, 
but  the  total  heat  per  pound  of  steam  is  little  affected— so  little  that  the 
total  heat  was  at  one  time  supposed  to  be  constant  for  all  pressures.  This 
is  shown  in  Table  143,  on  the  following  page  : 

553.  A  very  small  excess  of  demand  for  steam,  therefore,  will  cause 
the  pressure  to  fall  very  rapidly,  and  as  there  are  only  20  to  30  lbs.  of 
live  steam  stored  in  the  boiler  at  any  one  time,  what  is  gained  by  letting 


454 


CHAP.  XI.—LOCOMOTIVE  BOILER. 


Table  143. 
Weight  of  and  Heat  in  Steam  at  Various  Pressures. 


Pressure, 

Lbs.  per 

sq.  in. 

above 

atmosphere. 

Heat-units.* 

Weight 

per 
cu.  ft. 
Lbs. 

Sensible. 

TotaL 

o 

212.0 

II78.I 

.038 

20 

259-3 

II92.5 

.086 

50 

281.0 

II99.I 

.120 

ICO 

33S.0 

1216.5 

.263 

120 

350.1 

1220.2 

.308 

140 

361.0 

1223.5 

•350 

160 

370.8 

1226.4 

•393 

Full  tables  giving  these  properties  of  steam  for  each  point  of  pressure  will  be  found 
in  D.  K.  Clark's  "  Manual  for  Mechanical  Engineers,"  and  in  many  other  treatises.  The 
pressures  given  above  the  atmosphere  should  be  0.3  lb.  greater,  and  the  total  pressure 
measured  from  a  vacuum  15  lbs.  greater.  These  figures  rest  purely  on  experiment,  from 
which  accurate  formulae  have  been  deduced. 


Table  144. 
Available  Energy  in  Heated  Water  and  Steam  of  Locomotive 

Boilers, 

Between  normal  temperature  of  steam  and  212"   Fahr.,   or  that  available  in  case  of 

explosion.    For  practical  working  the  available  stored  energy  is  very  much  less  than 

this.     See  top  of  next  page. 

[Abstracted  from  a  paper  on  "  Boiler  Explosions,"  by  Prof.  R.  H.  Thurston,  Trans.  Am.  Soc. 

M.  E.,  Vol  VL,  Paper  CLXIL] 


Area 

OF — 

W 

EIGHT    OF— 

Stored  Energy  Available— 

Grate. 

Heat'g 
surface. 

Boiler. 

Water. 

Steam. 

Water. 

Steam. 

Total. 

sq.  ft. 
15 

sq.  ft. 

875 

lbs. 
14,020 

lbs. 

6,330 

lbs. 
19.02 

ft.-lbs. 

I  =  1000 
64,253 

ft.-lbs. 

I  =  1000 

2,385 

ft.-lbs. 

I  =  1000 

66.638 

mile-lbs 
1  =  1 
12,621 

20 

1,200 

20,565 

6,450 

25-65 

64,452 

3,226 

67,678 

12,818 

23 

1,070 

19,400 

5,260 

21.67 

52,561 

2,717 

55,278 

10,469 

30 

ii35o 

25,000 

6,920 

31-19 

69,149 

3,910 

73,059 

13.837 

*  The  heat-unit  must  be  carefully  distinguished  from  a  mere  degree  of  temperature,  from 
which  it  differs  much  as  2.  foot-pound  differs  from  a  pound  or  a  foot,  or  as  an  area  differs  from 
a  distance.  The  little  diagrams  on  the  next  page  (Figs.  118,  iig,  and  120)  will  make  this  clearer. 
A  heat-unit  is  a  quantity  of  heat.  What  is  called  temperature  is  merely  an  altitude  of  heat.  A 
high  altitude  of  temperature  is  consistent  with  a  very  small  quantity,  if  the  body  be  small,  or 
even  if  the  body  be  large  and  its  capacity  for  absorbing  or  holding  heat  small.  Different, 
materials  differ  greatly  in  this  respect. 


CHAP,  XI.— LOCOMOTIVE  BOILER. 


455 


Assumed  steam  pressure,  125  lbs. 

This  table  gives  the  entire  energy  in  the  steam  and  water  between  212°  and  353°,  or 
the  amount  of  work  which  would  be  done  if  the  pressure  were  allowed  to  fall  to  zero 
and  there  were  no  back  pressure  or  other  losses  in  the  cylinder.  It  will  be  seen  to  be 
about  equal  to  the  ordinary  working  tractive  power  of  a  powerful  engine  for  about  one 
mile.  Perhaps  one  half  of  this  stored  energy  is  a  practically  available  resource  in 
operating  emergencies. 


eoFf- 

■20  Fi- 
wFf- 


Areas 


Leii^fhs 


0 
Fig 


pressure  drop  from  140  lbs.  to  50  lbs.  is 
simply  this,  say,  for  the  second  engine 
given  in  the  preceding  Table  144  : 

In  Steam  Space:  Only  8.8  instead  of  25.6 
lbs.  of  steam  are  required  to  fill  the  steam 
space,  releasing  some  17  lbs.  of  steam. 

In  Water  Space:  The  fall  of  sensible 
temperature  from  361°  to  281°  releases  80 
heat-units  per  pound  of  water,  and  80  x  i 
(specific  heat  of  iron)  heat-units  per  pound 
of  boiler,  being  sufficient  to  convert  into 
steam  a  weight  of  water  equal  to  about 
-^-^  of  the  total  weight  of  boiler  and  con- 
tained water,  or  for  the  given  engine  728 
lbs.  of  steam. 

This  makes  a  total  gain  of  only  745 
lbs.  of  steam,  or  y]\  lbs.  per  square  foot 
of  grate,  which  is  about  what  a  square 
foot  of  grate  should  evaporate  in  3f  min- 
utes, at  the  rate  of  600  lbs.  per  hour. 

554.  As  respects  letting  the  supply  of  fig.  hq.-Relation  of  Foot- 


10  ft.       20ft       30ff.     -fOff; 

118. — Relation    of    Areas    to 
Altitudes  and  Lengths. 


^oF+- 


<30Ff.'^^ L I— 

Foot  Pound's 

■20Fi-\ \ J--- 

;    oF  WoRK.\ 
■/OFtA i \— 

zoibs  30  lbs  '=fo/jb3 


10  lbs 


water  fall  off,  here  also  the  gain  is  COmpar-     °^  ^°^^  ™  Distances  and  Weights. 

atively  slight,  because  the  heat  used  to 
raise  the  temperature  of  the  water,  say, 
from  60°  to  the  boiling-point  at  120  lbs. 
pressure,  350°,  is  only  290  heat-units  per 
pound  of  water,  or  one  third  f|||-)  as 
much  as  is  needed  to  change  the  water 
into  steam  after  it  has  reached  that  limit. 
Therefore,  even  if  we  allow  as  much  as  10 
per  cent  of  the  whole  water  in  the  boiler 

to   evaporate   without  replacing  it,  which    Fig.   120.— Relation    of    Heat-units 
will  lower  it  about  3  in.,  we  only  save  heat  ""^  Temperature  and  Mass. 

enough  to  evaporate  -^  of  the  whole  water  in  the  boiler,   or  215  lbs., 


0    \           f 
ko  /T.l.    ...4 4 

! 

i       i       ! 

f— « 

0     !      Heat  Un'/ts. 

so  F-T f i- — — - 

1 

1             '             ' 

/c'V-J- L ] 

I            [Mass.] 
!            !            : 

— 

0 

/olbs     2olbs     3olhs   40 

)lis! 

456 


CHAP.  XI— LOCOMOTIVE  BOILER. 


being  somewhat  over  lo  lbs.  per  square  foot  of  grate,  or  about  what  is 
evaporated  in  one  minute. 

555.  Nevertheless  it  helps ;  but  that  the  help  is  small,  is  clear  in  an- 
other way  from  Table  143,  which  gives  the  total  available  energy  in  the 
boiler  and  contents  if  the  boiler  pressure  were  allowed  to  fall  to  zero,  and 
the  steam  thus  produced  used  without  loss  (other  than  the  heat  in  the 
steam  at  212°)  in  the  cylinders. 

It  will  be  seen  from  Table  143  that  an  engine  which  is  working  fairly 
hard  (as  hard  as  it  can  continue  to  work  indefinitely),  and  evaporating 
600  lbs.  per  square  foot  of  grate,  will  evaporate  a  whole  boilerful  of  water 
in  from  20  to  40  minutes.     This,  again,  shows  that  the  available  reserve 

Table  145. 

Estimated  Approximate  Distribution  of  the  Loss  of  Heat  in  American 
Locomotive  Boilers  to  its  Various  Contributing  Causes. 


Theoretical  evaporation  of  fairly  good  (14,000  H.  U.) 
coal 


Actually  evaporated  in  fair  average  practice,  with 
such  coal 


Leaving  as  wastage  to  be  accounted  for,  which 
may  be  divided  between  the  various  sources 
of  loss,  as  follows  : 

I.  Heat  carried  off  in  the  gases  of  combustion  (ex- 
tremes of  smoke-box  temperature  taken  at  392'' 
and  724°) 


2.  Lost  in  the  ash 

3.  Getting  up  steam  and  banking  fires  (about  10  per 

cent,  but  not  included  above,  and  so  neglected.) 

4.  Unconsumed  coal  ejected  by  the  blast 

5.  Imperfect  combustion 

6.  External  radiation 

7.  Entrained  water  (a  real  loss  but  apparent  gain). 

8.  Lost  through  safety-valve 

Total  loss  as  above  estimated 


Maximum. 


Lbs.        Per  cent. 


12.07 
9.06 


3-OI 


.36 

1.44 
•0.12 
0.12 


3.01 


75- 


Minimum. 


Lbs. 


6.04 
6.04 


6.04 


Per  cent. 


0.+ 


1. 21 

10. 

.60 

1. 81 

15- 

0.61 

-5. 

0.61 

These  extremes  are  rarely  reached  in  the  same  engine,  but  the  maximum  is  only 
reached  under  favorable  and  the  minimum  under  unfavorable  conditions  for  economical 
combustion. 

In  marine  practice,  nearly  all  the  above  sources  of  loss  except  the  first  are  avoided.  An 
efficiency  of  from  80  to  90  per  cent  of  the  theoretical  evaporation  is  therefore  no  longer 
exceptional. 


CHAP.  XI.— LOCOMOTIVE— CYLINDER  POWER.  457 

in  the  boiler  is  a  pretty  small  affair,  and  the  normal  generation  of  steam 
we  have  seen  (Table  142)  to  be  quite  unequal  to  utilizing  the  full  tractive 
power  at  any  high  speed. 

556.  The  boiler  is  not  an  uneconomical  generator  of  power.  In  the 
last  types,  from  75  to  90  per  cent  of  the  potential  energy  which  goes  into 
it  in  the  form  of  fuel  leaves  it  in  the  form  of  steam.  Nor  is  the  locomo- 
tive boiler,  in  spite  of  its  great  efficiency  in  proportion  to  weight,  inferior 
to  other  types  in  economy,  the  very  best  of  stationary  and  marine  boilers 
alone  excepted.  Without  going  into  details,  for  which  space  cannot  be 
taken,  Table  145  gives  the  substance  of  the  facts  in  relation  to  its  ordi- 
nary working  when  not  burning  over  80  to  100  lbs.  of  coal  per  hour. 
When  combustion  is  pushed  harder,  the  loss  from  unconsumed  coal 
ejected  by  the  blast  is  much  heavier. 

THE   CYLINDER  POWER. 

557.  Since  we  have  seen  that  the  locomotive  boiler  is  quite  unequal 
to  supplying  steam  enough  to  utilize  the  full  adhesion  at  high  speeds,  it 
results  in  no  serious  loss,  and  need  occasion  no  surprise,  that  the  cylin- 
der, which  is  a  mere  transmitting  agency,  is  in  actual  practice  and  as 
actually  constructed  unequal  to  transmitting  such  an  amount  of  power, 
even  if  it  could  be  generated.  As  the  speed  rises  above  the  lower  work- 
ing speeds  for  which  the  locomotive  was  designed  there  is  a  very  great 
reduction  of  cylinder  efficiency  as  measured  by  the  average  pressure  in 
the  cylinders,  cut-off,  opening  of  throttle,  and  boiler  pressure  being  the 
same. 

558.  The  steam-engine,  even  in  its  most  perfect  forms,  attempts  only 
to  convert  into  work  the  expansive  energy  of  steam,  which  is  a  very 
small  part  of  its  total  energy.  All  that  great  proportion  of  the  heat 
energy  in  the  steam  which  has  been  required  for  the  purpose  of  chang- 
ing it  from  water  into  steam  is  wholly  thrown  away,  even  in  a  theoreti- 
cally perfect  steam-engine.  It  is  hardly  to  be  conceived  of  that  science 
will  not  eventually  discover  some  radically  different  device  for  convert- 
ing heat  into  work  which  will  be  many  times  more  effective,  but  at  pres- 
ent we  do  not  seem  to  be  even  tending  toward  it. 

559.  All  ordinary  forms  of  steam-engines  are  in  substance  similar  to 
the  engine  of  the  locomotive,  which  in  its  essential  outlines  is  simplicity 
itself,  consisting  only  of  a  piston  vibrating  back  and  forth  within  a  cylin- 
der to  which  steam  is  admitted  and  cut  off  at  each  end  alternately  by 
some  form  of  automatically-acting  valve — in  the  locomotive,  the  slide- 
valve.     The  steam  is  admitted  for  a  certain  fraction  of  the  stroke  (one 


458  CHAP.  XI.— LOCOMOTIVE— CYLINDER  POWER. 

quarter  to  three  quarters  in  the  ordinary  practice  of  the  locomotive),  called 
Xh^ period  of  admission;  then  cut  off,  permitting  what  steam  is  shut  up 
in  the  cylinder  to  expand  and  do  further  work  during  what  is  called  the 
period  of  expansio7i  ;  and  then  released  or  permitted  to  escape  at  or  be- 
fore the  end  of  the  stroke,  so  that  there  may  be  as  little  as  possible  back 
pressure  to  resist  the  return  stroke. 

While  this  division  of  the  work  done  in  the  cylinder  into  the  period 
of  "  admission"  and  of  "expansion"  is  convenient, yet  during  each  period 
alike  it  is  the  expansive  energy  of  the  steam,  and  that  alone,  which  does 
what  work  is  done. 

560.  On  the  proper  design  of  the  valve-gear  by  which  the  slide-valve  is 
moved,  and  so  the  admission,  cut  off  and  release  of  the  steam  controlled, 
hangs  nearly  the  whole  question  of  good  or  bad  working  of  the  cylinders,  and 
its  theory  is  a  study  in  itself,  into  which  we  need  not  enter  ;  contenting  our- 
selves with  determining  what  are  the  theoretical  limits  of  efficiency,  what  are 
the  results  actually  obtained  in  good  practice,  and  how  these  results  ought  to 
be  and  are  affected  by  varying  conditions. 

561.  The  form  of  valve-gear  known  as  the  link-motion  is  in  all  but  univer- 
sal use  on  American  engines,  and  is  used  on  a  large  majority  of  all  foreign 
engines.  It  was  invented  almost  contemporaneously  with  the  locomotive  itself, 
and  a  large  part  of  the  credit  for  it  is  due  to  the  same  man,  George  Stephenson; 
so  that  it  is  not  unjustly  known  by  his  name,  although  it  is,  properly  speaking, 
the  invention  of  Howe,  a  foreman  in  his  shops.  It  has  not  been  essentially 
modified  or  improved  upon  since  its  invention,  except  as  advancing  experience 
has  given  better  knowledge  of  the  precise  proportions  which  it  should  have, 
and  it  is  with  justice  regarded  as  one  of  the  most  notable  inspirations  in  the 
history  of  mechanism,  fulfilling  as  it  does  very  simply  yet  remarkably  well  all 
the  complex  requirements  which  a  locomotive  valve-gear  should  have. 

562.  Nevertheless  there  are  certain  desirable  ends  which  it  does  not  fulfil, 
and  in  recent  years  a  number  of  valve-gears  have  been  devised,  some  of  them 
of  a  highly  ingenious  character,  which  are  claimed,  and  probably  with  truth, 
to  possess  certain  practical  advantages  over  the  link-motion,  and  which  have 
met  wide  acceptance  abroad.  It  is  possible,  although  as  yet  hardly  probable, 
that  some  of  these  may  eventually  supplant  the  link-motion,  but  none  of  them 
have  yet  been  shown  to  give  such  radically  different  results  from  the  link-mo- 
tion that  any  of  the  conclusions  we  shall  reach  will  be  affected  thereby,  except 
in  degree. 

563i  Assume  such  a  cylinder  as  that  described  in  par.  559  to  have  a 
connection  opened  with  the  boiler,  at  the  beginning  of  the  stroke,  which 
continues  open  until  the  end  of  the  stroke.  Let  the  connection  with 
boiler  be  then  closed,  and  a  connection  with  the  outside  air  opened,  so 


CHAP.  XI.— LOCOMOTIVE— CYLINDER  POWER.  459 

as  to  permit  the  inclosed  steam  to  escape,  while  at  the  same  time  steam 
is  admitted  to  the  other  end  of  the  cylinder  and  the  operation  is 
repeated. 

564.  In  this  we  have  a  steam-engine  of  the  simplest  type,  which  was 
also  the  earliest  type,  and  an  indicator-diagram 
of  such  an  engine,  if  it  worked  perfectly  (which    ^ 
it  would  not  be  likely  to  do  at  very  high  speed),    £5 
would  resemble  Fig.    121.      The   boiler,   being 


constantly  generating  steam,  may  be  considered    b 
as,  for  the  time  being,  a  reservoir  of  infinite   c| 


Frr-LBS:oLWodi^ 


volume,  and  the  expansion  of  the  steam  to  fill 
the  cylinder  will  not  reduce  its  pressure.  Con- 
sequently, the  cylinder  pressure  throughout  the  F^^-  ^^i. 
stroke  will  be  equal  to  the  boiler  pressure,  and  the  diagram  will  be  a 
rectangle,  in  which  the  foot-pounds  of  work  done  will  be  represented 
by  stroke  m  ft.  x  area  of  piston  m  sq.  ms.  x  boiler  pressure  in  lbs.  per 
sq.  in.  The  efficiency  of  even  so  crude  an  engine  as  this  is  considerably 
over  three  fourths  of  what  is  actually  realized  in  fair  average  practice, 
and  fully  as  much  as  is  realized  under  unfavorable  conditions,  and  may 
be  determined  thus  : 

565.  A  17  X  24  in.  cylinder  has  a  capacity  of  3.1525  cu.  ft.,  and  will  hold 
almost  precisely  07ie  pound  of  live  steam  at  a  pressure  of  126  lbs.  per  sq.  in. 
above  the  atmosphere — an  ordinary  working  pressure.  The  work  done  by  this 
steam,  in  foot-pounds,  if  there  be  no  loss  by  condensation  or  other  disturbing 
cause,  will  be 

X  126  lbs.  X  2  ft.  =  57,200  ft.-lbs. 

4 

Dividing  this  amount  of  work  by  the  mechanical  equivalent  of  heat,  we  obtain 
as  the  useful  work  which  ought  to  be  realized  if  there  were  no  losses  by  back 
pressure  of  steam,  condensation,  or  otherwise, 

57,200  __    __ 

^^-^—  =  74.09  H.  U. 
772  '"^    ^ 

In  addition  to  this  useful  work  the  steam  has,  in  a  non-condensing  engine, 
done  this  work  against  the  pressure  of  the  atmosphere  on  the  opposite  side  of 
the  piston,  amounting  to  nearly  15  lbs.  per  sq.  in.,  or  about  11.2  per  cent  of  the 
useful  pressure.  Computed  to  include  work  done  against  this  pressure,  most 
of  which  is  avoided  in  marine  and  other  condensing  engines,  the  total  work 
done  is  equivalent  to  74.09  X  1.112  =  82.91  H.  U. 

Now  the  total  heat  in  this  quantity  of  steam  is  (Table  100)  1191  H.  U.,  so 
that  all  that  is  utilized  is  : 


460  CHAP.  XI.— LOCOMOTIVE— CYLINDER  POWER. 

Cutting  off  at  Full  Stroke. 

In  a  perfect  non-condensing  engine,  In  a  perfect  condensing  engine, 

74-09   ,        ^  82.9   ^  ^ 

=  6.22  per  cent. =  6.96  per  cent. 

1191  1191  ^    ^ 

Practically  even  this  result  is  7  or  8  per  cent  too  great,  owing  to  the  steam 
wasted  to  fill  the  passages  between  the  valve  and  the  piston,  which  does  no 
work  whatever  unless  the  steam  is  expanded  after  being  cut  off. 

566.  There  being  33,000  X  60  =  1,980,000  ft.  lbs.  in  a  horse-power  per 
hour,  we  shall  have  to  use,  in  order  to  develop  a  horse-power  per  hour  with  an 
engine  worked  in  this  way, 

1,980,000  ^    ,, 

• =  34.62  lbs.  of  steam. 

57,200 

And  if  we  had  a  boiler  able  to  utilize  the  full  evaporative  efficiency  of  fairly 

good  coal,  instead  of  only  one  half  to  three  fourths  of  it,  we  should  require 

34.62 

— '■ —  =  2.87  lbs.  of  coal  to  obtain  one  horse-power  per  hour. 

567.  Only  under  the  most  favorable  possible  circumstances  for  ob- 
taining the  last  degree  of  efficiency  out  of  the  locomotive  is  it  possible 
to  obtain  a  horse-power  per  hour  with  2.87  lbs.  of  coal,  or  with  less  than 
25  lbs.  of  steam.  Ordinarily  in  fact,  even  on  long  up  grades  which 
afford  the  most  favorable  localities  for  the  economical  working  of  the 
locomotive,  something  like  30  lbs.  per  horse-power  is  used  (see  Table 
146).  With  ordinary  evaporation  of  6  to  8  lbs.  of  water  per  pound  of 
coal  from  4  to  6  lbs.  of  coal  per  horse-power  per  hour  are  required,  and 
this  is  about  what  is  ordinarily  obtained  from  locomotives,  the  very 
finest  marine  engines  running  down  to  1.3  to  1.5  lbs. 

568.  Many  engines  in  times  past  have  been,  and  in  fact  still  are,  run 
at  nearly  full  stroke,  as  notably  high-pressure  engines  on  Mississippi 
River  steamboats.  In  the  locomotive  this  is  occasionally  done,  but 
usually  the  steam  is  permitted  to  expand  through  about  half  the  stroke. 
The  theoretical  gain  from  doing  this  is  large,  but  the  practical  gain 
small — so  small  that  nearly  all  that  is  gained  by  it  is  to  neutralize  the 
various  practical  obstacles  to  realizing  the  full  theoretical  work  of  steam 
at  full  stroke, 

569.  A  theoretically  perfect  condensing  steam-engine  and  boiler  requires 
only  f  lb.  per  H.  P.  per  hour  of  coal,  and  some  8  lbs.  of  water,  at  a  boiler 
pressure  of  120  lbs.  per  sq.  in.,  utilizing  a  scant  26  per  cent  of  the  energy  in  the 
coal.     A  theoretically  perfect  non-condensing  engine  utilizes  16.9  per  cent. 

570.  The  very  best  ever  claimed  to  have  been  realized  with  locomotives  is 
in  the  paper  by  Mr.  Wm.  Stroudley  before  referred  to  (par.  550),  where  it  is  stated 
that  in  a  trip  oi  50.4  miles  at  43.3  miles  per  hour  the  average  coal  consumption 


CHAP.  XI.— LOCOMOTIVE— CYLINDER  POWER. 


461 


(exclusive  of  coal  for  getting  up  steam,  which  is  about  3  lbs.  per  mile  run)  was 
24.87  lbs.  per  mile,  and  the  average  horse-power  developed  528.53  (see  Fig. 
123).  This  amounts  to  producing  a  horse-power  with  2.04  lbs.  of  coal  per  hour 
— a  result  which  has  been  approached  elsewhere  under  the  most  favorable  con- 
ditions, but  when  alleged  as  the  result  of  an  ordinary  service  run  over  undu- 
lating grades  it  is  all  but  certain  that  its  remarkably  favorable  result  is  largely 
due  to  serious  errors  in  the  record  ;  in  great  part  probably  originating  in  the 
shortness  of  the  run,  in  which  only  some  1200  lbs.  of  coal  is  alleged  to  have 
been  burned,  or  1.2  cu.  ft.  per  square  foot  of  grate.  The  same  allowance  must 
be  made  for  the  alleged  rate  of  evaporation,  11. 6  to  12.6  lbs.  per  pound  of  coal, 
which,  it  is  risking  little  to  say,  is  from  10  to  20  per  cent  beyond  the  limits  of 
physical  possibility,  in  view  of  the  fact  that  the  gases  in  the  smoke-box  seem 
to  have  had  a  temperature  of  600°  Fahr. 

571.    A  far  better  index  of  average  practical  results  is  that  given  in  Tables 


^~ 

r 

r" 

n 

{ 

■>, 

\\ 

1 

\ 

0 

Mj 

\ 

1/ 

A 

[3 

?e 

^ 

I"/ 

- 

s 

/ 

\ 

'K^ 

, 

\ 

0 
200  3 

/ 

A 

L^^ 



-V 

r-. 

N, 

\ 

s 

eo 

/ 

7 

"■ 

^ 

y 

-\ 

'\ 

H 

•^ 

■^ 

\ 

\ 

0 

J 

-^ 

\, 

20 

py 

y     r 

J 

•i  f 

/' 

V'P 

^ 

A. 

(" 

sS^ 

K> 

>e= 

} 

\ 

K 

^ 

/ 

\ 

\ 

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1/ 

f> 

\e 

i 

,- 

.-, 

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.-' 

-' 

>■. 

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, 

'-' 

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OS 

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... 

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,'■ 

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i^ 

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Fig.  122. 
Diagram  showing  Results  of  a  Test  of  a  Baldwin  Locomotive,  by  John  W.  Hill,  M.E., 
DURING  a  Run  between  Cincinnati  and  Hamilton,  24.7  Miles.    (See  Tables  146  and  147.) 
[The  abscissae  represent  the  intervals  between  indicator-diagrams,  which  were  taken  in  as 
quick  succession  as  possible  (40  in  25  miles,  or  ih.  26m.)  and  not  miles.] 

The  mean  effective  pressure  may  be  considered  as  the  equivalent  of  the  tractive  power, 
which  should  theoretically  fall  immediately  to  zero  on  striking  the  down  grade,  if  the  velocity 
were  to  remain  the  same,  but  instead  of  this  was  maintained  about  the  same  for  some  distance, 
with  the  effect  of  greatly  increasing  the  speed  and  horse-power. 

146  and  147,  where  from  d^\  to  5^  lbs.  of  coal  per  horse-power  per  hour  were 
required,  rising,  when  combustion  was  so  forced  as  to  expel  unconsumed  coal 


462 


CHAP.  XI.— LOCOMOTIVE— CYLINDER  POWER, 


Sf^A 


Fig.  123.— Experiments  on  the  London, 

Express  Passenger  Engine,  1814"  X  26"  cylinders.  6  ft.  6  in.  drivers.     Mean  weight,  67.2 

long-  tons,  including  tender;  31.14  tons  on  drivers.     Weight  of  engine  and  23  carriages,  335.7 

tons.     Average  of  Whole  Run:  Speed,  43.3  miles  per  hour;  indicated  horse-power,  528.53; 

tractive  power,  4477  lbs.;  maximum  power,  11,590  lbs.;  coal  per  mile,  24.87  lbs. 

from  the  smoke-stack  (as  it  often  is  in  practice),  to  over  7  lbs.  Fig.  122  shows 
the  fluctuations  of  speed  and  tractive  power  during  a  part  of  this  run  in  a  some- 
what similar  manner  to  Fig.  123. 


Table  146. 

Tests  of  a  Baldwin  i6  X  24  in.  American  Engine  in  Express  Freight 

Service. 

[Deduced  from  Records  of  Tests  by  John  W.  Hill,  M.  E.,  Jour.  Frank.  Inst.,  April-May,  1879. 
For  details  of  engine  and  train,  see  below.] 


Boiler  Performance. 

Cincinnati 

to 
Hamilton. 

Hamilton 

to 

Twin  Creek. 

Twin  Creek 

to 

Dayton. 

Apparent  evaporation,  actual 

"     less  5  p.  c.  primage 
Equivalent  from  and  at  212° 

lbs. 
7-44 
7.07 
8.36 

9.96 

83.9 
10,586 

sq.  ft. 

3-24 

lbs. 
4-75 
4-51 
5.34 

13-01 

172.0 
13,856 

sq.  ft. 

2.57 

lbs. 
6.55 
6.22 
7.30 

12.24 

117. 3 
12,918 

sq.ft. 
2.61 

Actual  evap.  (less  primage)  per  sq.  ft. 

of  heating  surface,  per  hour 

Coal    burned  per  sq.  ft.  of  grate,  per 

Evap'n  from  and  at  212°  per  hour 

Estimating  coal  burned   per  sq.  ft.  of 
grate  per  hour  with  natural  draft  at 
25  lbs.,  and  one  horse-power  =  15 
sq.  ft.,  we  have,  for  such  an  engine 
as  above,  for  a 
Heating  surface  per  H.  P.  of 

Ratio  of  effect  of  blast  (  coal  burned 

to    natural     draft,  \ 

comparing  by (  heating  surface 

3.36 
3.32 

4-34 
4.33 

4.04 
4.08 

CHAP.  XL— LOCOMOTIVE— CYLINDER  POWER. 


463 


Brighton  &  South  Coast  Railway. 

speed  in  miles  per  hour  is  indicated  by  the  fif^^es  ^t  the  top  of  the  diagram  ai^^^^^ 
hea/v  solid  line.     Horse-power  is  indicated  by  the  docted  line  made  of  points.     \^'^^^'^.' /fjl^ 
ishScatedbrthe  light-dotted  line.     The  dotted  lines  along  the  base  show  where  diagrams 
were  taken,  49  in  all.    The  three  arrow-heads  at  the  left  indicate  stops. 


Table  146. — Continued. 

Engine  Performance. 


Miles  run   

Speed,  miles  per  hour 

Mean  boiler  pressure 

•*      initial        "  

' '      cut-off 

"      effective  pressure 

Grade  of  expansion,  incl.  clearance.. 

Distribution  of  Power: 

Indicated  H.  P 

Power  absorbed  by  engine  only  above 

all  resistances 

Gross  load 

Extra  friction   due  to  load  (5  p.  c  of 

gross  load) 

Power  expended  in  moving  train.. . 
Per  cent  of  total  power  absorbed  by 

engine 

Cost  of  Power: 


Steam  per  hour  to  engines 

Steam  accounted  for  by  diagrams  . . 

Per  cent  of  do   

Steam  per  I.  H.  P.  from  boiler 

"  "         "         "     diagrams.. 

Coal  per  I.  H.  P.,  actual 

*'  "         "        at  I  to  9  evap'n. 


15.87 
22.67 
124.0  lbs. 
107.      " 
.515 
64.2  lbs. 
2.09 

H.  P. 

368.7 

41-3 
327-4 

16.4 
311. o 

15.63 

lbs. 
12,312 
9,883 
80.3 
33-4 
26.9 
7-03 
3.71 


16.267 
23.0 

123.0  lbs. 
105 -5   " 

•52 
63 . 2  lbs. 
2.03 

H.  P. 

388.5 

44-3 
344-2 

17.2 
327-0 

15.82 

lbs. 

12,415 
10,324 
83.2 
32.0 
26.6 
5.36 
3.55 


These  tests  are  perhaps  as  fairly  representative  of  every-day  American  practice  as  any 
which  exist.     See  details  on  following  page  and  Table  147. 


464  CHAP.  XI.—LOCOMO TIVE— CYLINDER  PO  WER. 

Details  of  Engine  and  Train  for  Tables  146,  147. 
Baldwin  American  engine,  16  x  24  in.  cylinders,  61  in.  drivers,  15.99  sq.  ft.  grate  area, 

898.7  total  heating  surface. 

Weight  on  drivers,  44,840  ;  trucks,  27,380  ;  total,  72,220  lbs. 
Weight  of  tender,  empty,  23,480  lbs.;  load,  24,000  lbs. 

Train,  35  loaded  box  cars  and  caboose,  weighing 782.94  tons. 

Average  of  engine  and  tender 55-72     " 

Total  weight  of  train 838.66  tons. 

Engine  in  ordinary  working  order,  out  of  shop  22  months  (55,471  miles),  Pittsburg  No. 
2  coal.     Date  of  tests,  July  28,  1878. 

Evaporation  per  sq.  ft.  of  fire-box  surface,  assuming  60  per  cent  of  the  evaporation  to 
have  been  from  that  surface,  93.53  lbs.  per  hour. 

Friction  of  engine  was  determined  by  series  of  indicator-diagrams  at  each  speed, 
averaging  15.8  per  cent  (including  the  allowance  of  5  per  cent  for  extra  work  due  to  load, 
which  is  probably  too  large),  while  the  weight  of  the  engine  was  only  6.65  per  cent  of  the 
total.  This  work,  however,  includes  atmospheric  head  resistance  as  well  as  rolling  and 
internal  friction. 

572.  A  more  reasonable  presentation  of  what  may  fairly  be  expected  from 
locomotives  under  the  most  favorable  vv^orking  conditions  for  developing  power 
economically  is  given  in  a  paper  on  "  The  Consumption  of  Fuel  in  Locomo- 
tives," read  before  the  Institution  of  Mechanical  Engineers,  by  M.  Georges 
Mari6,  engineer  of  the  Paris  &  Lyons  Railway,  of  France.  In  these  tests  a 
powerful  locomotive  (21^  X  26  in.  cylinders,  eight  4  ft.  if  in.  drivers,  carrying 
some   100,000  lbs.;  exact   figures   not  given)  was  loaded  with  a  light  train  of 

167. 8  to  183.2  tons,  and  run  up  a  long  grade  on  the  Mont  Cenis  line,  rising 
1709  ft.  in  171^  miles,  or  about  a  two  per  cent  average  grade  (the  maximum  being 
2.84  per  cent),  in  one  hour.  The  total  tax  on  the  adhesion  on  such  a  grade  was 
only  some  65  lbs.  per  ton  maximum  and  46  lbs.  average,  or  a  total  average 
traction  of  some  8000  lbs.  With  so  light  a  load  it  was  possible  to  cut  off  at  one- 
fifth  stroke.  The  author's  conclusions  from  the  tests  are  that  with  a  good  loco- 
motive and  a  good  driver  the  consumption  of  fuel  and  water  is  as  follows  : 

Consumption  of  fuel  per  effective  horse-power  per  hour. .  3.27  lbs. 

Consumption  of  fuel  per  indicated  horse-power  per  hour. .  2. 88  lbs. 

Ratio  of  consumption  of  water  to  consumption  of  fuel... .  8.88 

Ratio  of  dry  steam  produced  to  fuel  consumed 8.08 

These  satisfactory  result  are  attributed  to  the  following  causes:  "(i)  The 
total  heating  surface  of  the  boiler  is  very  large  compared  to  the  grate  surface, — 
96  to  I, — so  that  the  boiler  absorbs  the  heat  of  the  gases  very  completely  p 
(2)  the  cylinders  of  the  locomotive  are  very  large, — according  to  the  late  M. 
Marie's  system, — so  that  the  grade  of  expansion  is  high  ;  (3)  the  locomotive- 
was  very  well  looked  after,  which  is  an  important  point  in  economy  of  fuel." 


CHAP.  XI.— LOCOMOTIVE— CYLINDER  POWER. 


465 


Table  147. 

Details   as  to  TxIE  Resistances   of   Engine  and  Train   in  the  Tests 
Abstracted  in  the  Preceding  Table. 

~        ~~~  C.  to  H.      H.  to  T.  C.      T.  C.  toD. 

In  three  runs  of 24.7  miles.    15.87  miles.   16.27  miles.. 

At  speeds  in  miles  per  hour  of 17-23  22.67  '-^S-o 

Average  of — 
The  averag-e  indicated  H.  P. ,  as  determined  by  the  average    40  cards.        20  cards.        21  cards.. 
'      '     ■'        '    '  ■       ■  L  H.  P. . 


of  cards  taken  on  both  sides  of  the  engine  simulta- 
neously at  intervals  of  tvvro  minutes,  was  

The  entire  weight  of  the  train  having  been,  engine,  55.72  -}- 
782.94  =  838.66  tons,  we  may  compute  from  the 
above  data  that  the  average  tractive  energy  of  the 
locomotive  (including  its  own  internal  friction)  was 

Equal,  average  of  entire  train 

Of  the  above  H.  P.,  however,  it  was  determined  by  actual 
trial  that  the  indicated  H.  P.  necessary  to  move  the 
engine  alone  at  the  given  speeds  was 

And  it  was  estimated  that  when  the  engine  was  working 
hard  there  was  a  further  addition  to  its  internal 
friction  of  5  per  cent  loss  on  work  done,  = 

Making  total  H.  P.  absorbed  within  engine 

Deducting  this  from  the  work  done,  and  deducting  engine 
from  weight  of  train,  we  find  the  average  traction 
exerted  on  the  traiti  was 

Leaving  as  the  power  required  to  propel  the  engine  itself, 
without  load 

Add  estimated  addition  to  engine  resistance  when  work- 
ing hard  (5  p.  c.) 


291.9 


6,346 


368.7 


i-S 


-lbs. 


. 1. 

33-4 


12.9 

46.3 


6,097 

-lbs.  per  ton- 

727 


H.  P.,  engine  only ^ 

41-3  44-3 


6.83 


Total  continuous  force  in  lbs.  to  move  eng.  itself. 
Or  in  lbs.  per  ton  of  engine  and  tender: 

Locomotive  without  load 

Increase  due  to  load 

Total  locomotive  resistance 

Assuming  the  effective  end-area  of  the  engine  for  air  re- 
sistance to  be  100  sq.  ft.,  and  air  resistance  to  be 
1^  lb.  per  sq.  ft.,  at  10  miles  per  hour,  we  have  for 
air  head  resistance  only 

Leaving  as  the  tractive  and  internal  resistance  of  the 
engine  without  load 


i6.4 
57-7 

-lbs.  per  ton- 

6-57 
—Total  Ibs.- 

683. 

272. 

955- 
-lbs.  per  ton- 


17.2 
61.5 


6.78 


13.04 
5.06 


148 


26 
4.87 


17-13 


-Total  lbs. 
257 


12.96 
5-04 


265 
457 


In  round  figures,  we  may  deduce  from  the  preceding,  for 
locomotive  resistances  in  lbs.  per  ton,   of  engines 
of  the   American    type   (in   which  head-resistance  ^ 
would  be  a  larger  proportion  than  in  more  powerful 
engines)..... | 


579  426 

Lbs.  per  ton  of  eng. 

''Atmospheric 3.0 

Rolling  friction,  light  ...  5.0 

Internal     "  "      ...  5.0 

"  "  increase 

due  to  load 5.0 


TotaL 


The  average  of  the  train  behind  engine  is,  say 6.75 

Excess  of  engine  resistance,  lbs.  per  ton  of  engine , 11.25 

This  engine  excess,  when  distributed  through  the  entire  train  (of  35  loaded  cars)  makes  a  differ- 
ence, as  shown  above,  of  only  (average,  0.74,  0.70,  0.77),  say %  lb.  per  ton. 


30 


466 


CHAP.  XI.— LOCOMOTIVE— CYLINDER  POWER. 


Reference  is  also  made  in  the  same  paper  to  some  experiments  made  by 
M.  Regray,  Chief  Engineer  of  the  Eastern  Railway  of  France,  on  consumption 
of  fuel  in  express  engines  hauling  express  trains,  showing  3.01  lbs,  per  indi- 
cated horse-power  as  an  average,  and  2.48  lbs.  as  the  minimum.  These  satis- 
factory results  are  claimed  by  the  author  to  be  due  in  large  part  to  the  use  of 
large  heating  surfaces  and  large  cylinders  :  he  always  built  his  own  locomo- 
tives by  that  rule. 

673i  The  present  tendency  in  this  country,  however,  is  not  by  any  means 
toward  the  use  of  large  cylinders,  but  rather  toward  heavier  engines  and  boilers 
for  the  same  cylinders.     The  comparison  given  in  Table  148  shows  this  very 


Table  148. 

Increase  in  Total  Weight  of  Engines  having  the  Same-sized 

Cylinders. 

Baldwin  Locomotive    Works. 


Cylinders. 

Weight  in  Working  Order,     i  =  1000  Lbs. 

Class  of  Engine. 

On  Drivers. 

1        On  Track.       j 

Total. 

73- 

86. 

Inc. 

73- 

86. 

26 

28 

iS 

21 
24 
24 
13 

Inc. 

1 

73- 

86. 

72 
80 
72 

78 
88 

94 
108 

Inc. 

16  X   24 

17  X   24 

16  X   24 

17  X   24 

18  X   24 

19  X   24 

20  X    24 

42 

45 
51 
54 

58 
61 

87 

46 

52 

54 
57 
64 
70 

95 

4 
7 
3 
3 
6 

9 

8 

23 

25 
16 

18 

19 
20 

9 

\ 

5 
4 
4 

65 
70 
67 
72 
77 
81 
96 

7 

Mogul 

10 

5 

Consolidation 

6 
II 
13 
12 

Rhode  Island  Locomotive    Works. 


Year. 

Total  Weight  in  Pounds. 

16"  X  24" 

17"  X  24" 

18"  X  24" 

1871 

1880 

1885 

65,150 
67,630 
84.850 

70, 100 
75,665 
91,750 

83,730 
103,700 

Mogul  Engines. 

1871 

1876 

1880 

1885 

65,150 

70,  TOO 
77,010 

88,270 
j  94.850 
{  113,700 

CHAP.  XI.— LOCOMOTIVE— CYLINDER  POWER. 


467 


Table  148. — Continued. 
Taunton  Locomotive    Works. 


16"  X  24"  Cylinders. 

17"  X  24"  Cylinders. 

Year. 

Weight-Lbs. 

Year. 

Weight— Lbs. 

1848* 

i857t 

i859t 

i86ot 

1861 

1880 

1883 

1884 

50,000* 

SS.ooof 

52,ooot 

54,ooot 

62,400 

70,000 

82,000 

83,000 

1850* 

1857 

1S65 

1SS2 

18S3 

1884 

1885 

57,000* 

67,700 

67,000 

78,400 

80.000 

go, 000 

91,000 

*  16"  X  20  '  cylinders, 
t  16"  X  ■21" 

*  17"  X  20"  cylinders. 

See  also  Tables  127-130. 

Most  of  the  striking-  change  shown  in  this  table  is  accounted  for  by  the  gradual  in- 
crease in  boiler  pressure  carried.    See  par.  605. 

strikingly.  After  allowing  its  full  weight  to  the  effect  of  the  increase  in  boiler 
pressure  carried,  it  is  clear  that  there  is  no  tendency  toward  using  larger  cylin- 
ders for  the  sake  of  being  able  to  cut  off  earlier. 

THE   THEORETICAL    GAIN   BY    EXPANSION. 

574.  Under  "  Mariotte's  Law"  (given  in  any  text-book  on  physics)  the  vol- 
ume of  a  gas  is  inversely  as  the  pressure,  so  that  if 
the  gas  has  expanded  into  twice  the  volume  it  exerts 
half  the  pressure,  etc. 

In  "  cutting  off  "  steam  at  some  point  in  the  stroke, 
say  half-  or  quarter-stroke,  the  steam  in  the  cylinder 
expands  according  to  this  law  (theoretically),  and 
thus  continues  to  push  the  piston  before  it  with  a 
gradually  decreasing  pressure  as  the  interior  volume 
increases,  until  at  the  end  of  the  stroke  the  pressure 
is  (or  ought  to  be,  with  a  perfect  gas)  just  half  or  a 
quarter  of  the  initial  boiler  pressure.  A  perfect 
indicator-diagram  of  such  a  stroke  would  have  the 
form  of  Figs.  124,  125,  the  bounding  curve  being  a 
hyperbola,  as  in  Fig.  97.  The  shaded  portion  in 
these  cuts  represents  what  is  gained  by  expansion, 
or  ought  to  be. 

575.  But  steam  is  not  affected    in   precisely  the 


Fig.  125.— The  Katio  of  the 
Shaded  Portion  to  the 
Unshaded  Rectangle  im- 
dicates  the  Theoretical 
Gain  by  Expansion. 


same  way  as  a  perfect  gas  by  changes  of  pressure  and  volume;  and,  moreover, 


468 


CHAP.  XI.— LOCOMOTIVE— CYLINDER  POWER. 


Table  149. 

Theoretical  Efficiency  of  Steam,  Expanded  in  Non-conducting 
Cylinders,  involving  no  Waste  of  Heat. 

[Rearranged  from  "  Steam  Using,  or  Steam-Engine  Practice,"  by  Prof.  Chas.  A.  Smith.] 
Boiler  pressure  assumed  at  120  lbs.  per  sq.  in.  above  atmosphere. 


Theoret.  Pounds 

Theoret.  Gain 

Mean  Effective 
Pressure  per  Sq.  In. 

Steam  Per 

by  Expansion. 
Full  Stroke 

Gain  Per 

Cut-off. 

Horse-power 

Cent  by 

Per  Hour  (120  lbs. 

=  1. 00 

Non-con- 

Condens- 

Condensmg. 

over  Atmos.) 

(absolute  press.) 

densing. 

ing. 

Full  Stroke. 

31.3 

1. 000 

119 

131 

10. 1 

1         "     . 

23.8 

1.285 

115 

127 

10.4 

i       "    .. 

21.4 

1-459 

107 

119 

II. 2 

i       •*    .. 

18.8 

1.666 

96 

108 

12.5 

■1       "    . 

16.4 

1.905 

81 

93 

14.8 

i       "    .. 

15-4 

2.278 

60.7 

72.7 

19.8 

i       ''    . 

II. 0 

2.854 

32.1 

44.1 

37-4 

^       "    . 

10.3 

3.034 

25.0 

37-0 

48.0 

^       "    . 

8.8 

3-547 

7-9 

19.9 

151-8 

^       "    . 

8.2 

3-835 

1-3 

13-3 

923 

The  mean  effective  pressure  is  computed  by  assuming  a  minimum  back  pressure  of 
1.3  lbs.  per  sq.  in.  above  the  atmosphere  in  non-condensing  engines,  and  a  minimum- 
back  pressure  of  4  lbs.  (or  12  lbs.  gain  by  condensing)  in  condensing  engines. 


Table  150. 

Theoretical  Economy  of  Steam  from  carrying  higher  Boiler 

Pressures. 

[Abstracted  from  "  Steam  Using,  or  Steam-Engine  Practice,"  by  the  late  Prof.  Chas.  A.  Smith,] 


Pressure 
ABOVE  Atmos- 
phere, Pounds 

Pounds  of  Dry  Steam,  if  Worked  in  a  Perfectly  Non-conducting  Cylin- 
der Per  Total  Horse-power  Per  Hour,  with  Cut-off  at— 

Per  Sq.  In. 

Full  Stroke. 

%  Stroke. 

1^  Stroke, 

J4  Stroke. 

^  Stroke, 

o 

35-7 
33-7 

32.5 
31.7 
30.9 
30.5 
30.2 

24.9 
23.6 
22.7 
22.2 
21.6 
21.4 
21,1 

21.4 
20,3 
19.5 
19.0 
18,5 
18.3 
18,1 

15-7 
14.9 
14.3 
13-9 
13.6 

13-4 
13-3 

II. 7 
II. I 

20 

60         

10.7 
10.4 
10,2 

100 

14.0 

180      

10, 1 

220 

10,0 

Per    cent    of 
Economy     be- 
tween   20    and 
220  lbs.  Press. 

VII. 6  p,  c. 

ii.7p.  c. 

12.2  p.  C, 

12.0  p.  c. 

II. 0  p.  c. 

CHAP.  XL— LOCOMOTIVE— CYLINDER  POWER.  469 


its  expansion  in  the  cylinder  means  the  doing  of  work,— which  means  loss  of 
heat, — which  means  loss  of  pressure, — which  means  a  reduction  in  the  work 
done;  so  that  the  true  curve  which  should  bound  a  theoretical  diagram  (which 
was  called  by  Prof.  Rankine  an  ''adiabatic"  curve)  and  the  precise  theoretical 
gain  which  should  result  from  expansion  is  all  but  incapable  of  rigorous  an- 
alysis. It  has  been  shown  that  there  is  little  error  of  practical  moment  in  as- 
suming that  the  steam  expands  in  accordance  with  Mariotte's  law,  and  it  is  laid 
down  that  it  does  so,  without  qualification,  in  some  popular  text-books;  but  we 
may  as  well  use  the  correct  theoretical  quantities,  as  given  in  Prof.  Chas.  A. 
Smith's  "Steam  Using,  or  Steam-Engine  Practice,"  by  whom  they  were  care- 
fully determined  from  a  large  diagram.  According  to  these  figures,  if  we  can 
conceive  of  a  non-conducting  cylinder  we  obtain  the  following  figures,  abbrevi- 
ated from  Table  149.  The  boiler  pressure  assumed  is  j20,Ibs.  per  square  inch 
above  the  atmosphere,  but  the  results  are  but  little  affected  by  the  initial  boiler 
pressure,  as  will  be  evident  from  Table  150  : 

576.  If  steam  be  cut  off  at 

Full  stroke,     f  f  i  f  i  i 

The  theoretical  gain  by  expansion  (Table  149)  is  as 

I. 000         1.285         1.459         1.666         1.905         2.278        2.854 
Whereas  by  Mariotte's  law  it  is  somewhat  less,  viz. : 

1. 000         1. 261         1.425         1. 616         1.837         2.139        2. 511 
The  theoretical  pounds  of  steam  required,  per  horse-power  per  hour,  are 

31.3  23.8  21.4  18.8  16.4  15.4  TI.O 

And  the  mean  effective  pressure  in  pounds  per  square  inch,  allowing  a  certain 
minimum  of  i  (1.3)  lb.  per  square  inch  for  unavoidable  back  pressure,  should  be 

119.  115.  107.  96.  91.  60.7  32.1 

In  a  condensing  engine  the  mean  effective  pressure  should  be  some  12  lbs. 
more  than  this  in  each  case,  representing  the  gain  by  the  additional  complication 
of  the  condensing  apparatus. 

577.  The  locomotive  engine  is  run,  as  an  average,  cutting  off  at  half-stroke; 
it  is  rarely  possible  to  cutoff  at  less  than  quarter-stroke (6  inches,  with  a  24-inch 
cylinder)  or  at  more  than  seven-eighths  stroke.  The  maximum  gain,  therefore, 
which  it  ought  in  theory  to  result  from  expansion  is  only  some  67  percent,  and 
if  we  had  an  engine  so  perfect  that  it  could  utilize  without  loss  of  heat  the  entire 
expansive  energy  of  the  steam,  so  as  to  discharge  it  into  the  air  at  atmospheric 
pressure,  it  will  be  seen  (Table  149)  that  the  utmost  possible  economy  would  be 
about  four  times  that  of  using  steam  at  full  stroke;  so  that  at  best  only  some  82 
X4=  328  heat-units  out  of  1159,  o^  28.3  per  cent,  could  be  utilized.  The  utmost 
that  is  actually  realized  in  the  very  finest  marine  engines  burning  1.3  to  1.5 
lbs.  of  coal  per  horse-power  per  hour  is  some  16  or  18  per  cent  of  the  heat  put 
into  the  steam,  which  is  perhaps  three  fourths  of  that  which  comes  out  of  the 
coal. 


4/0  CHAP.  XL— LOCOMOTIVE— CYLINDER  POWER. 

578t  Such  engines  as  we  have  been  discussing,  which  would  give  a  diagram 
similar  to  Figs.  124,  125,  are  practically  out  of  the  question.  It  is  impossible 
to  admit  a  full  pressure  of  steam  instantly,  and  it  is  impossible  to  retain  the 
steam  shut  up  within  the  cylinder  until  the  very  end  of  the  stroke  or  leave  the 
?)pposite  end  entirely  without  resisting  pressure  to  absorb  the  momentum  of  the 
approaching  piston,  or  the  engine  would  speedily  pound  itself  to  pieces.  The 
valve  is  therefore  given  a  lead  so  that  the  steam  is  admitted  in  front  of  the  pis- 
ton and  released  from  behind  it  a  little  before  the  end  of  the  stroke,  and  the 
combined  effect  of  the  lead  and  the  lap  (the  meaning  of  which  is  explained  in 
any  treatise  on  the  steam-engine)  results  in  giving  to  the  theoretical  diagram 
of  a  high  pressure  steam-engine,  as  actually  worked  in  practice,  the  form  shown 
in  Figs.  126  to  148,  in  which  the  pressure  does  not  remain  full  during  admis- 
sion, the  expansion  curve  is  not  by  any  means  true,  the  lower  or  exhaust  line 
is  not  by  any  means  at  a  zero  pressure,  and  the  lower  left-hand  corner  is  not 
by  any  means  a  sharp  angle,  as  in  Figs.  124,  125,  but  much  rounded  by  com- 
pression at  the  end  of  the  stroke.  Not  all  of  this  compression  is  lost,  it  is 
true,  since  it  saves  some  of  the  work  done  in  giving  motion  to  the  recipro- 
cating parts  ;  but  how  much  the  theoretical  loss  amounts  to  it  is  needless  to  in- 
quire, for  we  may  now  summarize  the  various  other  and  far  more  important 
sources  of  loss,  and  see  by  the  records  of  experience  what  their  aggregate 
amounts  to. 

579.  The  chief  sources  of  loss  of  C3'linder  efficiency  in  the  locomotive 
engine  are  those  numbered  i  to  8  below : 

1.  The  steam  is  wzre-draw?t,  so  that  its  pressure  in  the  cylinder  is 
never  equal  to  that  of  the  boiler,  and  often  10  and  even  20  lbs.  below  it. 

2.  The  steam-poris  are  7iot  large  ejiongh  to  admit  steam  as  fast  as  the 
pisto7i  moves,  especially  if  it  be  moving  fast.  Both  of  these  sources  of 
loss  are,  owing  to  the  peculiarities  of  the  link-motion,  more  serious  at 
high  speed  and  with  early  cut-offs,  and  the  last  one  hardly  occurs  at  all 
under  other  circumstances. 

These  two  causes  together  have  so  important  an  effect  on  the  tractive 
power  of  engines  that  they  are  separately  discussed  below  (par.  587). 
Their  effect  is  illustrated  practically  in  nearly  all  the  indicator-diagrams 
which  follow. 

580.  3.  All  e7itrained  water  in  the  steam  has  to  be  evaporated ;  a  loss, 
however,  more  properly  chargeable  to  defects  of  the  boiler  than  to  the 
cylinder.  M.  Marie  found  in  his  carefully  conducted  experiments  that 
something  over  10  per  cent  of  the  apparent  evaporations  was  really  only- 
vapor  carried  along  mechanically  with  the  steam  at  the  same  sensible 
temperature,  350°,  but  unevaporated.  Other  tests  show  3  and  5  per 
cent,  and  some  none,  but  it  is  probably  rarely  less  than  5  per  cent.     This 


CHAP.  XI.— LOCOMOTIVE— CYLINDER  POWER.  471 

means  that  with  the  half-pound  or  more  of  steam  which  enters  the 
cylinder  at  each  stroke,  from  half  an  ounce  to  an  ounce  of  hot  water  is 
injected  with  it.  The  loss  involved  is  not  simply  the  300°  of  heat  which 
have  been  given  to  the  water,  but  as  soon  as  the  pressure  and  tempera- 
ture fall  during  expansion  and  exhaust  this  hot  water  flashes  into  steam, 
absorbing  the  necessary  heat  for  that  purpose  from  the  hotter  walls  of 
the  cylinders,  and  having  all  the  practical  effect  upon  the  temperature  of 
the  walls  of  the  cylinder  of  a  spray  of  cold  water  at  every  stroke. 

581.  4.  A  constant  radiation  of  heat  from  the  metallic  cylinder  (only  a 
part  of  which  is  lagged)  and  its  connected  parts  into  the  surrounding  air, 
so  that  a  certain  small  fraction  of  the  steam  must  be  condensed  at  each 
stroke  to  supply  this  loss. 

Perhaps  Figs.  126  to  130  are  as  good  direct  evidence  as  any  of  the  very  great 
loss  which  results  from  this  cause.  It  will  be  seen  from  them  that  the  mere 
effect  of  leaving  off  the  cover  from  one  end  of  the  cylinder  was  to  make  a  very- 
noticeable  reduction  in  the  effective  average  pressure.  It  is  to  be  remembered 
in  comparing  these  two  diagrams  that  this  "cover,"  the  removal  of  which 
caused  so  great  a  difference,  is  nothing  but  a  thin  plate  of  metal,  in  direct  metallic 
contact  with  the  cylinder  at  many  points,  and  including  only  a  thin  space  of  dead 
air  between  them.  We  are  not,  therefore,  comparing  a  well-protected  with  a 
badly-protected  cylinder,  but  a  badly-protected  with  a  worse-protected  one. 

It  is  not  probable  that  the  absolute  loss  of  heat,  measured  merely  by  heat- 
units,  is  anything  hke  as  great  from  the  cylinders  and  connected  parts  as  from 
the  boiler;  but  each  unit  of  heat  subtracted  from  the  boiler  can  be  replaced  by 
another  without  any  indirect  loss,  whereas  after  the  steam  has  once  entered  the 
steam-chest  and  cylinder  the  loss  of  a  few  units  of  heat,  by  reducing  the  pressure, 
means  the  loss  of  much  of  the  efficiency  of  what  heat  is  left. 

582.  5.  Still  more  important  than  direct  external  radiation  is  the  phe- 
nomenon known  as  internal  radiation  into  the  exhaust  steam.  The  steam 
enters  at  120  to  140  lbs,  pressure,  corresponding  to  350°  to  360°  Fahr. 
It  leaves  the  cylinder  at  4  to  7  lbs.  pressure  and  225°  to  230°  Fahr.  In 
entering  it  heats  the  interior  walls  of  the  cylinder,  which  it  finds  at  per- 
haps 250°  Fahr.,  to  nearly  its  own  temperature,  and  some  steam  is  con- 
densed thereby,  reducing  by  so  much  the  pressure  and  the  work  done. 
When  the  exhaust  opens  and  the  temperature  of  the  steam  falls  these 
hot  walls  radiate  their  heat  back  again  into  the  steam,  wasting  it  by  re- 
evaporating  the  vapor  carried  out  in  the  exhaust.  Thus  a  certain  large 
fraction  of  the  heat  passes  through  the  cylinder,  by  a  kind  of  side-path, 
without  really  taking  any  part  in  the  work  done  in  the  cylinder,  as  a 
leaky  flume  might  let  a  portion  of  the  water  past  a  water-wheel  without 
its  doing  an}^  work  on  it. 


472  CHAP.  XI.— LOCOMOTIVE— CYLINDER  POWER. 

583.  The  loss  from  this  source  may  amount,  it  is  alleged  by  D.  K.  Clark,* 
to  anywhere  from  ii  to  42  per  cent,  the  latter  only  with  very  short  cut-offs.  As 
its  amount  increases  (i)  with  the  range  of  temperature  and  (2)  with  the  time  of 
exposure,  it  is  less  at  high  speeds  or  with  late  cut-offs.     Mr.  Clark  adds: 

*'  These  results  sufficiently  explain  how  it  happens  that  expansive  working 
in  locomotives,  especially  in  outside  cylinder  engines,  is  in  practice  carried  out 
to  such  a  limited  extent.  We  have  rarely  found  (1850)  on  the  Caledonian  Rail- 
way— a  line  stocked  with  outside-cylinder  locomotives — that  a  cut-off  materially 
less  than  30  per  cent  is  voluntarily  adopted  by  the  engine-drivers.  In  their  own 
words,  they  '  lose  as  much  as  they  gain '  if  they  endeavor  to  work  with  a  sup- 
pression much  less  than  30  per  cent." 

This  still  (1886)  remains  as  true  for  American  practice  as  when  Mr.  Clark 
first  wrote  it,  except  that  for  30  per  cent  we  should  read  37^  or  perhaps  40  per 
cent.  But  little  gain  results  in  practice  from  cutting  off  shorter,  if  any;  and 
accordingly  the  all  but  universal  rule,  where  parts  of  the  road  are  struck  which 
require  only  a  light  power,  is  to  throttle  the  steam,  and  reduce  its  initial  pres- 
sure even  so  much  as  one  half  rather  than  attempt  to  cut  off  earlier.  While 
this  practice  is  often  pushed  too  far,  it  is  better  than  attempting  to  cut  off  at 
less  than  three-eighths  stroke  or  more,  except  at  very  high  speeds. 

584-  Prof.  Charles  A.  Smith,  who  studied  this  question  with  great  care  as 
respects  stationary  engines,  lays  down  the  approximate  rule,  as  the  average  re- 
sult of  some  49  tests,  that  the  average  loss  may  be  estimated  at  3.6  lbs.  of  ex- 
cess water  (i.e.,  ^X.^^.vci)  per  hour,  per  foot  of  piston  diameter  per  deg.  Fahr. 
difference  of  initial  and  final  temperature.  This  is  on  the  assumption  that  time 
is  so  important  an  element  in  the  amount  of  this  loss  that  the  number  of  strokes 
per  hour  is  unimportant,  which  is  far  from  literally  true.  At  this  rate,  assuming 
an  average  range  of  temperature  of  100°  Fahr.  in  the  cylinder,  there  would  be 
some  500  lbs.  of  steam  per  hour  condensed  internally  in  a  17-in.  cylinder,  and 
some  600  lbs.  in  a  20-in.  cylinder. 

585.  6.  The  back  pressure,  amounting  to  anywhere  from  4  to  7,  or 
even  (in  bad  practice)  10  or  12  lbs,  per  sq.  in.,  or  to  from  2  to  20  per  cent 
of  the  total  power  developed.  It  is  caused  chiefly  (until  compression 
begins  at  the  end  of  the  stroke)  by  the  contraction  of  the  exhaust-nozzles 
to  produce  the  draft  which  keeps  up  the  fires,  but  in  part  by  the  impossi- 
bility of  the  steam  escaping  quickly  enough  without  a  considerable  pres- 
sure to  drive  it  out. 

7.  The  clearance  spaces,  already  alluded  to,  waste  a  considerable 
amount  of  steam,  from  7  to  9  per  cent  when  cutting  off  at  full  stroke, 
but  less  when  cutting  off  short,  since  the  steam  in  the  clearance  spaces 
expands  with  the  rest  and  does  a  certain  amount  of  work  in  that  way. 

*  "  Manual  for  Mechanical  Engineers,"  p.  880. 


CHAP.  XI— LOCOMOTIVE— CYLINDER  POWER.  473 

586.  8.  The  energy  communicated  to  the  piston  and  connected  parts 
during  the  first  half  of  the  stroke,  in  order  to  give  it  a  velocity  of  from 

/  stroke         \ 

^  to  i    -r-. T~:r~- 01  the  train,  and  then  surrendered  again  during: 

\diam.  of  drivers/  ^  » 

the  last  part  of  the  stroke,  is  in  great  part  lost,  so  far  as  useful  work  is 
concerned.  It  is  expended  on  that  portion  of  the  exhaust  which  is  shut 
up  in  the  cylinder  by  the  preclosure  of  the  valve  and  practically  recon- 
verted into  heat,  by  raising  the  steam  so  shut  up  from  a  pressure  of  per- 
haps 4  lbs.  and  temperature  of  225°  to  perhaps  120  lbs.  and  350°. 

587.  The  aggregate  effect  of  these  differences  is  to  very  greatly  de- 
crease the  TRACTIVE  FORCE  which  it  is  mechanically  possible  for  the 
locomotive  to  exert  at  the  higher  working  speeds,  but  not  therefore  the 
HORSE-POWER  which  the  engine  is  capable  of  exerting,  nor  (within  reason- 
able limits)  the  economy  with  which  that  power  is  obtained.  This  is 
especially  true  of  the  first  two  causes  (par.  579),  which  we  may  now  con- 
sider, in  connection  with  diagrams  which  will  show  more  clearly  the  ex- 
act limits  of  the  effect. 

588.  Under  the  most  favorable  circumstances,  with  the  throttle  wide  open 
and  speed  slow,  the  pressure  in  the  steam-chest  hardly  ever  rises  within  5  lbs. 
of  the  boiler  pressure,  and  this  is  still  further  reduced  when  the  steam  enters 
the  cylinders,  so  that  the  initial  pressure,  with  all  the  assistance  of  compression, 
is  rarely  within  10  lbs.  of  the  boiler  pressure.  When  the  throttle  is  only  partially 
•open  (Figs.  127,  128)  or  the  speed  is  very  high,  or  especially  with  both  together, 
there  is  a  still  further  and  great  loss  of  pressure,  often  more  than  one  half.* 
Throttling  is  also  a  very  common  resort  in  preference  to  using  an  earlier  cut-off, 
as  the  engine  runs  more  smoothly  and,  practical  experience  shows,  with  but 
little  more  waste  of  steam. 

589.  In  all  such  reductions  of  initial  pressure  as  those  alluded  to  there  is  a 
<:ertain  theoretical  loss,  but  only  a  small  one.  It  is  greatly  exaggerated  in 
popular  belief  (as  well  as  in  certain  text-books  of  excellent  standing)  by  con- 
fusing a  loss  of  mere  pressure,  or  pounds  of  traction,  with  a  loss  of  energy.  The 
tractive  force  in  pounds  is  undoubtedly  reduced  in  rather  more  than  constant 
ratio  with  the  reduction  of  initial  pressure;  but  then,  if  this  occurs  only  when  a 
larger  tractive  force  is  not  required  or  cannot  be  sustained  by  the  boiler,  this  is 
in  itself  of  no  importance,  and  as  respects  the  amount  of  work  which  can  be 
done  with  the  same  quantity  of  steam,  it  is  but  very  little  affected  by  the  reduc- 
tion of  pressure,  either  theoretically  or  practically.     Theoretically,  the  amount 

*  On  some  diagrams  taken  on  an  express  passenger  engine  on  the  Philadelphia  & 
Reading  Railroad,  taken  at  65  miles  per  hour,  it  was  found  that  the  average  effective 
pressure  was  actually  less  when  cutting  off  at  10  in.  than  when  cutting  off  at  5  in., 
^though  the  amount  of  steam  used  was  far  greater. 


474 


CHAP.  XI.— LOCOMOTIVE— CYLINDER  POWER. 


of  steam  required  per  horse-power  per  hour  for  pressures  varying  by  20  lbs.  per 
square  inch  is — 

Pressure  above  atmosphere,  .  . 
Lbs.  steam  per  H.  P.  per  hour,  . 
Loss  p.  c.  by  diff.  of  20  lbs.,   , 


20        40        60        80 

33-7     32.9     32.5     32.1 
2.43     1.23     1.25 


100      120      140 
31.7     31.3     30.9 
1.26     1.28     1.30 


A  difference  which  in  no  case  is  worth  much  discussion,  unless  without  cor- 
travening  advantage.  Practically  it  has  been  shown  in  many  experiments  of 
late  years,  and  especially  in  a  remarkable  series  of  experiments  by  Mr.  Dela- 
ford,  engineer-in-chief  of  the  mines  at  Creusot,  France,*  that  "  the  difference  in 
economy  between  steam  of  no  lbs.  and  steam  of  64  lbs.  is  very  small,  and  when 
we  take  the  generation  of  steam  into  consideration,  as  well  as  its  use,  the  lower 
pressure  is  the  more  economical." 

Similarly,  Mr.  D.  K.  Clark, f  who  is  certainly  one  of  the  most  careful  students 
of  the  theory  and  practice  of  the  locomotive,  concludes  that  "as  the  loss  from 
wire-drawing  is  of  little  or  no  moment,  and  as  wire-drawing  was,  to  some  de- 
gree, equivalent  to  an  earlier  cut-off,  it  might  even  prove  advantageous  in  point 
of  economy." 

590.  But  wire-drawing  does  very  seriously  reduce  the  tractive  power 
of  engines.  When  it  occurs  only  when  the  speed  rises  considerably- 
above  ordinary  working  speeds,  say  28  miles  per  hour  in  freight  engines, 
or  50  miles  per  hour  in  passenger  engines,  this  is  no  great  disadvantage, 
because  such  speeds  are  only  desired  when  the  grades  are  favorable  or 
train  light,  and  much  tractive  power  is  not  required  ;  but  when  it  occurs 
to  any  material  extent  with  late  cut-offs  at  ordinary  working  speeds  of  12 
to  15  miles  per  hour,  it  is  more  objectionable. 

591.  Unfortunately,  experiment  seems  to  indicate  quite  uniformly 
that  it  is  rather  the  rule  than  the  exception  for  freight  engines  to  show  a 
considerable  reduction  in  cylinder  efficiency  even  at  their  lower  working 
speeds,  so  that  speeds  as  low  as  it  is  safe  to  use  without  danger  of  the 
train  being  brought  to  a  stop  by  slight  additional  resistance  from  curves, 
grades,  head  winds,  or  bad  track,  do  cause  a  very  material  decrease  of 
available  average  cylinder  pressure  ;  and  hence  the  engine  cannot  possibly 
utilize  its  available  ultimate  tractive  power — i.e.,  very  nearly  slip  its 
wheels — at  any  practicable  working  speed,  however  low,  although  the 
difference  is  small  compared  with  the  effect  of  further  increase  of  speed. 

592.  That  it  is  so  is  shown,  perhaps,  as  conclusively  as  in  any  other  way,  in 
the  following  diagrams  (Figs.  134  to  139)  of  the  engine  whose  performance  is 


*  Annates  Industriel,  Feb.,  1885. 

t  "  Manual  for  Mechanical  Engineers,"  p.  879. 


CHAP.  XI.— LOCOMOTIVE— CYLINDER  POWER.  475 

recorded  in  Table  146  and  Fig.  123  (par.  571).     The  same  thing  appears  in  the 
diagrams  accompanying  Mr,  Stroudley's  paper  (par.  570  and  Fig.  122),  where, 

With  a  cut-off  of i  i 

At  a  speed  in  miles  per  hour  of 12  m.  30  m. 

And  j/m;7z-<:>^^j/ pressure  of 140  lbs.      130  lbs. 

The  average  pressure  was 74.8  lbs.     57.2  lbs. 

The  horse-power  being 262  502 

At  12  miles  per  hour,  with  60  per  cent  cut-off  and  125  lbs.  steam-chest  pres- 
sure (boiler  pressure  full  5  lbs.  more),  the  average  cylinder  pressure  was  95.4 
lbs.,  whereas  at  4  miles  per  hour  an  average  of  about  85  per  cent  of  the  boiler 
pressure  was  obtained  in  the  cylinder— about  the  best  which  is  ever  possible.    — ^ 

593.  That  this  should  occur  at  high  speeds  is  practically  unavoidable, 
but  that  it  should  occur  at  slow  speeds  of  less  than  15  miles  per  hour  is 
in  no  respect  a  mechanical  necessity,  nor  does  it  require  any  radical 
modification  of  existing  engines  to  cure  it,  whenever  it  appears  desirable, 
but  merely  some  slight  modification  of  the  valves.  Some  engines  do  not 
show  it,  but  more  do.  The  chief  reason  why  it  is  not  done  is  that  no 
particularly  useful  end  would  be  served  thereby,  since  the  imperfections 
of  the  gradients  and  of  the  locomotive  serve  to  justify  each  other,  by  de- 
stroying to  a  very  large  extent  the  advantage  of  remedying  one  without 
the  other.  It  is  important  that  the  true  nature  of  the  difficulty  should  be 
clearly  understood. 

594.  The  largest  tractive  pulls,  by  far,  on  nearly  all  railways,  are  ex- 
erted in  getting  trains  under  way  from  stopping-places  on  unfavorable 
grades  or  curves.  There  are  few  roads  indeed,  and  those  only  having 
very  heavy  grades,  on  which  the  traction  between  stations  is  the  heaviest. 
So  long  as  this  is  so,  the  need  is  not  felt  that  an  engine  should  be  able  to 
exert  something  like  its  maximum  pull  between  stations  at  fair  working 
speeds,  and  as  a  very  natural  consequence  their  valves  are  not  arranged 
so  that  they  can  do  so. 

Now,  as  a  rule,  a  large  part  of  the  additional  tractive  force  demanded 
at  stations  may  be  saved  by  more  careful  study  of  the  grades  at  stations  ; 
but  if  this  be  done,  and  it  be  attempted  to  increase  the  trains  correspond- 
ingly, the  only  effect  with  very  many  engines  will  be  that  they  will  either 
"  stick  on  the  grades"  or  lose  so  much  time  that  to  utilize  the  improvement 
at  stations  will  be  impracticable.  For  the  same  reason,  if  it  be  endeavored 
to  find  out  where  the  engines  are  really  most  taxed  it  will  often  be  diffi- 
cult to  do  so.  They  slip  their  wheels  most  at  stations,  but  "they  have 
all  they  can  do"  to  make  time  on  the  grades ;  so  that  from  the  bare  face 
of  the  statements  there  will  be  little  to  show  where  the  weakest  point  is, 

{seepage  478) 


476 


CHAP.  XI.— LOCOMOTIVE— CYLINDER  POWER. 


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CHAP.  XI.— LOCOMOTIVE— CYLINDER  POWER. 


A77 


Figs.  126  to  133  were  taken  in  some  tests  on  the  Cincinnati,  New  Orleans  &  Texas 
Pacific  (Cincinnati  Southern)  Railway,  from  a  fine  Baldwin  passenger  engine  of  the  follow- 
ing dimensions  : 


Weight, 


Cylinders 18  x  24  in. 

Drivers 68  in. 

on  drivers 60,000  lbs. 

total 90,000  lbs. 

Tractive  force  per  pound  of  av. 

press,  in  cylinder  (Table  151)...  114. 4  lbs. 
TT  ,          j  Allen-Richardson: 
valves,  -j  Lap,  %  in.  ;  lead,  ^V  in. 


Ports  isteam 16  x  ij  in. 

'^"'^'■'''  I  e.xhaust 16  x  2I  in. 

Exhaust  nozzle si  in. 

(  tubes 1,325  sq.  ft. 

Heating  J  fire-box 133  sq.  ft. 

surface,  "j  

Grate  area. 


Total 1,458  sq.  ft. 

17  sq.  ft. 

The  train  hauled  consisted  of  8  cars,  weighing  480,000  lbs. 


Fig.  129. 

Fig.  130. 

Fig.  129. 

Fig.  130. 

Boiler  pressure 

Cut-off 

145  lbs. 
8  in. 

53-4  m. 
37-2  lbs. 
583 
32  lbs. 

145  lbs. 
8  in. 

45.0m. 

44-3  lbs. 

608 

22  lbs. 

140  lbs. 
6  in. 

54-6m. 
32.5  lbs. 

541 
24  lbs. 

135  lbs. 
4  in. 

X 

Throttle  open 

Speed 

55-9m. 
28.0  lbs. 

477 
26  lbs. 

Av.  cylinder  pressure. . 
Indicated  horse-power. . 
Loss  initial  pressure 

Figs.  129,  130  show  the  same  effect  of  speed  as  Figs.  126-128  very  forcibly,  both  by 
comparison  of  the  full  and  dotted  diagrams  and  (still  more  forcibly)  by  comparing  the 
solid  diagrams  in  Figs.  120  and  121,  which  may  be  said  to  be  taken  under  precisely 
similar  circumstances  (balancing  difference  in  throttle  against  difference  in  boiler  pressure) 
except  that 

Fig.  128.        Fig.  129. 

Speed  was 29.1  53.4 

Reducing  average  pressure  from 61.8     to       37.2 

Yet  that  this  does  no  real  harm  to  hauling  capacity  is 
evident  from  the  fact  that  the  horse-power  at  which 
the  engine  was  working  increased  from 549        to     583 

Comparing  the  dotted  Fig.  131  with  the  solid  Fig.  132  we  see  that  the  combined 
effect  of  5  lbs.  higher  boiler  pressure,  4  ins.  longer  cut-off,  and  a  throttle  %  instead  of 
J^  open,  gave  only  a  slightly  higher  average  pressure  (6.8  lbs.),  indicating  that  the  slight 
difference  of  0.8  mile  per  hour  in  speed  very  largely  counterbalanced  all  these  advantages. 
Fig.  132,  contrasted  with  the  dotted  Fig.  129,  illustrates  a  truth  which  might  be  proved 
in  many  other  ways,  that  after  the  speed  gets  fairly  high  it  does  little  or  no  good  to 


478 


CHAP.  XI.— LOCOMOTIVE— CYLINDER  POWER. 


admit  more  steam  to  the  cylinders.      The  greater  average  pressure  which   should  be 
gained  is  used  up  in  back  pressure  and  wire-drawing.     See  also  Figs.  133-135. 


Fig.  131. 


Fig.  132. 


Fig.  131. 

Fig.  132. 

Boiler  pressure 

Cut-off 

145  lbs. 
14  in. 

f 
26.3  m. 

83.3  lbs. 

668 

24  lbs. 

142  lbs. 
14  in. 

f 

24.3  m. 

81.3  lbs. 

603 

20  lbs. 

141  lbs. 
II  in. 

46.9  m. 

37-9  lbs. 

542 

50  lbs. 

Throttle  open 

Speed  

Av.  cylinder  pressure. 
Indicated  horse-power 
Loss  initial  pressure.. 

nor  to  indicate  that  the  one  arises  from  excessive  demand  on  the 
tractive  power,  which  is  remediable  only  by  changing  the  grades,  while 

I j  143  the  other  is  caused  by  deficiency  of  cylin- 

I     -  '  der  power  only,  which  is  remediable  for 

the  most  part  by  trivial  changes  in  the 

valves. 

|\        ^\^  /  I  595.  By  the  use  of  smaller   drivers, 

/j  both  the  cylinder  and  boiler  power  are  in 

1  effect  increased  proportionately,  so  far  as 

I    ^x:;;^  ^^'^""^^^-^  I  tractive  power  in  pounds  is  concerned, 

at  the  expense  of  speed  ;  so  we  may  con- 
FiG.  133.  elude,  as  we  began  (par,  483),  by  saying 

Boiler  pressure, 148  lbs.  that  within  the  limits  of  necessar}^  freight 

Throttle  open,  .*  .'  !  .*  .'  .'  ^\  *°'  Speeds  any  tractive  power  is  feasible 
Av^^cyi  press,'  '.'.'.'.'.  39.4 Ss.  which  the  adhesion  between  the  drivers 
ind.  H.  P., 584         and  rails  is  capable  of  transmitting.     At 

Grade,       level.  ^ .     .     .  .  ,  ^ 

Loss  init.  press., 44  lbs.  passenger  speeds  it  is  quite  otherwise. 

596.  Passenger  engines,  running  at  speed,  almost  never  need  to  have  their 
ultimate  tractive  power  in  pounds  available,  and  accordingly  we  find  that  they 


CHAP,   XI.— LOCOMOTIVE— CYLINDER  POWER. 


479 


often  fall  in  practice  very  far  below  it;  nor  can  this  be  considered  an  evil.  As 
a  small  reduction  of  speed  means  a  considerable  increase  of  tractive  power,  we 
see  another  reason  beside  the  great  aid  given  by  momentum  (par.  397)  why  the 
practical  limit  to  the  power  of  passenger  engines  is  but  little  affected  by  the 
grades,  within  moderate  limits,  provided  the  average  speed  is  not  brought  too 
low  by  the  necessary  reduction  at  a  few  points. 

597.  Tables  151  and  152  and  Figs.  140  to  148  not  unfairly  represent  the 
riverage  conditions  of  Ainerican  freight  practice.  The  full-line  diagram  in  Fig. 
132  shows  about  the  highest  average  cylinder  which  is  ever  practically  realized 
except  in  starting,  and  comes  very  near  to  the  latter  in  the  form  of  the  diagram, 


Table  151. 
Cylinder  Tractive  Pov^er  of  Various  Engines  for  an  Average 
Effective  Pressure  of  too  Lbs.  Per  Square  Inch. 
diam.2  cylinders  X  stroke 


Formula:  T  = 


diam.  drivers. 


Size 
OF  Drivers. 

Size  of  Cylinders. 

Inches. 

16  X  24 

17  X  24 

18  X  24 

19  X  24 

20  X  24 

48 

50 

52 

54 

56 

58 

60 

62 

64 

66 

68   

70 

72 

12,800 

12,288 

11,815 

11.378 

10,971 

10,593 

10,240 

9,910 

9.600 

9309 

9.035 

8,778 

8,533 

14,450 
13-872 
13,339 
12,844 
12,386 
12,237 
11,560 
11,187 
10,838 
10,509 
10,200 
9,909 
9,633 

16,200 

15,553 
14.954 

14.400 

13,886 
13,407 

12,960 

12,542 

12,150 

11,782 

11,435 
11,109 
10,800 

18,050 
17,328 
16,662 
16,044 

15,474 
14,938 
14,440 
13,974 
13,538 
13,128 

12,749 
12,377 
12,033 

20,000 
19,200 

18,468 
17,778 
17.143 
16,552 

16,000 

15.484 
15,000 
14,546 
14,118 
13.714 
13,333 

For  a  Different  Stroke. — For  a  stroke  of  22  instead  of  24  in.,  diminish  the  tabu- 
lar tractive  force  for  given  diameter  of  cylinder  and  drivers  by  xj,  or  multiply  by  \\  (S|). 
For  a  26  in.  stroke,  increase  the  tabular  quantity  by  jV- 
"     28  "        "  "  "         "  "  "  \. 

For  a  Different  Size  of  Drivers.— The  tractive  force  is  inversely  as  the  diameter 
of  the  drivers,  whence  it  may  usually  be  determined  from  the  above  table  by  a  simple  pro- 
portion, or  computed  directly,  as  also  for  a  different  diameter  of  cylinder. 

One  hundred  pounds  average  pressure  is  as  high  as  can  be  counted  on,  even  in  starting 
from  130  to  140  lbs.  boiler  pressure. 


48o 


CHAP.  XI.— LOCOMOTIVE— CYLINDER  POWER. 


\ 

i 

Lbs.  per 

i 

sq.  in. 

i               Boiler  Pr.  129. 

!                Initial 

''    112.S 

j                Back 

"        2.0 

i               Mean 

"      55-4 

1 

1 

V 

Fig.  135-                       •^^^'^^ 

s^^      31.66  miles  per  hour.      ^/        ^V, 

1 

s 

! 

Lbs.  per 

sq.  in. 
Boiler  Pr.  135. 
Initial   "    122.0 
Back     "       9.6 
Mean    "     48.9 


Fig.  136 


Lbs.  per 
sq.  in. 
Boiler  Pr.  98. 
Initial  •'    78.6 
Back     "     2.8 
Mean    "    33.2 


All  three  of  the  above  diagrams  have  the  same  cut-oflf,  \i.    Had  the  full  boiler  pressure 
been  as  effective  as  initial  pressure  in  each  diagram,  we  should  have  had — 

Fig.  134. 
Speed  19-8  M. 

Theoretical  mean  pressure  93.66  lbs. 
Actual  "  "         55-4 


Fig.  135. 

Fig. 136. 

31.66  M 

38.76  M. 

98.01  lbs. 

71.15  lbs 

48.9 

33-2 

Loss  of  pressure 


38.3 


but  there  would  not  ordinarily  be  quite  so  great  a  falling  off  in  initial  pressure, 
although  Fig.  144  shows  a  still  greater  one;  the  main  loss  in  both  cases  being  due 
to  cylinder  condensation.  As  this  is  nearly  constant/-??-  hour,  it  becomes  a  very 
serious  matter  unless  steam  is  rapidly  passing  through  the  cylinders.     It  will 


CHAP. 


LOCO  MO  TIVE—C  YLINDER  PO  WER. 


Lbs,  per 

sq.  in. 
Boiler  Pr.  130. 
Initial   "    123.8 
Back     ''        2.1 
Mean    " 


Lbs.  per 
sq.  in. 
Boiler  Pr.  132. 
Initial  "    115. 
Back     "       1.9 
Mean    "     72.2 


Figs.  134  to  139,  diagrams  of  16x24  American  Eng-ine,  61 
of  which  details  are  given  in  Table  146-7. 


-in.  drivers,  taken  on  the  test  trip 


be  seen  that  only  71  per  cent  of  the  boiler  pressure  is  realized  in  the  cylinders, 
and  that  even  then  it  is  developing  a  fairly  high  average  horse-power.  Both 
Figs.  140  and  141  develop  the  effect  of  higher  speed  to  reduce  tractive  force 
very  clearly,  and  also  show,  by  the  comparative  indicated  horse-power,  that  it 
31 


482 


CHAP.  XI.— LOCOMOTIVE— CYLINDER  POWER. 


Table  152. 

Indicator  Tests  of  Mogul  Engine,  i8  x  24,  Cincinnati,  New  Orleans 
&  Texas  Pacific  Railway,  hauling  Train  of  ii  Loaded  and  23  Empty 
Cars,  836,000  Lbs. 


Boiler  pressure 

Cut-off 

Throttle  open.. 
Speed  per  hour 
Av.  cyl.  pres . . 

ind.  H.  P 

Loss  init.  pres. 


29.3  m. 

48.8  lbs. 

680 

34  lbs. 


P"-- 


Boiler  pressure 

Cut-off 

Throttle  open.. 
Speed  per  hour 
Av.  cyl.  pres  . . 

Ind.  H.  P 

Loss  init.  pres. 


140  lbs. 
7  in. 

i 
12.5  m. 
47 .  o  lbs 

279 
17  lbs. 


127  lbs. 

7  in. 

\ 

31.2  m. 

30.6  lbs. 

455 
12  lbs. 


CHAP.  XI.— LOCOMOTIVE— CYLINDER  POWER. 


483 


Table  153. 

Indicator  Tests  of  Mogul  Engine,  19  x  24,  Cincinnati,  New  Orleans 
&  Texas  Pacific  Railway,  hauling  a  Heavy  Freight  Train,  28  Cars, 
weighing,  with  Load,  969,000  Lbs.  Average  Speed  of  all  Tests,  26.4 
Miles  Per  Hour.     Average  L  H.  P.  426. 


Fig.  144. 


Boiler  pressure 

Cut-off 

Throttle  open.. 
Speed  per  hour 
Av.  cyl.  pres. . 

Ind.  H.  P 

Loss  init.  pres. 


110  lbs. 
I2i  in. 

f 

18.7  m. 

55-7  lbs. 

460 

10  lbs. 


Fig.  145. 


125  lbs. 
7  in. 

29.4  m. 

30.6  lbs. 

396 

9  lbs. 


132  lbs. 
7  in. 

f 
27.5  m. 
29.0  lbs. 

351 
20  lbs. 


Boiler  pressure 

Cut-off 

Throttle  open.. 
Speed  per  hour 
Av.  cyl.  pres. . 

Ind.  H.  P 

Loss  init.  pres. 


30.6  m. 

33.9  lbs. 

456 

14  lbs. 


484 


CHAP.  XI.— LOCOMOTIVE— CYLINDER  POWER. 


can  do  no  possible  harm,  so  far  as  the  load  hauled  is  concerned.  Figs.  142- 
and  143  develop  the  same  facts  still  more  forcibly.  Seven  of  the  eight  dia- 
grams of  Table  152,  it  will  be  seen,  develop  nearly  the  same  horse-power,  600 
being  about  the  maximum  for  this  type  of  engine,  and  amounting  to  35  horse- 
power per  square  foot  of  grate  per  hour — which  is  more  than  can  be  averaged, 
but  is  often  reached  for  the  moment  (see  par.  550). 

598.  Table  153  shows  the  performance  of  a  somewhat  heavier  en- 
gine hauling  a  heavier  train,  but  doing  less  work.  Very  naturally,  the 
effect  of  speed  to  modify  the  average  cylinder  pressure  is  less  conspicuous. 
In  the  two  diagrams  given  in  Fig.  147  we  see  the  effect  of  speed  to  re- 
duce the  effective  pressure  very  clearly,  for  Fig.  146  and  others  show- 
that  throttling  alone  accounts  for  but  a  small  part  of  the  difference. 

599.  Fig.  148  shows  a  couple  of  diagrams  taken  from  a  test  of  a  Con- 
solidation engine  on  the  same  road  when  doing  fairly  heavy  work,  about 
20  H.  P.  per  square  foot  of  grate  per  hour,  or  about  80  per  cent  of  an 
everyday  maximum.  The  way  in  which  the  same  horse-power  is  pro- 
duced and  used  up  in  a  very  different  way  is  very  clearly  brought  out. 


Fig.  148. 


Boil. 
Pres- 
sure. 
Lbs. 

Cut- 
off. 
Ins. 

Throt- 
tle. 

Speed. 
Miles 

Hour. 

Av. 

Cyl. 
Pres- 
sure. 
Lbs. 

Indi- 
cated 
H.  P. 

Loss 
with- 
out 
Pres. 
Lbs. 

IS- 
13- 

12.4 
29.1 

93-3 
40-5 

605 
616 

II. 

35- 

140. 

CHAP,    XII.— ROLLING-STOCK.  485 


CHAPTER  XII. 

ROLLING-STOCK. 

600.  One  of  the  greatest  changes  in  the  recent  history  of  American 
railways,  and  one  which  has  contributed  as  powerfully  as  any  to  the  great 
reduction  in  cost  of  transportation  which  has  taken  place,  is  the  marked 
increase  in  the  average  capacity  of  freight  cars — an  increase  which  has 
been  accompanied  by  a  very  slight  increase  in  the  dead  weight  of  the 
cars.  In  Table  154  are  given  the  leading  dimensions  of  both  the  new 
and  old  standard  freight  cars  of  the  Pennsylvania  Railroad,  which  may 
be  accepted  as  in  a  measure  typical  of  all  American  rolling-stock,  and 
the  contrast  is  at  once  evident. 

This  change  has  taken  place  almost  entirely  since  the  first  edition  of 
this  treatise  was  prepared,  in  1876,  and  is  in  good  part  the  result  (and  the 
most  useful  result)  of  the  narrow-gauge  movement,  which  concentrated 
attention  upon  admitted  extravagances  of  past  administration.  In  part 
it  is  an  indirect  effect  of  the  introduction  of  steel  rails.  A  still  more  po- 
tent cause,  however,  has  probably  been  the  enormous  increase  in  volume 
of  traffic,  especially  in  bulky  freight  to  be  transmitted  great  distances  at 
low  rates,  which  made  the  last  degree  of  economy  indispensable. 

601,  Ten  or  twelve  years  ago,  ten  tons  (20,000  lbs.)  was  the  ordinary 
maximum  load  for  freight  cars,  24,000  lbs.  only  occasional,  and  30,000 
lbs.  almost  unheard  of;  but  of  the  capacities  now  specified  (1885),  40,000 
lbs.  is  more  common  than  any  other,  anything  less  than  28,000  or  30,000 
quite  exceptional,  and  50,000  lbs.  no  longer  rare.  There  were  in  1885, 
180  flat  cars  and  10  box  cars  of  60,000  lbs.  capacity  on  the  Northern  Pa- 
cific, and  from  2  to  10  of  the  same  capacity  on  a  number  of  other  roads. 
Of  50,000-lb.  or  25-ton  cars  there  are  far  more,  numbering  several 
thousands  on  many  roads,  and  this  bids  fair  to  become  the  standard  coal 
car ;  while  there  are  not  a  few  box  cars  in  use  of  that  capacity.  As  fair 
evidence  as  any,  perhaps,  of  the  gieat  increase  in  the  average  car-load  in 
recent  years  is  the  classification  list  of  the  Pennsylvania  Company,  given 
in  Table  155,  which  includes  all  the  freight  rolling-stock  of  that  com- 
pany's system,  existing  in  sufficient  numbers  to  form  a  class,  in  1885. 


486 


CHAP.   XII.— ROLLING-STOCK. 


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.23   a 


CHAP.   XII.— ROLLING-STOCK. 


487 


Table  155  is  interesting,  not  only  as  giving  the  average  capacity,  but 
for  the  variety  of  dimensions  appearing  among  the  standard  types  of  a 
single  line.  It  will  be  seen  that  in  these  13  classes  there  are  10  different 
lengths  (not  counting  differences  of  less  than  an  inch),  and  9  different 
widths,  ranging  by  jumps  of  a  few  inches  each  from  7  ft.  5  in.  to  8  ft.  11 
in.;  all  in  freight  service  only.  This  diversit}'-  is  in  part  because  the  cars 
must  be  adapted  to  many  different  uses,  but  in  the  main  it  is  evidence  of 
the  fact  that  a  process  of  evolution  is  still  going  on,  so  that  the  rolling- 
stock  of  the  country  is  for  the  present  in  a  transition  state.  The  general 
tendency  of  this  process  can  alone  be  stated  :  to  increase  the  capacity  of 
freight  cars  up  to  25  or  even  30  tons  of  paying  load,  and  perfect  their  con- 
struction so  that  such  loads  may  be  handled  with  safety,  at  fairly  high 
speeds. 

602.  Two  changes  which  may  reasonably  be  expected  to  come 
about  in  the  next  few  years  will  greatly  strengthen  this  tendency,  and 
probably  materially  modify  the  handling  of  freight  trains  as  well — the 


Table  155. 
Classification   List  of   Freight  Cars  of  the  Pennsylvania  Company, 

1885. 


Kind  of  Car. 


Class. 


Inside  Dimensions. 


Length. 


Width. 


Height. 


Standard 
Capacity. 


Long  box*... 

Box* 

Refrigerator. 


Provision 

Stock  (standard) 


Gondola  (standard) 

"        (widened) 

"  (standard,  long)  . . 
Drop  bottom  (standard)*. . . 
Hopper  bottom  (standard)*, 
Stone  flat  (standard) 


Q. 

M. 

R. 
M.  &0, 
M.  &0. 

O. 
P.  B. 
P.  D. 
P.E. 

E. 

D. 

C. 

S. 


ft.  in. 

33  ioJ4 

27  sM 

27  4^ 

21  5 

23  I 

33  10 

29  4% 

29  8M 

29  8% 

33  o 

33  o 

23  5 

35  7 


ft.  in. 
8    4^ 

711M 
7  -^o^i 
7  10 

7  10 

8  5 
8  3 
8  o 
8  4 
7  5 
7  5 
7  7 


ft.  in. 
7    4 
5  loM 
5    8^ 
5  10 

5  10 
7    2 

6  9 
2  6 
2  6 
2    6 

2  6 

3  " 


lbs. 
40,000,  50,000 

26,  30,  40,000 

40,000 

40,000 

40,000 

40,000 
26,  28,  30,000 
26,  30,  40,000 
50,000,  60,000 

40,000 

40,000 

50,000 

50,000 


Standard  height  of  floor  from,  rail,  all  cars,  4.034.  P-  D.  gondolas,  built  before  present 
standards  were  adopted,  have  sides  only  20  in.  and  2  ft.  high. 

The  weights  of  these  cars  are  substantially  the  same  as  those  for  the  Pennsylvania 
Railroad,  given  in  the  preceding  table,  those  marked  *  being  substantially,  if  not  exactly, 
the  same  cars. 


488  CHAP.   XII.— ROLLING-STOCK. 

adoption  of  some  form  of  automatic  coupler,  and  the  adoption  of  a 
freight-train  brake.  The  effect  of  all  these  causes  combined  will  prob- 
ably be  to  assimilate  the  handling  of  freight  trains  more  and  more  to  the 
handling  of  passenger  trains,  except  that  the  speed  will  be  much  more 
variable  :  as  low  as  now  on  heavy  grades,  but  very  much  higher  on  the 
easier  sections  of  the  line,  where  great  tractive  force  is  not  demanded, 
and  where,  consequently,  higher  speed  is  entirely  feasible.  As  the  ordi- 
nary passenger  piston  speed  is  not  found  to  be  injurious,  we  may  expect 
with  some  confidence  that  at  no  distant  day  maximum  freight  speeds  of 
28  to  30  miles  per  hour,  which  would  give  about  the  same  piston  speed, 
will  be  established  in  general  practice. 

The  effect  of  this  change  will  be  to  greatly  facilitate  the  hauling  "of 
heavy  trains,  even  without  considerable  modification  of  gradients,  for 
reasons  discussed  in  Chapter  IX.,  and  elsewhere.  With  the  more  per- 
fect road-beds  and  track  which  become  every  year  more  general  there  is 
no  reason  to  believe  that  wear  and  tear  will  be  materially  increased, 
while  the  ^ost  of  power  per  ton-mile  will  certainly  be  rather  less  than 
more,  not  only  because  of  the  less  time  afforded  for  radiation  of  heat 
from  the  exterior  of  the  locomotive  and  journal-boxes  and  interior  of  the 
cylinders,  but  from  less  destruction  of  energy  by  brakes,  since  it  can  be 
stored  in  the  train  in  the  form  of  velocity,  and  afterwards  used,  to  a 
much  greater  extent. 

603.  The  primary  requirement  for  the  attainment  of  this  desirable  end 
is  the  adoption  of  a  freight-train  brake,  and  fortunately  there  now  appears 
every  prospect  that  some  approved  form  of  freight-train  brake  will  come  into 
general  use  within  a  few  years,  and  thus  greatly  simplify  the  problem  of  ob- 
taining the  most  favorable  virtual  gradients  cheaply,  in  addition  to  the  direct 
advantages.  The  latter  alone  are  much  considered  by  the  public,  but  on  cer- 
tain lines  at  least  their  effect  on  the  virtual  gradients  will  almost  certainly  be  of 
more  financial  importance,  and  make  the  expenditure  for  train-brakes  a  most 
profitable  one,  independently  of  the  greater  safety  and  convenience. 

604.  The  ultimate  solution  of  the  problem  of  automatic  couplers  is  a  more 
doubtful  matter,  and  it  may  be  well  on  toward  the  close  of  this  century  before 
automatic  couplers  come  into  use.  To  the  highest  efficiency  of  train-brakes 
they  are  almost  essential,  and  the  breaking  in  two  of  trains  is  another  evil, 
tending  to  discourage  the  hauling  of  heavy  trains,  which  they  will  very  largely 
remedy.  The  chief  obstacle  to  their  introduction  is  and  has  always  been,  not 
the  mechanical  difficulty  of  the  problem,  but  the  fact  that,  owing  to  the  contin- 
uous interchange  of  cars,  no  real  benefit  would  be  derived  from  such  a  coupler 
until  it  had  come  into  almost  universal  use,  whereas  a  passenger-coupler  was 
as  useful  to  the  road  applying  it  as  it  ever  could  be,  as  soon  as  it  was  applied 


CHAP.   XIL—ROLLING-STOfK. 


489 


to  their  own  cars,  or  even  to  a  few  trains.  The  consequence  of  this  difference 
is  that  the  usual  cut-and-try  process  of  development  and  survival  of  the  fittest 
was  impossible  with  freight  couplers,  whereas  the  first  practicable  passenger- 
coupler  was  adopted  by  a  few  roads  almost  immediately,  from  which  the  conta- 
gion of  example  sped,  each  gaining  the  full  benefit  of  their  own  expenditure  as 
soon  as  made,  and  losing  nothing  by  the  backwardness  of  others. 

The  greatest  immediate  obstacle  to  a  general  agreement  on  some  one 
freight-coupler,  or  on  two  or  more  couplers  working  well  together,  is  the  exist- 
ence of  two  distinct  types  of  such  couplers,  which  have  become  known  as  the 
"link"  and  (by  a  somewhat  awkward  and  inappropriate  term)  "vertical-plane" 
or  lateral-hook  couplers.  The  link  type  resembles  more  or  less  closely  the 
ordinary  form  of  coupler,  but 
arranged  to  work  automatical- 
ly, and,  in  the  best  types,  dis- 
pensing with  loose  links  and 
pins.  The  hook  type  is  model- 
led after  the  couplers  which 
have  been  so  successful  in  pas- 
senger service.  Fig.  149  shows 
one     of    the     most    approved  ^^^^  ^49-Ames  (Link)  Car-coupler. 

forms  of  link-couplers — the  Ames,  and  Figs.  150,  151  one  of  the  most  approved 
forms  of  hook-couplers — the  Janney.     Neither  of  these  couplers  has  been  se- 


FlG.  150. 
Janney  (Hook)  Car-coupler. 


Fig. 


lected  for  illustration  as  the  best  of  its  type,  but  merely  as  fairly  representative 
and  among  the  best  and  most  approved. 

605.  Each  of  these  types  has  strong  advocates,  but  it  may  be  expected  with 
some  confidence  that  the  hook  type  will  ultimately,  and  perhaps  very  speedily, 
prevail,  for  the  reason  that  it  insures  a  steadier  and  smoother  motion  of  the 
train  by  doing  away  with  loose  slack,  which  is  the  chief  provocative  of  breaking 
in  two  of  trains  and  of  broken  draw-bars  and  other  damage,  while  it  has  been 
proved  not  to  be  of  appreciable  advantage  in  starting  heavy  trains.     There  is 


490 


CHAP.    XII.— ROLLING-STOCK. 


a  general  impression  to  the  contrary,  and  not  a  little  floating  evidence;  but  in 
careful  tests  at  Burlington,  la.,  1886,  it  was  found  that  there  was  nothing 
gained  by  loose  slack  more  than  could  be  secured  by  first  backing  the  locomo- 
tive against  brakes  set  at  the  rear  of  the  train,  and  so  compressing  the  springs 
throughout  the  train.  On  the  locomotive  starting  forward  the  compressed 
springs  give  a  push  to  each  car,  and  this  push  seems  to  be  more  effective  than 
when  the  same  thing  is  done  with  a  train  having  slack. 

As  several  good  couplers  of  each  type  now  exist  which  will  work  quite 
well  together,  nothing  now  impedes  a  decision  of  the  coupler  question  except 
the  existence  of  these  two  types,  each  of  which  has  certain  advantages. 
The  advocates,  of  each  are  indisposed  to  proceed  very  actively  with  the  equip- 
ment of  their  cars  until  the  vexed  question  of  a  choice  is  settled. 

606i  In  Table  156  are  given  various  details  as  to  certain  very  large  or 
heavy  freight  cars,  and  in  Table  157  the  leading  dimensions  of  the  more  usual 
passenger  cars.  In  respect  to  the  latter,  the  tendency  is  more  and  more  toward 
the  use  of  the  heavy  sleeping  and  drawing-room  cars  for  a  large  percentage  of 

Table  156. 
Dimensions  of  Certain  Very  Large  and  Heavy  Freight-Cars. 


Furniture 

Car 
Chicago  & 

N.  W. 
Railway. 


M.  C.  B. 

Standard 
60,000-lb. 
Box  Car. 


Pile-driver 

Car 
Ga.  Central 
Railroad. t 


Philadelphia 
&  Reading 
Standard 
Coal  Car. 


Length  over  sills. 
Width  over  sills. . 
Length  over  roof. 
Width  over  roof. . 
Inside  length 

"       width  .... 

"       height 

Extreme  height  . . 
"  length.. 
Total  wheel-base 

Weight 

Capacity 


tt.     in. 
38     o 

8  6 
38     7i 

9  li 
37     6i 

8     oi 

8     5f 

13     8i 

40  Hi 

31  lof 


40,000  lbs. 


ft. 

35 
9 
9 

34 


II    lO"* 

31     6 


60,000  lbs. 


ft.  in. 
44  o 
10    o 


32,000  lbs. 
-1-39,000    " 


ft.  in. 

24  O 

7  6 

22  o 

7  6 


7  II 
24    6 

18,480  lbs. 
56,000    " 


*  To  top  of  brake-shaft,  12  ft.  10  in. 

t  Leaders  to  hammer,  40  ft.  high,  taking  a  pile  18  in.  X  50  ft.;  58,000  lbs.  on  one  truck  when 
moved  back  to  let  the  front  of  the  car  project.  Four  trucks  in  all.  Hammer,  8000  lbs.;  drives- 
piles  to  18  ft.  below  the  rails. 

The  Baltimore  cSr'  Ohio  Railroad  have  a  large  and  increasing  number  of  coal  cars^ 
in  use  carrying  50^000  lis.,  and  weighing,  loaded,  3614  lbs.  per  running  foot;  76,000 
lbs.  in  all  on  21ft.  out  to  out  of  buffers;  3100  to  3275  lbs.  being  the  weight  per  foot  of 
Consolidation  locomotives. 


CHAP.    XII.— ROLLING-STOCK. 


491 


the  travel,  and  many  through-trains  consist  of  them  almost  exclusively — a  fact 
which  tends  to  make  the  rate  of  long  grades  and  of  grades  at  stations  of  almost 
as  much  importance  to  them  as  to  freight  trains,  but  owing  to  the  fact  that,  by 
varying  high  velocities  slightly,  a  great  difference  in  tractive  power  on  up 
grades  results,  and  all  but  quite  long  grades  may  be  operated  almost  as  virtual 
levels  (par.  397),  the  disadvantage  of  dead  weight  is  very  much  less  in  passen- 
ger service  than  is  sometimes  assumed,  and  the  tendency  toward  luxury  in  that 
respect  may  be  expected  to.  continue. 

Drawings  and  dimensions  of  a  great  variety  of  cars,  and  of  all  car  details, 
will  be  found  in  the  Car-Builders'  Dictionary,  as  revised  by  the  writer. 


Table  157, 
Leading  Dimensions  and  Weight  of  Sundry  Passenger  Cars. 


Penna.  Railroad. 

Length. 

Width. 

Height. 

Weight 

Capacity. 

Wei 

ght 

Standards. 

Body. 

Out  to 
Out. 

Body. 

Max. 

Truck. 

Passenger* 

ft.  in. 

t46    6 

40    0 

Xeo  9>4 
§58   0 

ft.  in. 
52    9 
46    0 
6611% 
64    8 

ft.  in. 
9  10 

9  loM 
9  loM 
10    0 

ft.  in. 
10    iM 
10    iM 
10     i^ 
10     I 

ft.  in. 
14    1% 
14    1% 
14    ^M 
13  10 

lbs. 
*44,989 

32,000 

58,000 

Pass. 

51 

20,000  lbs. 

lbs. 
7.200 

Postal 

Sleeper  (old  style) 

... 

Dining II  (C,  B.  &Q.).. 

Monarch  sleeping-cars.. 

Mann  sleeping-cars. . . 

Parlor  Car  (B.&O.R.R.) 

Woodruff  sleeper 

Harl.  &  H.  Co.,  ist-class 
passenger 

64  0 
58   0 

49    6 

75    0 

65     0 
71     0 

57    8 

10    4 

9    6 

9    6 

10    6 

10    0 
10    3 

14    2 

14  0 

15  5 

13    6 

82,500 
75,000 
71,000 
70,000 
60,000 

10  sec. 

28 
58 

II 15 
16 

500 
200 

*  The  Lehigh  Valley  standard  passenger  car,  of  the  same  general  dimensions  as  this,  weighs 
45,136  lbs.;  one  truck,  8624  lbs. 

t  Centre  to  centre  of  truck,  33  ft.;  7  ft.  wheel-base. 

X  Centre  to  centre  of  truck,  46  ft.  2%  in  ;  10  ft.  wheel-base. 

§  Centre  to  centre  of  truck,  44  ft.;  14  ft.  wheel-base. 

II  Six-wheel,  10  ft.  6  in.  wheel-base. 

Sleeping-cars  have  usually  12  sections  and  a  state-room  and  smoking-room  ;  sometimes 
only  10,  rarely  14;  and  a  few  cars  have  16  sections,  but  without  state-room  or  smoking- 
room.  Many  sleepers  and  parlor  cars  weigh  75,000  to  78,000  lbs,  Pullman  sleeping-cars 
built  for  English  service  are  much  narrower  than  in  American  practice,  and  weigh  only 
some  48,000  lbs. 


492  CHAP.   XIII.— TRAIN  RESISTANCE. 


CHAPTER  XIII. 

TRAIN     RESISTANCE. 

607.  Although  over  fifty  years  have  passed  since  experimental  inves- 
tigations in  respect  to  it  began,  there  is  no  single  element  of  train  re- 
sistance whose  laws  can  be  said  to  be  definitely  known.  Within  the 
years  187 5-1 88 5,  however,  much  progress  has  been  made,  and  although 
our  knowledge  is  still  defective,  yet  the  limits  of  error  are  now  quite 
narrow. 

608.  Train  resistance,  properly  so  called,  may  be  defined  as  the  sum 
of  all  the  resistances  which  constitute  a  tax  UPON  the  adhesion 
of  the  locomotive ;  thus  excluding  all  those  resistances  which  are 
internal  to  the  locomotive  itself,  and  hence  are  a  tax  upon  the  cylinder 
power  only,  which  is  a  much  less  serious  matter.  These  latter  resist- 
ances are  (i)  all  the  friction  of  the  valve-gear,  piston,  and  connecting- 
rods,  and  (2)  ^  j ournal-irXoXAOVi  of  the  driving-wheels.  The  resistances 
which  do  tax  the  adhesion  are  (i)  the  rolling-irioxXon  proper  (between 
wheel  and  rail,  Fig.  152)  of  the  drivers,  with  (2)  both  the  rolling  and  the 
journal  friction  of  the  truck-wheels,  or  of  any  other  wheels  not  drivers ; 
(3)  all  head  and  other  atmospheric  and  oscillatory  resistance  of  the  loco- 
motive ;  (4)  all  grade  resistance  of  the  locomotive  and  (5)  all  resistances, 
of  every  kind,  of  the  train  behind  the  locomotive. 

609.  Simple  as  would  seem  the  problem  of  determining  what  is  and 
what  is  not  a  tax  upon  the  adhesion,  frequent  errors  have  arisen  in  de- 
termining it,  both  by  including  among  the  resistances  which  tax  the  ad- 
hesion the  journal-friction  of  the  drivers  and  even  the  friction  of  the 
machinery,  and  by  excluding  from  it  the  atmospheric,  oscillatory,  and 
even  grade  resistance  of  the  locomotive. 

610.  It  seems  especially  plausible  to  assume  that  all  resistances  which  would 
still  exist  if  the  engine  were  a  dead  engine,  with  disconnected  side-rods,  hauled 
by  another  engine  in  front  of  it,  are  a  tax  upon  the  adhesion  when  the  engine 
is  under  steam.  This  is  not  correct,  for  it  includes  as  a  tax  on  the  adhesion 
the  considerable  item  of  the  journal  friction  of  the  locomotive. 

The  true  test  for  what  is  and  is  not  a  tax  upon  the  adhesion,  is  to  conceive 


CHAP.   XIII  —  TRAIN  RESISTANCE.  493 

the  locomotive  to  be  stationary  and  lifted  from  the  rails  with  belts  on  the 
drivers.'  Whatever  power  would  then  be  lost  by  friction  within  the  locomotive 
itself,  before  it  reached  the  belts,  is  similarly  consumed  in  the  locomotive  with- 
out taxing  the  adhesion.  All  the  remainder  of  the  power,  including  any  loss 
by  the  friction  or  wear  of  belt  or  driver,  would  be  transmissible  only  by  the  ad- 
hesion of  the  belt  to  the  driver,  and  the  measure  of  that  adhesion  would  be  the 
measure  of  the  net  power  of  the  engine  aside  from  its  own  internal  friction. 

The  locomotive  engine,  in  fact,  is  to  all  intents  and  purposes  a  mechanical 
equivalent  for  a  stationary  engine  with  fly-wheel  and  belt,  the  rail  being  the 
belt.  Only,  instead  of  the  engine  being  stationary  and  the  belt  moving,  the 
belt  is  stationary  and  the  engine  moves  along  it.  The  locomotive,  it  is  true, 
uses  a  large  part  of  its  power  in  raising  and  lowering  itself  on  grades,  but  a 
stationary  engine  might  easily  be  made  to  do  the  same  without  altering  any  of 
its  essential  features. 

611.  Regarding  train  resistance,  therefore,  as  the  sum  of  all  those  re- 
sistances which  tax  the  n       v     / 
adhesion,   they   may  be  ^       ^^ 
subdivided  as  follows  :        ■ '    ■ 

1.  The  journal-fric- 
tz'oft,  between  journal  and 
bearing.  ^^^-  ^s^- 

2.  The  rolling-friction  proper,  between  wheel  and  rail,  from  the  cause 
outlined  in  Fig.  152. 

Both  these  together  are  commonly  included,  both  in  this  volume  and 
elsewhere,  under  the  general  name  of  rolling-friction,  and  their  ag- 
gregate only  has  been  determined  with  approximate  exactness.  Experi- 
ment indicates  that  their  aggregate  varies  somewhat,  but  not  materially, 
with  the  velocity, 

612.  The  three  following  are  known  collectively  as  the  "velocity  re- 
sistances ; "  and  experiment,  so  far  as  it  goes  (which  is  not  far),  seems  to 
agree  with  the  requirements  of  theory,  that  they  should  vary  as  the 
square  of  the  velocity  : 

3.  Atmospheric  head  and  tail  resistance,  including  the  head  resistance 
of  the  locomotive  and  of  the  front  car  above  the  tender,  and  that  result- 
ing from  the  suction  of  the  last  car. 

4.  Atmospheric  side  resistance,  including  that  between  the  successive 
cars. 

5.  Additional  rolling  and  journal  friction  resulting  from  oscillation 
and  concussion. 

As  with  the  rolling-friction,  the  aggregate  of  these  three  items,  and 
especially  of  the  last  two,  is  far  better  known  than  the  separate  impor- 


494  CHAP.  XIIL— TRAIN  RESISTANCE. 

tance  of  each.  The  doubt  on  this  subject  goes  so  far,  indeed,  that  some 
modern  formulae  of  reputation  (e.g.,  the  two  compared  with  the  author's 
in  Table  i66)  assume  the  velocity  resistance  to  be  all  atmospheric,  whjle 
others  assume  it  to  be  all  oscillatory. 

613.  An  additional  velocity  resistance,  but  one  not  commonly  so 
called,  and  too  easily  forgotten  to  be  an  element  of  train  resistance  at 
all,  although  an  essential  and  important  element  thereof,  is — 

6.  Stopping  and  starting  resistance.  The  nature  of  the  large  addition 
which  it  makes  to  the  permanent  train  resistance  has  been  considered  in 
par.  368  et  seq. 

Finally  we  have,  as  the  only  known  and  invariable  element  of  train 
resistance — 

7.  Grade  resistance,  which  is  sensibly  the  same  rate  per  cent  of  the 
total  weight  of  the  train  as  the  rate  per  cent  of  the  grade  ;  i.e.,  20  lbs. 
per  ton  of  2000  lbs.  for  each  i  per  cent  of  grade  (par.  382). 

On  badly  located  lines  only  we  need  also  to  consider — 

8.  Curve  resistance.  On  any  well-located  line  its  amount  is  consider- 
ed only  for  the  purpose  of  making  such  reduction  of  grade  as  shall 
eliminate  it  altogether.  Therefore,  after  once  completing  such  a  line  it 
does  not  constitute  an  element  of  train  resistance  which  affects  the 
movement  of  trains. 

614.  Another  element  of  train  resistance,  in  a  certain  sense,  is  brake-fric- 
tion. While  it  will  be  most  appropriately  considered  in  this  chapter,  as  relat- 
ing to  its  general  subject,  it  can  only  in  a  very  figurative  sense  be  said  to  be  an 

element  of  train  resistance, 
^'**^ri?/  properly    so  called.       The 


■     ^o^>^<Q.  simplest  method  of  compu- 

Vei.\     ^^^^^^^^r  ting  the  efficiency  of  brakes 

HQad\                    ^^-^Ogc  is  given  beneath  Table  118, 

_^  ^1^                          ''^"^"-^^^  page    336,     and    Fig.    153 

— ^  -^^^^lii^Stop                '^^^^  outlines    the    principle    of 

.^^  Q           the  method  there  given.   It 

P<  ^^^^^''"''^''       —     need  only  be  added  that  the 

STOP  ON  DKOENDING  GRADE  ,,,,^g,  \^^^^^.^^  ^^^.^^_ 

cy  of  brakes  may  be  now 
(1886)  considered  as  from  10  to  14  per  cent  o/tAe  load  on  the  braked  wheels  \x\  pas- 
senger service,  with  air-brakes,  and  from  i\  to  5  per  cent  with  hand  and  driver 
brakes  on  heavy  freight  trains.  The  safe  pressure  on  the  brake-shoes  is  not 
much  over  two  thirds  of  the  load  on  the  wheels.  The  maximum  retardation 
which  has  ever  been  realized  was  with  an  ingenious  apparatus  devised  by  Mr. 
George  Westinghouse,  by  which  the  pressure  was  very  great  at  high  speeds  and 


CHAP.   XIII.— TRAIN  RESISTANCE. 


495 


Table  158. 

Maximum  Efficiency  of  Power  Brakes  during  all  Parts  of  Stops  in 
Passenger  Service  or  with  Short  Freight  Trains. 

[Abstracted  from  computations  by  the  writer,  being  averages  of  a  large  number  of  stops.] 


Portions  of  Stops. 


"LzsX  fraction  of  loo  ft 

Last  even  loo  ft 

Preceding  loo  ft 


Averages,  excluding   last 
fraction  of  loo  ft 


Average 

Speed, 

Miles 

Per  Hour. 


28 
35 
40 

44 

47-5 
50 
52 


20  to  52 


Ratios  of  Brake  Retarda- 
tion TO  Load 
on  Braked  Wheels. 


Westinghouse 
Brake. 


Regular     Against 
Stop.        Engine. 


20.9 

13-9 
14.7 

13-75 

12.9 

14.2 

14.8 

14-75 

(4-5) 


19-3 
12.9 

14-5 

15-55 
13-6 

11-95 

13-85 
13-8 

13-3 

(II. 6) 

(8.65) 


Smith 

Vacuum 

Brake. 


19 


Ratios  of  Brake 

Retardation  to 

Pressure  on 

Brake-blocks. 


Galton.     Theoreti- 
cal (Table  112) 
Uniform  Pressure. 


After  10 
Sections. 


24.0 

13-3 
H.9 

8.5 
7-7 
7-3 
7.0 
6.7 
6.4 


Initial. 


25.0 
18.2 
17. 1 

15-3 
14.4 
13.8 

13.0 
12.0 

II. o 


N.  B. — The  "average  speed"  given  in  the  first  line  of  this  table  is  for  the  period  of  a 
stop  beginning  at  15  to  20  miles  per  hour  and  ending  at  zero,  so  that  it  averages  8  to  10 
miles  per  hour. 

For  the  original  records  of  these  stops,  with  very  valuable  further  data  on  brake 
efficiency  and  the  laws  of  brake  friction,  see  Dredge's  "  Pennsylvania  Railroad  "  (Wiley  & 
Sons). 

From  analysis  of  these  and  other  data  the  writer  concluded  that  the  following  ratios 
represent  the  maximum  efficiency  of  brakes  in  ordinary  practice,  being  such  as  is  fairly 
attainable,  and  is  in  fact  attained  under  favorable  conditions  with  all  in  good  order  and 
with  the  best-known  appliances  : 

Retardation  of  Brakes  in  per  cent  of  Load  on  Braked  Wheels. 

With  special  apparatus  not  ijt  practical  use  : 

About  oneffth,  or  20  per  cent  at  all  speeds. 
With  efficient  power  brakes  of  ordinary  type  : 

At  speeds  decreasing  from  15  to  20  miles  per  hour,  about  one  fifth  or  20  per  cent. 

At  all  speeds  exceeding  15  to  20  miles  per  hour,  about  one  seventh,  or  14.14  per  cent. 

For  entire  stops  of  long  trains  at  high  speeds,  including  lost  time  in  applying  full 
brake-power,  one  eighth  to  one  ninth. 


49^  CHAP.    XIII.— TRAIN  RESISTANCE. 

was  reduced  automatically  as  the  speed  fell,  so  as  to  keep  the  retardation  just 
within  the  nearly  constant  force  necessary  to  skid  the  wheels,  which  is  one 
fourth  of  the  insistant  weight.  This  apparatus,  moreover,  was  applied  only  to 
a  single  car,  and  thus  did  away  with  another  serious  obstacle  to  the  efficiency 
of  brakes — that  it  takes  a  considerable  time  after  they  are  applied  on  the  engine 
for  them  to  even  begin  to  apply  on  the  last  car.  With  50-car  freight  trains 
over  ten  seconds  is  lost  in  this  way.  ^ 

With  this  apparatus  an  average  efliciency  of  over  0.2  was  obtained  for  the 
entire  stop;  but  it  has  never  been  introduced  into  service,  extreme  efficiency 
not  being  the  end  aimed  at  so  much  as  cheapness,  simplicity,  and  certainty 
of  action.  It  is  possible  that  the  near  future  will  bring  about  considerable 
differences  in  the  brake  question,  and  until  then  it  is  dangerous  to  prophesy. 

615.  In  the  analysis  of  the  preceding  elements  of  train  resistance,  and 
in  presenting  and  reconciling  the  inconsistencies  of  the  experimental 
facts  on  record,  a  volume  might  easily  be  written,  and  perhaps  not  un- 
profitably  ;  but  for  our  immediate  purpose  it  will  suffice  to  dismiss  at  once 
a  large  fraction  of  such  experimental  facts — or  what  purport  to  be  such, 
but  are  not — as  for  one  reason  or  another  worthless  as  practical  guides. 

616.  From  a  practical  point  of  view,  train  resistance  must  be  considered 
from  two  aspects,  viz. : 

1.  As  respects  freight  trains,  to  which  speed  is  unimportant  compared 

with  hauling  the  largest  possible  loads  over  the  points  of  maximum 
resistance. 

2.  As  respects  passenger  trains,  to  which  the  possibility  of  high  speed  is 

the  more  important  consideration. 

In  each  case  formulae  which  deal  with  the  car  resistance  only,  neglect- 
ing the  head  and  rolling  resistance  of  the  engine,  are  comparatively 
valueless.  What  we  deed  to  know  most  is  the  sum  of  all  the  resistances 
which  tax  the  adhesion.  We  will  consider  each  class  of  train  resistance 
separately. 

FREIGHT-TRAIN  RESISTANCE. 

617.  The  best  existing  evidence  known  to  the  writer  as  to  what  is  the 
absolute  amount  of  the  train  resistance  of  entire  American  freight  trains 
in  the  ordinary  routine  of  service  are  the  observations  made  at  the  Bur- 
lington, la.,  first  (1886)  series  of  brake  tests.  These  tests  were  for  the 
primary  purpose  of  determining  precisely  how  much  dift'erence  there 
might  be  in  the  normal  train  resistance  of  the  various  trains,  apart  from 
the  action  of  the  brakes.     They  were  made  by  the  "  gravity  method  "  de- 


CHAP.    XIII.— FREIGHT-TRAIN  RESISTANCE. 


497 


scribed  in  Appendix  A,  the  train  being  caused  to  approach  the  starting 
post  at  as  nearly  as  might  be  20  miles  per  hour,  when  steam  was  shut  off 
and  the  train  permitted  to  run  over  a  very  slight  down  grade  till  it  came 
to  a  stop.  It  was  then  caused  to  approach  a  succeeding  stop-post  at  a 
sharp  down  grade,  having  a  slightly  curved  alignment,  at  5  miles  per 
hour,  and  permitted  to  acquire  what  velocity  it  would  (about  35  miles 
per  hour)  for  a  certain  distance.  There  v/as  no  wind ;  and  the  ther- 
mometer averaged  about  80°  Fahr.  The  results  of  the  tests  are  summa- 
rized in  Table  160  and  Fig.  154,  which  maybe  accepted  as  an  almost 
absolutely  accurate  record  of  actual  resistances*  over  the  entire  range  of 


Fig.  154.— Results  of  the  Burlington,  Ia.,  Tests  of  the  Resistance  of  Entire  Trains, 

AS  Summarized  in  Table  i6o,Page  500. 

[Computed  by  the  method  shown  in  Table  159,  on  following  page,  and  in  Appendix  A,] 

(The  dotted  lines  give  the  tests  made  on  curved  track  corrected  for  curve  resistance  as  per 

Table  160.    The  dotted  line  marked  "A,  M.  W."  is  that  given  by  the  writer's  formulae,  Fig. 

163  and  Appendix  A.) 

*  As  the  writer  was  referee  of  these  tests  he  was  familiar  with  the  condition 
of  the  cars  and  all  other  modifying  circumstances.     Therefore  he  can  voucli 
for  the  accuracy  of  the  results,  which  seem  somewhat  peculiar. 
32 


498 


CHAP.    XIII.— TRAIN  RESISTANCE. 


Table  159. 

Manner  of  Computing  Gravity  Tests  of  Train  Resistance  of   Entire 

Freight  Trains, 

Speeds  decreasing  from  20  miles  per  hour — 25  mixed-car  trains,  12  loaded,  13  empty,  with 

dynamometer  car  and  way  car — American  17  x  24  in.  engines. 

[Computed  by  the  writer  from  test  runs  down  a  slight  grade  with  steam  shut  off,  at  the 

Burlington,  la.,  freight-train  brake  tests,  July,  1886.] 

(This  table  covers  only  the  computation  of  the  four  lowest  resistances  in  Fig.  154, 
marked  "  Westinghouse  Tangent.") 


Station. 

Kiev. 
Track  at 
c.  g.  of 

Train. 

Speed. 

Miles 

Per  Hour. 

Vel.-Head 

(by  Table 

118). 

Virtual 
Elevation. 

Differ- 
ences in 
ditto. 

Pounds 
Per  Ton 
Resist- 
ance. 

0 

724.2 
723.0 
721.3 
720.0 
715-8 
710.2 

21.5 
21.3 
20.6 
21.0 
21.0 
23-9 

16.4 
16. 1 
15. 1 
15-7 
15-7 
20.3 

740.6 
739-1 
736.4 
735-7 
731-5 
730.5 

I  000 

1.5 
2.7 
1.7 
4.2 
I.O 

2  000 

a  000 

A  000       

c  000 

First  5,000  feet 

21-55 

2    22 

4-44 

6,000 

704.4 
702.4 
701.6 

699-3 
698.1 

24.8 
25-3 
25-3 
24-3 
24.2 

21.9 
22.7 
22.7 
21.0 
20.8 

720.2 

725-1 
724-3 
720.3 
718.9 

3-3 
I.I 
0.8 
4.0 
1-4 

y  000 

8  000 

Q,000 



10  000     

Second  5,000  feet 

24.78 

2.12 

4.24 

11,000 

694-4 
692.0 
694.2 
695.0 
697.0 

24.6 

24-5 
21.8 
19.8 
17.2 

21.5 
21.3 
16.9 

13.9 
10.5 

715-9 
713-3 
711. 1 
708.9 
707-5 

3-0 
2.6 
2.2 
2.2 
1-4 

12  000 

13,000 

14,000 

15,000 

Third  5  000  feet 

2.28 

4-56 

16,000 

698.5 

695-9 
693.1 

690.3 
684-4 

14-3 
14.6 
16.2 
16.7 
18.5 

7.3 
6.6 

9-3 

9-9 

12.2 

705.8 
702.5 
702.4 
700.2 
696.6 

1.7 

?:? 

2.2 

17  000       . .    . . 

18,000 . 

19.000 



20,000 

3.6    i 

Fourth   5,000  feet 

2.18  !    4.36 

21,000 

682.2 
684-3 
682.5 

19.0 

16.4 
15-4 

12.9 
9.6 

8.4 

695.1 

693-9 
690.9 

1-5     1 

12      

22  000  

23,000 

3-0      

3  000  feet 

16.93 

1.90       3.80 

20.51 

2 .  16          1  -  •s^ 

CHAP.    XIII.— TRAIN  RESISTANCE. 


499 


As  an  illustration  of  the  accuracy  of  the  method,  at  station  9000  the  resistance  will  be 
observed  to  be  abnormally  large.  The  same  peculiarity  ran  through  all  the  diagrams. 
It  was  found  on  investigation  that  the  track  at  9000  (which  was  in  the  hollow  of  a  grade) 
had  been  reballasted  after  the  profile  levels  were  taken  and  raised  by  some  unknown 
amount  (probably  something  over  a  foot),  accounting  for  the  error.  All  the  irregularities 
of  the  table  are  due  to  two  defects  of  observation  :  (i)  Lack  of  absolute  precision  in  the 
track  elevations,  and  (2)  lack  of  exact  correctness  in  the  speeds  read  off  from  the  dyna- 
mometer record,  which  was  on  a  scale  of  ^  in.  per  mile  per  hour,  or  2  ft.  of  paper  per  mile 
run.  To  attempt  to  compute  the  resistance  separately  for  each  successive  1000  ft.  is  a  very 
crucial  test  of  the  accuracy  of  the  method,  and  a  quite  unnecessary  one  from  a  practical 
point  of  view.  The  computations  over  5000  ft.  stretches  are  very  regular,  illustrating 
that  no  other  method  can  approach  this  in  precision  and  certainty. 

The  weights  of  the  trains  tested  were  as  follows,  in  tons  of  2000  lbs. : 


Westinghouse. 

Eames. 

American. 

25  box-cars,  empty  weight 

301.07 
240. 
0.25 
16.50 

13-55 

261.41 
240. 

39-83 
16.50 

13-55 

344.79 
240. 

16.50 
13-55 

12  loads,  at  20  tons  each 

Equalizing  load,  when  used.    

Dynamometer  car,  with  15  persons. . . 
Way  car,  with  10  persons 

Total  train 

571-37 
26.54 
14.07 

12.35 
15-15 

571-29 
26.40 
14.52 
12.35 
15-15 

614.84 
25.02 
14.25 
12.35 
15-15 

Engine  on  drivers 

'*       on  truck 

Tender  empty 

Total  engine  and  train 

639-48 

339.96 

53-16 

639-71 

300.16 

46.90 

681.61 

382.16 

56.04 

Of  which  there  was  braked 

Per  cent  braked 

Every  box-car  truck  but  one,  as  well  as  the  tender  and  engine  drivers,  had  brakes  on — 
a  very  unusual  proportion. 

All  the  trains  had  Master  Car-Builders'  standard  axles  (3%  X  7  in.),  except  the  Widdi- 
field  &  Button,  which  had  3^4  X  7. 

A  full  report  of  these  tests,  as  prepared  and  computed  by  the  writer,  will  be  found  in  the 
Railroad  Gazette,  June  to  August,  1886.  The  results  of  a  later  series  of  tests 
IN  1887  (see  Engineering  News,  May,  June,  1887)  were  as  follows  : 


[Tests  had  not  been  made  when  the  first  edition  of  this  treatise  was  issued.] 


500 


CHAP.    XIIL— FREIGHT-TRAIN  RESISTANCE. 


Table  160. 

Train  Resistance  of  Entire  Freight  Trains,  including  Engine. 

[Giving  the  mean  resistances  in  pounds  per  ton  (of  2000  lbs.)  computed  as  shown  in 

Table  159,  with  the  corresponding  velocities  in  miles  per  hour.] 

(Each  of  the  resistances  on  tangent  is  the  average  on  a  run  of  5000  ft.     Each  of  the 

resistances  on  curves  the  average  on  a  run  of  2500  ft.) 


Resistances  on 
Tangent. 

Resistances  on  Curves. 

Tangent 

Vel. 

Resist. 

Vel. 

Resist. 

Curve. 

Resist.* 

r 

Westinghouse  (C,  B.J 
&Q.  cars) "> 

16.93 
16.06 
21.58 
24-78 
21.55 

3 
4 
4 
4 

4 

80 
36 
56 
24 

44 

18.86 
33-90 
34-90 

4 
7 
6 

56 
56 
41 

1.08° 
2.60° 
1.47° 

4.02 
6.26 
5.68 

Mean    

20.51 

4 

32 

26.33 

6 

07 

1.75°         6.20 

Eames   (I.,   D.    &   S.  ( 
cars)  and  Widdifield  \ 
&  Button  (L.V. cars)  ( 

8.42 
18.28 
19.70  , 

6 
6 

7 

50 
76 
04 

14.03 

24-55 
30.10 

9 
9 
9 

68 
20 
36 

1.08° 
2.60° 
1-47° 

9.14 
7.90 
8.63 

Mean 

16.82 

6 

84 

21.70 

9 

42 

1-75° 

8.55 

American  (St.  L.  &  S.  ( 
F.  cars) "j 

9.62 
13-72 

9 
7 

30 

88 

13-03 
24-45 
30.75 

8 

10 
7 

08 
40 

84 

1.08° 
2.60" 
1.47° 

7-54 
9.10 
7.21 

Mean 

11.66 

8 

50 

21.19 

8 

94 

1.75° 

8.07 

*  Tangent  resistance  determined  by  subtracting  i^  lb.  per  degree  of  curve  .from  the  total 
resistance.  Average  degree  of  curve  determined  by  determining  degrees  of  central  angle 
passed  over  by  head  and  rear  of  train  on  given  distance,  averaging  the  two,  and  dividing  by 
number  of  stations. 

Velocities  are  in  miles  per  hour ;  resistances  in  pounds  per  ton. 

practicable  freight  speeds.     The  track  was  in  fair  but  not  remarkably 
good  condition. 

618.  The  conditions  of  the  trains  tested  (which  will  be  seen  to  have 
shown  quite  different  results)  were  as  follows  : 

I.  Westi7ighouse\  train. — Made  up  of  old  cars  in  excellent  running 
order,  with  well-worn  journals  and  wheel-treads.  The  performance  of 
this  train  should  fairly  represent  the  ordinary  conditions  of  practice. 

2.  American  train. — Made  up  of  entirely  new  and  very  heavy  cars^ 
which  had  only  run  some  300  to  500  miles  since  leaving  the  shop,  and 

f  The  trains  are  designated,  for  convenience,  by  the  names  of  the  brakes 
with  which  they  were  fitted,  although  these  brakes  had  nothing  to  do  with  the 
tests. 


CHAP.    XIII.— FREIGHT-TRAIN  RESISTANCE.  50I 

consequently  had  bearings  and  wheel-treads  still  comparatively  rough, 
and  7iot  fairly  representing  the  average  conditions  of  practice. 

3.  Eames  train. — Made  up  of  fairly  old  but  poorly  built  cars,  and 
generally  in  rather  inferior  condition. 

619.  The  effect  of  these  differences  in  the  trains  is  clearly  visible  in 
Fig.  154,  where  the  Westinghouse  train  shows  rather  less  than  half  the 
rolling  resistance  of  the  other  two,  or  about  4  lbs.  per  ton  for  all  speeds 
up  to  25  miles  per  hour.  The  general  fact  that  speed  causes  very  little 
increase  in  train  resistance  up  to  speeds  of  30  miles  per  hour  is  clearly 
indicated  ;  and  this  many  other  indications  tend  to  confirm,  as  notably 
various  dynamometer  tests  made  by  the  Pennsylvania,  New  York,  Lake 
Erie  &  Western,  Chicago,  Burlington  &  Quincy,  and  other  roads,  where 
ver}^  low  car  resistances,  running  down  to  from  2^  to  4  lbs.  per  ton,  have 
been  indicated,  with  little  variation  as  an  effect  of  speed. 

These  latter  tests  alone  would  leave  the  question  open  to  much  doubt, 
since  they  do  not  include  any  of  the  head  or  engine  resistances,  which 
at  high  speeds  become  more  important  than  any  other,  but  the  tests 
given  in  Fig.  154  include  ALL  resistances  and  lead  to  the  same  conclusion 
so  clearly  as  to  be  unmistakable. 

620.  The  peculiar  manner  in  which  the  Eames  and  American   resistance 
lines  on  curves  cross  each  other,  as  shown  by  the  fol- 
lowing sketch,  may  appear  to  indicate   that  there  is 
something  wrong  in  the  computed  results.   This  is  by 
no  means  so.     The  anomaly  may  be  thus  explained  : 

{a)  Each  train  was  made  up  of  25  cars  from  the  same  road  and  built  nearly  at 
the  same  time. 

(^)  All  freight  cars  are  roughly  built.  The  axles  are  not  likely  to  be  pre- 
cisely parallel,  except  by  accident.  To  have  the  axles  enough  out  of  parallel  to 
precisely  fit  a  1°  curve  requires  that  the  wheel-base  shall  be  only  -^h^  P^-^t  longer 
on  one  side  than  the  other,  or  -^  in.  A  lot  of  cars  built  at  one  time  are  very 
likely  to  have  the  error  all  on  one  side. 

{c)  Resistances  a  and  c  (see  sketch  above)  were  on  curves  turning  to  the  right; 
resistance  b  was  on  a  curve  turning  to  the  left. 

If,  therefore,  the  American  train  curved  most  easily  to  the  right,  resistances 
a  and  c  would  be  abnormally  low,  or  very  near  the  tangent  rate,  and  resistance 
b  abnormally  high;  while,  if  the  contrary  was  the  case,  with  the  Eames  train  re- 
sistance a  and  c  would  be  abnormally  high,  and  resistance  b  abnormally  low,  or 
well  down  toward  the  tangent  rate. 

Whether  this  or  other  cause  led  to  the  variation,  it  is  certain  that  it  was  an 
actual  one,  and  the  fairer  plan,  therefore,  seems  to  be  to  take  the  average  of  both 
trains.     The  trottle  of  each  engine  was  absolutely  tight. 


502 


CHAP.    XIIL—FREIGHT-TRAIN  RESISTANCE. 


621.  The  experiments  by  the  writer  recorded  in  Appendix  A  were 
made  by  the  same  general  method  as  those  just  described,  and  were  the 
first  in  which  the  very  low  train  resistances  for  trains  in  motion  which  are 
now  generally  admitted  were  observed.  They  indicated  that  the  normal 
magnitude  of  the  rolling- friction  at  speeds  of  lo  to  30  miles  per  hour  was  : 

For  passenger  and  loaded  freight  cars, 4  lbs.  per  ton 

For  empty  freight  cars  and  other  light  loads,       ....       6    " 

For  street  cars  and  other  still  lighter  loads, 10    "  " 

For  freight  trucks  without  load, 14    " 

The  starting-friction  is  very  much  higher,  rising  to  over  20  lbs.  per 
ton  in  some  cases.     (See  Appendix  B.) 

622.  Some  experiments  on  train  resistance,  both  on  curves  and  tan- 
gents, made  in  1885  on  the  Breslau-Schmoltz  line  in  Germany,  apparently 
in  an  accurate  and  careful  manner,  but  covering  only  the  resistance  of 
cars  behind  the  tender  and  dynamometer  car,  gave  still  lower  results  than 
these,  as  shown  in  Table  161.  The  tests  covered  also  the  question  of 
remedies  for  oscillation  and  the  advantages  of  a  device  for  radiating  axles 
on  curves,  as  to  which  nothing  important  was  developed.  The  resist- 
ances are  noticeable  as  being  among  the  lowest  ever  reported  for  similar 
speeds.  Similar  tests  on  the  Freiburg-Sulzbrunn  line,  with  the  same 
apparatus  and  by  the  same  individuals,  gave  somewhat  higher  average. 

Modern  evidence  to  the  same  general  purport  as  that  which  precedes 
might  be  multiplied  almost  indefinitely,  but  it  appears  needless  to  do  so. 

623.  We  may   conclude,  therefore,  as    to   freight-train 

RESISTANCE 

I.  The  particular  velocity  adopted  is  wholly  unimportant,. 
both  because  it  makes  absolutely  but  little  difference  in  the 
resistance,  and  because,  if  the  resistances  are  m.ounting  too  high 
for  the  power  of  the  engine,  the  speed  can  always  be  cut  down, 
at  critical  points.     The  total  work  in  foot-pounds  done  to  move 


Table  161. 
Resistance  of  European  Cars  (16  to  23  ft.  rigid  wheel-base). 

[Reported  in  full  in  the  Railway  Engineer,  Dec.  1884  et  seq.     Resistance  in  Pounds  Per  Ton. 


Speed. 
Miles  Per  Hour. 

Radiating  Axles. 

Fixed  Axles. 

Limits. 

Average. 

Limits. 

Average. 

12.4 
21.8 

28 

2.0      to   3.75 

3.97   to  4.19 

5-07 

2.65 
4.08 
5.07 

2.42  to   3.75 

3.97  to   4.85 

6.17 

3.09 
4.19 
6.17 

CHAP.    XIII— FREIGHT-TRAIN  RESISTANCE.  503 

the  train  is  not  affected  enoua^h  to  have  any  measurable  effect  on 
the  cost  of  power  (see  par.  664). 

2.  The  normal  tangent  freight-train  resistance  in  summer, 
ENGINE  AND  ALL  INCLUDED,  is  often,  and  perhaps  usually,  as  low 
as  4  lbs.  per  ton,  up  to  speeds  as  high  as  25  miles  per  hour,  run- 
ning down  in  cases  to  3  lbs.  and  even  less;  and,  on  the  other 
hand,  rising  in  cases  as  high  as  6  or  8  lbs.  per  ton  when  the  cars 
are  in  bad  order,  or  against  a  head  or  side  wind,  or  (as  we  are 
about  to  see)  at  winter  temperatures ;  these  latter  figures  being 
a  fair  working  maximum  for  freight  service. 

Four  pounds  per  ton  will  make  a  difference  of  some  2400  lbs.  in  tractive  re- 
sistance with  an  average  train  of  25  cars,  which  will  use  up  the  adhesion  of  4.8 
tons  of  weight  on  drivers,  or  12  to  20  per  cent  of  the  total  load. 

624.  It  is  entirely  uncertain  how  much  of  the  so-called  rolling-friction  is 
journal-friction,  and  how  much  rolling-friction  proper.  The  present  proba- 
bilities are  that  most  of  it  is  journal-friction.  Experimental  determination  of 
the  rolling-friction  proper,  apart  from  all  journal-friction,  is  a  matter  of  the 
greatest  difficulty,  and  has  never  been  attempted.  Journal-friction  has  been 
far  more  thoroughly  investigated  within  the  last  few  years,  but  until  then  the 
laws  of  it  also  had  been  but  little  investigated,  and  what  investigation  had  been 
made  was  largely  erroneous. 

625.  By  some  singular  chance, — probably  the  beautiful  simplicity  of  the  laws 
developed,  which  only  lacked  correctness  to  make  the  laws  of  friction  very 
easily  understood, — some  experiments  made  by  M.  Morin,*  a  French  officer  of 
artillery,  in  1831,  obtained  almost  universal  acceptation  as  a  final  determination 
of  the  laws  of  friction.  There  is  even  at  the  present  day  (1885)  hardly  a  single 
text-book  of  engineering,  at  least  in  English,  in  which  these  laws  are  not  laid 
down  as  facts,  yet  they  are  now  generally  admitted  to  be  entirely  incorrect. 
They  were  in  substance  that  the  coefficient  of  friction  was  independent  both  of 
the  pressure  and  of  the  velocity,  so  that,  once  determined,  it  was  universally 
applicable.  The  range  of  the  experiments  was  very  limited,  and  Morin  himself 
disclaimed  any  extension  of  them  beyond  the  range  of  his  experiments;  but  it  is 
clearly  proven  that  there  are  no  limits  nor  conditions  under  which  his  laws  are 
approximately  true,  since  the  coefficient  varies  materially  both  with  pressure 
and  velocity,  with  both  lubricated  and  unlubricated  surfaces,  and  with  tempera- 
ture and  other  conditions  as  well  ;  as  notably  with  the  character  of  the  surface, 
which  makes  any  general  coefficient  of  "iron  on  iron,'"  or  "  iron  on  brass,"  for 
example,  rather  worse  than  useless. 

*  "  Nouvelles  Experiences  sur  le  Frottement.  Faites  a  Metz  en  1831."  Par 
Arthur  Morin,  Capitaine  d'Art'llerie.  128  pp.,  4°,  plates.  Seconde  Memoire, 
1832,  103  pp.,  4",  plates.     Tro  sieme  Memoire,  1833,  142  pp.,  4°,  plates. 


504 


CHAP.    XIII.— FREIGHT-TRAIN  RESISTANCE. 


626.  Prof.  R.  H.  Thurston  was  among  the  first,  if  not  the  first,  to  discover 
and  announce  the  true  laws  of  friction,  in  1876-78,  having  made  a  large  number 
of  experiments  on  an  ingenious  machine  of  his  invention.  The  writer,  in  the 
summer  of  1S78,  made  a  series  of  tests  of  rolling-stock  resistances,  summarized 
in  Appendix  A,  by  dropping  cars  down  grades  and  registering  velocities  elec- 
trically, in  which  he  believes  he  was  the  first  to  discover  and  announce  the 
variation  in  coefficieni  for  loaded  and  empty  cars  and  the  aggregates  of  4,  6, 
and  10  lbs.,  above  mentioned,  which  at  the  time  appeared  quite  without  prece- 
dent, as  Prof.  Thurston's  results  were  not  at  that  time  generally  known,  and 
were  not  at  all  known  to  the  writer.  A  large  number  of  dynamometer  tests 
on  various  roads  were  made  shortly  after,  and  in   fact  were  then  in  progress, 


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1                   '                                       ■                                    Co\fFICIENT  OF  FRICTION 
«)                 20                 30                40                 SO                ^                  TO                80                 30                 100 

Lbs  Per  Toil  Train  Resistance. 


(The  velocity  given  for  the  rubbing-surfaces  of  300  ft.  per  minute  is  equivalent  to  a  train 
speed  of  some  34  miles  per  hour.) 

Fig.  155. 


showing  the  same  low  rate  of  4  lbs.  per  ton  or  even  less  for  loaded-car  resist- 
ances, although  empty-car  resistances  were  less  carefully  determined.  Shortly 
thereafter  Mr.  C.  J.  H.  Woodbury  began  tests  of  great  interest  for  mill-work, 
which  give  strong  confirmatory  evidence  of  the  above  results  as  respects  the  gen- 
eral laws  of  friction,  although  not  directly  applicable  to  railroad  practice.  Finally, 
in  1883-4  Mr.  Beauchamp  Tower  made  a  series  of  elaborate  and  remarkable 
tests  under  the  auspices  of  the  Institution  of  Mechanical  Engineers,  which 
appear  to  have  been  the  first  made  in  England  of  a  character  to  reveal  the 


CHAP.    XIII.— FREIGHT-TRAIN  RESISTANCE. 


505 


errors  of  Morin's  results.     The  Germans  and  French  do  not  appear  to  have 
shown  their  usual  scientific  activity  in  this  matter, 

627.  All  these  modern  results  agree  in  essentials  with  each  other,  although 
some  have  covered  results  not  touched  by  the  others.  Their  general  results 
and  indications  are  summarized  in  Appendix  B.  Mr.  Woodbury's  results*  begin 
with  the  lowest  pressures,  and  are  shown  in  Table  162,  and  graphically  in  Fig. 
155.  For  the  very  reason  that  this  diagram  is  for  pressures  lower  than  ever 
occur  in  normal  railroad  practice,  it  is  particularly  interesting,  since  it  furnishes 
a  check  on  the  conclusions  which  have  been  reached  by  other  experimenters 
operating  within  the  limits  of  railroad  practice  only,  by  beginning  as  it  were  at 
the  foundation,  and  showing  the  law  of  change  in  journal-friction  from  i  lb.  per 
square  inch  of  journal-pressure  upwards.  There  has  been  added  below  the 
diagram  a  line  showing  the  equivalent  in  pounds  per  ton  of  train  resistance  to 
the  abstract  "coefficients  of  friction"  given,  as  being  a  unit  better  suited  for  our 
immediate  purpose. 


Table  162, 
Coefficients    of    Friction   with   Very    Low    Pressures,    and    Effect 

THEREON    of   TEMPERATURE. 
[Abstracted  from  records  of  tests  of  C.  J.  H.  Woodbury.] 


Total  Friction  at  Tempera- 

Pressure 

Coefficient 

OF  Friction. 

ture 

of— 

Per  Cent  of 

Per  Sq.  In. 

100°  to  40°. 

40°. 

100°. 

40°. 

100°. 

lbs. 

lbs. 

I 

.538 

.138 

.538 

.138 

25.6 

2 

.299 

.080 

•598 

.160 

26.8 

3 

.211 

.060 

.633 

.180 

28.5 

4 

.167 

.050 

.668 

.200 

30.0 

5 

.140 

■044 

.700 

.220 

31-3 

6 

.122 

.039 

•732 

.234 

32.0 

7 

.109 

.036 

.763 

.252 

33.0 

8 

.098 

.034 

.784 

.272 

34-7 

9 

.090 

.032 

.810 

.288 

35-7 

10 

.084 

.030 

.840 

.300 

35.8 

15 

.063 

.025 

•945 

.375 

39-7 

20 

.053 

.023 

1.060 

.460 

43-3 

25 

.046 

.021 

1. 150 

•525 

45-7 

30 

.041 

.020 

1.230 

.600 

48.8 

35 

.038 

.019 

I -330 

.665 

51. 1 

40 

.035 

.018 

1.400 

.720 

51-5 

*  For  complete  paper,  which  is  full  of  interesting  information  on  friction, 
see  "Measurements  of  the  Friction  of  Lubricating  Oils,"  by  C.  J.  H.  Woodbury, 
Trans.  Am.  Soc.  M.  E.,  1884-85. 


505  CHAP.    XIII.— FREIGHT-TRAIN  RESISTANCE. 

628.  The  diagram  is  especially  useful  to  afford  some  indication  as  to  the 
comparative  train  resistance  in  winter  and  summer,  as  to  which  there  are  no 
experimental  records.  Since  the  diagram  fixes,  as  it  were,  a  superior  limit  for 
the  friction  of  railroad  journals,  we  might,  on  studying  it,  fairly  draw  three 
conclusions  : 

I.  Since  friction  can  in  no  case  be  less  than  zero,  lines  representing  all 
possible  loads  on  railroad  journals  must  lie  in  the  narrow  space  at  the  left  of 
the  diagram  between  the  zero  line  and  that  for  40  lbs.  per  square  inch  pressure, 
which  is  the  last  given.  This  means  that  all  railway -journal  friction  ought  ta 
lie  between  these  narrow  limits  : 

Temperature  of  Coefficient  of  Pounds  per  ton  train 

journal.  friction.  resistance. 

40°  Fahrenheit o  to  .035  o  to  7.0  lbs. 

100°  Fahrenheit o  to  .018  o  to  3.6  lbs. 

This  closely  corresponds  with  the  result  of  all  the  latest  tests,  which  show 
from  3i  to  6  lbs.  per  ton  resistance. 

629.  2.  Within  the  temperature  limits  of  40°  and  100°,  the  effect  of  the 
higher  temperature  is  to  decrease  materially,  and  of  the  lower  temperature  to 
increase  materially,  the  amount  of  loss  by  friction.  At  40  lbs.  per  square  inch 
the  friction  is  nearly  twice  as  much  at  the  lower  temperature,  while  at  still 
lower  pressures  of  i  to  10  lbs.  per  square  inch  it  is  from  three  to  four  times  as 
much.  Extending  the  indications  of  these  tests  to  the  higher  pressures  of  rail- 
way practice,  we  might  expect  that  the  effect  of  a  fall  of  temperature  in  the 
journals  from  100°,  which  we  may  call  an  average  summer  temperature,  to  40°, 
which  we  may  call  an  average  winter  temperature,  would  be  to  make  journal 
friction  in  summer  and  winter  railway  service  compare  somewhat  as  follows  : 

Loaded.  Empty. 

Summer,  as  shown  by  various  tests,  say 4  lbs.  6  lbs. 

Winter  (not  directly  shown  by  any  tests),  say 5i  to  6  lbs.         8  to  9  lbs. 

630.  Whether  this  conclusion  be  true  or  not  cannot  be  proven  by  direct 
evidence,  for  lack  of  recorded  train-resistance  tests  which  have  been  made  in 
cold  weather,  but  the  circumstantial  evidence  that  some  change  of  this  kind 
takes  place  is  very  strong.  Among  such  evidence  is  one  small  fraction  of  the 
series  of  tests  by  Mr.  Beauchamp  Tower,  above  alluded  to,  for  determining  the 
effect  of  temperature  on  journal- friction.  The  loads  and  journal-speeds  in  this 
case  closely  paralleled  railway  practice,  but  the  lubrication  was  vastly  more 
efficient,  being  by  a  bath  of  lard-oil.  Lard-oil  is  affected  by  temperature  much 
as  are  ordinary  railroad  lubricants,  but  the  superior  method  of  lubrication, 
in  addition  to  giving  rates  of  friction  which  are  far  below  the  possibilities  of 
railway  practice,  would  be  likely  to  have  the  effect  of  exaggerating  the 
beneficial  effect  of  high  temperature,  since  the  more  perfect  the  supply  of 
oil,    the   greater  might  be   expected  to   be  the  advantages   of  great   fluidity. 


CHAP.    XIII— FREIGHT-TRAIN  RESISTANCE. 


507 


Nevertheless,  with  these  allowances  remembered,  some  of  Mr.  Tower's 
results,  as  summarized  in  Table  163,  are  very  instructive.  Translating  co- 
efficients of  friction  into  pounds  per  ton  of  train  resistance,  as  in  Fig.  155, 
by  multiplying  them  by  200,  and  translating  the  journal-speeds  into  train- 
speeds  by  multiplying  by  10  (these  methods  being  approximate  only,  but 
sufficiently  exact),  we  have  in  Table  163  some  vefy  definite  indications  of  the 
effect  of  temperature  on  axle-friction. 

631.  To  draw  any  positive  conclusions  from  this  table  we  must  make  a  cer- 
tain "scientific  use  of  the  imagination,"  by  making  allowances  both  in  the 
temperatures  and  in  the  observed  friction  for  the  difference  in  manner  of 
lubrication.  As  these  allowances  might  or  might  not  be  correct,  we  will  not 
attempt  them;  but  it  is  clear  that,  be  the  allowances  thus  made  what  they  may, 
these  results  support  the  general  conclusion  strongly,  that  the  external  tem- 
perature of  the  air  may  have  a  most  important  influence  on  the  normal  rolling- 
friction,  as  do  experiments  by  Professor  Thurston  and  others.  On  the  other 
hand,  there  are  many  experiments  which,  at  least  in  appearance,  would  tend 
to  controvert  these  conclusions,  for  one  has  only  to  look  long  enough  to  find 
experimental  records  to  support  or  controvert  almost  anything.  But  such  con- 
troverting evidence  is  in  this  case  not  abundant,  nor  of  the  highest  class,  and 
as  a  general  rule  the  apparent  discrepancies  all  result  from  two  apparent 
anomalies  which  are  in  no  respect  inconsistent  with  what  has  preceded  : 

1.  At  a  certain  temperature  not  far  above  100°  Fahr.,  and  with  some  fluid 
oils  below  it,  the  law  changes,  and  increase  of  temperature  causes  a  rapid  in- 
crease of  resistance. 

2.  At  very  slow  speeds,  especially  when  combined  with  very  high  pressures, 
the  law  often  changes,  and  a  higher  temperature  has  an  injurious  effect, 
apparently  because  a  certain  viscosity  is  necessary  for  efficient  lubrication 
under  such  circumstances. 


Table  163. 
Effect  of  Temperature  on  Journal  Friction. 

[Deduced  from  tests  of  Beauchamp  Tower;  bath  of  lard  oil;  load,  100  lbs.  persq.  in.  (about 
that  of  an  ordinary  empty  freight-car  journal.)] 


Pounds  Per  Ton  of  Train  Resistance  at  Speeds  in  Miles 
Per  Hour  of — 

Train  speed. . 

At  120°  Fahr. 
At  60°  Fahr.. 

8.8 

0.48 
1. 18 

13.2 

0.58 
1.68 

17.6 

0.70 
2.06 

21.9 

0.80 

2.38 

26.3 

0.88 
2.60 

35.1 

1.02 
2.96 

39-5 

1.08 
3.12 

Difference. . 

0.70 

I. 10. . 

1.36 

1.58 

1.72 

1.96 

2.04 

5o8  CHAP.    XIII.— FREIGHT- TRAIN  RESISTANCE. 

632t  Zero  temperatures  are  not  favorite  ones  for  dynamometer  experi- 
ments, but  experience  in  the  running  of  trains  in  winter  and  summer  indicates 
in  the  most  positive  manner  that  summer  trains  must  be  cut  down  by  two  to 
four  cars  in  winter,  or  say  lo  to  15  per  cent,  in  order  to  run  them  at  all.  This 
practice  has  not  become  universal  without  some  real  necessity;  but  it  is  more 
difficult  to  account  for  the  necessity  than  is  generally  realized,  for  some  of  the 
explanations  which  are  given  will  certainly  not  hold  water,  as  pointed  out  in 
par.  345.  It  need  only  be  added,  that  the  loss  by  radiation  from  the  loco- 
motive will  hardly  explain  any  part  of  this  need  for  cutting  down  trains,  since 
the  difference  between  winter  and  summer  temperatures  is  a  small  and  unim- 
portant one  to  the  locomotive,  though  a  very  important  one  to  the  human 
body. 

633.  Let  us  see  how  radical  is  the  difference  in  its  effect  on  them.  The 
human  body  can  manage  to  sustain  for  a  short  time  a  temperature  of  say  40" 
below  zero,  or  138°  below  its  natural  temperature,  and  it  can  do  this  only 
when  "lagged"  with  skins  and  such  like,  to  the  last  degree  of  perfection,  at 
every  exposed  point.  The  boiler  is  subjected  to  an  equally  unpleasant  extreme 
of  temperature  when  the  external  temperature  is  350  —  138  =  212°  Fahren- 
heit, or  just  hot  enough  to  cause  water  to  boil  in  the  open  air.  To  get  a 
fair  parallel,  we  must  consider  how  much  warmer  the  average  man  would  think 
it  with  the  temperature  140°  below  zero  than  when  it  was  down  to  200°  below 
zero.  It  is  not  probable  that  he  would  find  that  the  difference  was  of  great 
consequence. 

To  be  sure,  the  fire  inside  the  boiler  is  more  efficient  than  the  fire  inside 
the  human  body,  but  the  demands  on  it  are  greater  and  the  difference  of 
winter  and  summer  less.  The  average  winter  temperature  of  Pittsburgh,  for 
example,  is  about  38°  and  the  average  summer  temperature  72  degrees,  so  that 
we  have  as  the  difference  between  the  inside  and  outside  temperature  of  the 
boiler — 

In  winter 350'  -  38°  =  312° 

In  summer 350°  —  72°  =  278° 

Difference 34°  34° 

or  about  11  per  cent. 

This  difference  is  far  too  small  to  explain  the  necessity  for  any  material 
difference  in  winter  and  summer  loads.  Assuming  that  as  much  as  20  per  cent 
of  the  heat  generated  is  lost  by  external  radiation,  which  is  a  large  estimate, 
not  more  than  2  per  cent  difference  of  load  could  be  accounted  for  in  this  way. 

634.  We  seem  driven,  therefore,  as  a  net  result  of  all  the  preceding,  to  this 
interesting  and  important  conclusion,  to  directly  support  which  there  is,  as 
already  stated,  little  or  no  experimental  evidence,  although  the  circumstantial 
evidence  in  favor  of  it  is  very  strong  :  that  a  difference  in  the  rolling-friction 
of  cars  is  the  chief  reason  why  trains  must  be  cut  down  in  winter.     As  this 


CHAP.    XIII.— FREIGHT- TRAIN  RESISTANCE,  509 

probably  results  from  difference  of  temperature  of  the  journals,  and  this  again 
from  radiation  from  the  boxes  of  the  heat  which  the  journals  are  constantly 
generating,  and  as  radiation  can  be  checked  by  a  very  slight  covering  which 
will  hold  a  little  dead  air  around  a  hot  metallic  surface,  we  have  in  these  facts 
indications  which  might  lead  to  the  important  practical  conclusion  that  some 
very  slight  covering,  which  would  merely  check  radiation  from  the  journal- 
boxes  somewhat,  might  have  an  appreciable  effect  on  the  loads  which  can  be 
hauled  in  severe  cold  weather. 

635.  In  Appendices  A  and  B  will  be  found  further  and  more  detailed  infor- 
mation as  to  the  laws  of  journal-friction,  and  especially  as  to  the  important 
question  of  starting  trains.  The  normal  journal-friction,  under  favorable  con- 
ditions, as  determined  in  various  series  of  tests,  is  summarized  in  Appendix 
B  as  follows,  for  velocities  greater  than  10  miles  per  hour,  or  90  ft.  per  minute^ 
journal-speed: 

Lbs.  per  ton. 
Beauchamp  Tower,  bath  of  oil o. 278 

"  "         pad  or  siphon 1.9 

Thurston,  light  loads 2.75 

"  heavy  loads 1.75 

Wellington  (gravity  tests  of  cars  in  service),  light  loads. . .  6.0 

"  "  "  "  "        heavy  loads..  3.9 

"  direct  tests  (as  shown  in  Appendix  B) i  ^ '  ^ 

{  3-7 

Thurston,  inferior  oils  ("  Friction  and  Lubrication," p.  173)  \z' 
Morin,  continuous  lubrication 6.0  to  10.8 

636.  The  great  discrepancies  in  these  results  will  be  seen  to  point  directly 
to  one  conclusion — that  the  character  and  completeness  of  lubrication  seems  to 
be  immensely  more  important  than  the  kind  of  the  oil,  or  even  pressure  and 
temperature,  in  affecting  the  coefficient  of  friction.  Mr.  Tower  found  that 
lubrication  by  a  bath  (whether  barely  touching  the  axle  or  almost  surrounding 
it)  was  from  six  to  ten  times  more  effective  in  reducing  friction  than  lubrication 
by  a  pad.  By  immersing  the  journal  in  a  bath  of  oil  Mr.  Tower  succeeded  in 
reducing  the  coefficient  in  a  large  number  of  tests  to  as  low  a  point  as  o.ooi — 
equivalent  to  only  0.2  lb.  per  ton  of  tractive  resistance;  and  the  general  average 
in  the  bath  tests,  under  all  varieties  of  load  and  speed,  is  given  as  only  0.00139, 
or  0.278  lb.  per  ton,  against  1.96  to  1.95  lbs.  per  ton  with  siphon  lubricator, 
or  pad  under  journal.    These  results  are  very  far  below  any  heretofore  reported. 

637.  The  overmastering  effect  of  minute  differences  in  the  condition  of  the 
lubrication  was  curiously  shown  in  two  ways  in  Tower's  experiments  ; 

I.  It  was  accidentally  discovered  that  with  bath  lubrication  the  bearing  is 
actually  floated  on  a  film  of  oil  between  the  lubricated  surfaces,  which  is  so  truly 
a  fluid  that  it  will  rise  through  a  hole  in  the  top  of  the  bearing  in  a  continuous 


510  CHAP.   XIII.—FREIGHT-TRAIN  RESISTANCE, 


■stream  and  exert  a  pressure  against  a  gauge  equal  to  more  than  twice  the 
average  pressure  per  square  inch  on  the  bearing.  This  is  precisely  what  theory 
would  require  if  the  lubricant  were  a  perfect  fluid. 

2.  Tower's  apparatus  required  that  the  journal  should  be  revolved  first  one 
way  and  then  the  other.  It  was  found  that  the  friction  was  always  greater 
when  the  direction  of  motion  was  first  reversed.  The  increase  varied  consid- 
erably with  the  newness  of  the  journal.  "  Its  greatest  observed  amount  was  at 
starting,  and  was  almost  twice  the  nominal  friction,  and  it  gradually  diminished 
until  the  normal  friction  was  reached,  after  about  ten  minutes'  continuous  run- 
ning. This  increase  of  friction  was  accompanied  by  a  strong  tendency  to  heat, 
even  under  a  moderate  load.  In  the  case  of  one  brass  which  had  worked  for  a 
considerable  time  it  almost  entirely  disappeared."  It  is  with  apparent  justice 
concluded  that  the  phenomenon  must  be  due  to  the  interlocking,  point  to  point, 
of  the  surface  fibres  after  having  been  for  some  time  stroked  in  one  direction. 

638.  It  appears  not  impossible,  therefore,  that  a  great  further  reduction  in 
the  axle-friction  of  trains,  as  well  as  a  great  saving  of  oil,  may  result,  within 
a  few  years,  from  the  adoption  of  something  better  than  the  crude  and  wasteful 
axle  box  which  is  now  common.     The  objections  to  it  are  : 

1.  It  leaks  badly  at  the  back,  around  the  axle,  letting  oil  out  and  grit  in. 
Therefore — 

2.  The  oil  has  to  be  frequently  renewed,  requiring  a  loose  lid  in  front,  from 
which  more  oil  escapes  and  more  grit  gets  in. 

From  this  it  very  naturally  results  that  in  spite  of  the  large  expense  of  about 
a  cent  per  train-mile  (Table  78)  for  oil  there  is  often  very  little  of  it  where  it  is 
wanted,  and  that  dirty  and  gritty  ;  while,  on  the  other  hand,  the  ties  and  road- 
bed are  saturated  with  it  from  one  end  of  the  United  States  to  the  other. 

639.  In  Figs.  156-159  is  shown  a  French  oil-box  which  obviates  many 
■of  these  objections  and  has  made  the  very  remarkable  record  given  below. 
The  Germans  have  similar  oil-boxes  in  extensive  use.  The  oil  reservoir  is 
entirely  below  the  axle,  so  that  oil  cannot  escape,  and  it  is  supplied  to  the  bear- 
ing by  a  pad  fed  by  wicks.  Could  an  oil-tight  stuffing-box  be  used  at  the  back 
of  the  box,  and  the  box  be  kept  completely  full  of  oil,  it  is  more  than  probable 
that  even  greater  reduction  of  axle-friction  and  waste  of  oil  would  follow. 

The  lower  half  of  these  boxes  is  furnished  inside  with  a  partially  horizontal 
diaphragm  in  the  portion  toward  the  wheel,  for  the  purpose  of  preventing  the 
forcing  out  of  the  oil  by  violent  side  blows.  They  have  proved  so  efficient 
that  the  consumption  of  oil  has  fallen  from  2.3  ounces  per  1000  miles  to  less 
than  one  fourth  that  amount  (41.25  grammes  per  1000  kilometres  to  9.93)— a 
most  remarkable  showing,  and  a  marvellous  contrast  to  the  results  obtained 
here.  The  dust  guard  is  formed  of  five  to  six  thicknesses  of  fluffy  woollen 
cloth,  held  between  two  leather  diaphragms  by  screws  like  those  used  for 
shoe  soles.     The  diaphragms  are  in  halves,  and  are  pressed  up  against   the 


CHAP.    XIII.— FREIGHT-TRAIN  RESISTANCE. 


511 


axle  by  steel  springs  behind  them,  and  the  leathers  on  opposite  sides  of  each 
half  diaphragm  break  joints  with  those  on  the  other  half. 

The  oiling  cushion  in  this  box  has  its  oiling  plush  firmly  tacked  to  a  beech 


l»4^/«. 


Lower  RartofStx.         Plan. 

1,1,1,11?       \       f      P 


-L_L 


113/8"— 
Front  Elevation 

Y        42  Indies. 


^ 


Figs.  156-159.— Standard  Journal-box  of  the  Eastern  Railway  of  France. 
block,   and  to  this  plush  are  fastened  several  little  tufts  projecting  above  its 
surface  and  keeping  the  plush  from  matting  down  by  too  hard  pressure  against 
the  journal.     The  plush  is  of  wool  with  a  long  silky  warp. 

640.  The  important  question  of  the  comparative  resistances  in  start- 
ing trains  is  discussed  so  fully  in  Appendices  A  and  B  that  it  appears  un- 
necessary to  devote  space  to  a  repetition  of  the  same  matter  here.  From 
all  the  facts  there  given  the  following  conclusions  may,  it  is  believed,  be 
■drawn  : 


512  CHAP.    XIIL— TRAIN  RESISTANCE— STARTING. 

1.  The  resistance  at  the  beginning  of  motion  in  each  journal  is  equal 
(as  before  stated)  to  about  20  lbs.  per  ton,  or  say  1 5  lbs.  per  ton  over  the 
average  friction  in  motion.  Except,  therefore,  for  the  elasticity  of  the 
springs  or  the  equivalent  effect  of  the  "  slack "  which  always  exists  in 
freight  trains,  enabling  the  cars  to  be  set  in  motion  one  at  a  time,  such 
trains  as  are  usually  hauled  could  not  be  started  at  all  by  the  locomotive. 

2.  A  velocity  of  0.5  to  3  miles  per  hour,  or,  as  an  average,  2  miles  per 
hour,  must  be  attained  before  the  journal-friction  falls  to  10  lbs.  per  ton^ 
or  5  lbs.  above  the  average  motion. 

The  average  during  this  period  may  be  taken  at  12  lbs.  per  ton. 

3.  At  a  miles  per  hour  the  journal-friction  is  at  least  i  lb.  per  ton 
higher  than  at  usual  working  speeds.  The  average  journal-friction  be- 
tween 2  and  6  miles  per  hour  may  be  taken  as  at  least  2.\  if  not  3  lbs. 
per  ton  higher  than  the  normal. 

4.  During  the  period  of  getting  up  speed,  the  normal  law  of  accelera- 
tion of  velocity  is  so  interfered  with  by  the  varying  coefficient  of  friction 
that  the  velocity  attained  at  any  given  point  may  be  rudely  taken  as 
directly  proportional  to  the  distance  run,  so  that  the  increase  of  velocity 
would  be  more  correctly  represented  graphically  by  a  right  line  than  by 
the  parabola  tangent  to  the  horizontal  line  of  normal  velocity  in  motion 
which  theory  requires. 

641.  Assuming  these  facts,  we  having  the  following  conditions  in  a 
freight  train  which  is  so  heavily  loaded  that  it  may  be  assumed  to  have 
to  run  3340  ft.,  or  f  of  a  mile,  to  acquire  a  velocity  of  10  miles  per  hour. 

1.  The  average  velocity  will  be  under  5  miles  per  hour  and  the  time 
occupied  over  'j.^  minutes. 

2.  The  increased  tractive  force  needed  merely  to  accelerate  the  speed 
will  be  2  lbs.  per  ton ;  since  communicating  that  velocity  is  equivalent 
(Table  118)  to  lifting  the  train  through  3.34  ft.  vertically,  and  ^^  =  o.io 
per  cent  grade  =  a  resistance  of  2  lbs.  per  ton. 

3.  For  the  first  one-fifth  of  this  distance,  or  66Z  ft.,  the  total  demand 
upon  the  tractive  power  is — 

2  lbs.  per  ton  for  acceleration. 
12  lbs.  per  ton  for  extra  rolling-friction. 

14  lbs.  total  additional  tractive  resistance,  equal  to  a  grade  of  0.70,  or 
37  ft.  per  mile. 

4.  For  the  next  1336  ft.  the  total  demand  upon  the  tractive  power  is 
similarly  found  to  be  4. 5  to  5  lbs.  per  ton  over  the  normal,  equivalent  to 
the  effect  of  a  0.225  to  0.25  per  cent  grade,  or  12  to  13  ft.  per  mile. 


CH.  XIII.— TRAIN  RESISTANCE— SIZE   WHEEL  AND  AXLE.     513 


642.  These  grades,  therefore,  represent  the  reduction  at  stations  or 
stopping-places  which  it  is  essential  to  make  to  fully  and  certainly  equal- 
ize the  demands  upon  the  tractive  power  of  locomotives  while  in  motion 
and  when  getting  under  way.  The  fact  that  such  heavy  reduction  of 
grade  at  stations  may  be  said  never  to  exist,  while  yet  such  heavy  trains 
are  hauled,  is  due  in  part  to  the  use  of  sand  in  starting,  in  part  to  the 
greater  starting  traction  which  is  realized  in  practice  from  the  same 
average  cylinder  pressure  (see  end  of  Appendix  B),  and  in  part  to  the  fact 
that  the  full  adhesion  of  the  locomotive  is  not  used  up  on  the  open  road 
(par.  557).  To  utilize  to  theut  most  the  power  of  locomotives,  and  to 
make  the  hauling  of  heavy  trains  easy,  such  reductions  are  the  first 
thing  which  should  be  attended  to  in  laying  out  a  new  road  or  in  improv- 
ing an  old  one. 

Wherever  possible  the  reduction  of  grade  at  stations  should  be  liberal, 
since  there  is  in  no  case  danger  of  having  it  too  great  for  convenience. 
On  the  other  hand,  when  the  lower  grades  at  stations  are  only  obtainable 
at  the  certain  cost  of  higher  grades  between  stations,  then  it  becomes 
necessary  to  be  more  cautious,  although  the  tendency  will  always  be  to 
have  the  starting  resistances  the  true  limiting  cause. 

643.  Effect  of  Size  of  Wheel  and  fourna/.—Theortt\c3.\\y,  the  less 
the  diameter  of  the  journal  and  the  larger  the  diameter  of  the  wheel  the 
less  the  axle-friction.  The  standard  diameter  of  car-wheels  in  America 
is  33  inches,  with  a  very  few  only  (chiefly  on  the  Baltimore  &  Ohio  lines) 
of  30  inches,  and  with  a  still  smaller  but  increasing  number  of  42-inch 
wheels  in  passenger-car  service.  The  weight  of  the  latter  is  more  than 
double  that  of  33- inch  wheels  (say  1200  lbs.  against  550,  as  an  average) 
and  their  primary  purpose  is  to  promote  easy  riding  of  cars. 

The  Master  Car-Builders'  Association  standard  journal  is  3f  x  7 
inches,  giving  a  nominal  bearing-surface  (the  horizontal  mid-section)  of 
26i  sq.  in.  A  very  few  4  x  8-inch  journals,  giving  32  sq.  in.  bearing,  are 
in  use  for  cars  carrying  very  heavy  loads,  and  a  very  large  but  decreasing 
number  smaller,  down  to  as  small  as  3^x6,  giving  19.5  sq.  in.  of  bearing. 

The  maximum  loads  which  are  carried  in  practice  on  these  journals, 
allowing  eight  per  car,  may  be  estimated  as  follows  : 


Journal. 

Square  Inches  Area. 

Maximum  Load. 

Load  Per  Square 
Inch. 

Maximum,  4     X  8 

Standard,     3f  X  7 

Minimum,  3^  X  6 

32        X  8  =  256 
261    X  8  ==  210 
19.5  X  8  =  154 

64,000 
52,500 
38,500 

250  lbs. 
250    " 
250   " 

33 


514    CH.  XIII.— TRAIN  RESISTANCE— SIZE  WHEEL  AND  AXLE. 


As  an  average  of  the  entire  service  of  the  car  th^se  loads  will  hardly 
in  any  case  exceed  200  lbs.  per  sq.  in.,  but  they  will  often  run  up  to  300 
lbs.  This  pressure,  however,  is  very  unequally  distributed,  being  great- 
est (about  twice  the  average)  at  the  top  of  the  journal  and  running  down 
to  nothing  at  the  sides.  The  bearing,  in  fact,  for  this  and  other  good 
reasons,  is  never  made  to  cover  the  whole  semicircular  top  of  the  jour- 
nal. For  example  there  are  only  21.94  sq.  in.  of  bearing-surface  in  the 
American  standard  journal-bearing  against  26i  sq.  in.  in  the  section  of 
the  journal  itself. 

644.  The  only  purpose  in  increasing  the  size  of  the  journal  is  to  di- 


6.  Centre  of  axle.  (The  standard  axle  differs 
a  little  from  this,  tapering  more  toward 
the  centre.) 

7.  Flange. 

8.  Journal-box. 

9.  Journal-box  lid. 
46.  Brass  or  journal  bearing. 


Fig.  160.— Usual  Form  of  American  Car-wheel,  Journal,  and  Journal-box. 
[53  is  the  so-called  dust-guard  bearing  oi  the  axle,  surrounded  by  a  flat,  square  dust-guard 
of  wood,  leather,  or  vulcanized  fibre,  which  is  slipped  in  from  above  through  a  slot  in  the  cast- 
ing not  shown  in  the  cut  (in  which  respect  it  is  incorrect),  and  constitutes  the  onlj^  protection 
against  the  escape  of  oil  at  the  back.  The  oil  freely  escapes  through  this  dust  guard  until  it  has 
drained  out  so  far  below  the  level  of  the  under  side  of  the  axle  that  there  is  no  more  to  escape.] 

minish  the  pressure  per  sq.  in.  so  as  to  prevent  heating.     Experience  has 
amply  shown  this  to  be  necessary,  with  such  lubrication  as  is  attained  in 


CH.  XIII.— TRAIN  RESISTANCE— SIZE   WHEEL  AND  AXLE.     515 

America,  because,  although  99  per  cent  of  the  car  miieage  may  be  said 
to  be  made  with  journals  in  good  order,  and  in  fact  with  surfaces  in  a 
high  state  of  perfection,  yet  the  inconvenience  and  danger  resulting  from 
possible  heating  of  the  remaining  one  per  cent  is  the  important  thing  to 
obviate.  In  France  and  Germany,  where  much  more  carefully  con- 
structed axle-boxes,  insuring  far  more  reliable  lubrication,  are  in  use 
than  here,  as  shown  in  Figs.  156  to  159,  far  higher  pressures  are  likewise 
in  use,  without  evil  results,  up  to  fully  double  American  practice,  and  with 
great  economy  of  lubricants  ;  but  the  crude  form  of  axle-box  usual  in 
this  country,  shown  in  Fig.  160,  permits  fully  nine  tenths  of  the  oil  sup- 
plied to  the  journal  to  drip  out  upon  the  track  before  it  has  done  much 
service. 

645.  The  coefficient  of  train  resistance  due  to  axle-friction 
coeff.  of  fric.  x  diam.  of  axle  ,        ^.        ^ 

= diam.  of  wheel <^'^^  ^'^'  '^'^'  ^^^  ^^'^  ^  ^°°°  ^^  ^^^o 

=  journal  train  resistance  in  lbs.  per  ton.   With  the  same  axle,  therefore, 

by  increasing  the  diameter  of  the  wheel 

from  33  to  42   in.  we  should  decrease  ^>^ — »s^ 

axle-friction  to  |f  of  its  former  amount,  /^  \. 

or  about  4.      With  the  same  wheel,  the  /  .  \ 

comparative  axle- friction   is  directly  as  I  G)* """--%"----> 

the  diameter  of  the  journal.  y  / 

646.  If  the  average  journal-friction  >v  y^ 

in  motion  be  taken  at  4  lbs.  per  ton,  the  ^  

larger  wheels,  therefore,  will  save  about  ^'^-  ^^^• 

0.8  lb.  per  ton  of  rolling-friction,  but  they  will  add  possibly  10  per  cent 
to  the  weight  of  the  car,  and  therefore  to  grade  resistance.  Hence, 
wherever  the  grade  resistance  exceeds  about  8  lbs.  per  ton  (=  that  on  a 
0.4  per  cent  grade ;  21  feet  per  mile),  the  use  of  42-inch  wheels  is  a  losing 
operation,  so  far  as  mere  train  resistance  in  motion  is  concerned,  but 
there  still  remains  as  a  net  gain  the  improvement  in  riding  qualities  of 
the  cars  and  in  ease  of  starting — both  very  important  gains. 

647.  Many  circumstances  indicate  that  the  rolling-friction  proper,  between 
the  rail  and  wheel,  is  an  element  of  considerable  importance  in  the  aggregate 
of  the  so-called  "rolling  friction."  One  is  the  known  and  great  effect  of  the 
condition  of  the  track  on  the  resistance.  It  is  probably  largely  due  to  this 
cause  that  modern  determinations  of  rolling-friction,  both  in  this  country  and 
abroad,  are  so  much  below  what  was  formerly  the  assumed  average.  Another 
is  the  ordinarily  very  perfect  condition  of  railway  journals  and  the  very  low  co- 
efficients which  have  been  obtained  by  Thurston,  Tower,  and  others  for  journal- 


k 


5l6    CH.  XIIL— TRAIN  RESISTANCE— SIZE  WHEEL  AND  AXLE. 

_ — , 

friction  proper,  as  above  given.  Another  is  the  high  tractive  coefficients  of 
wheeled  vehicles  with  very  small  axles  and  very  large  wheels  on  the  most  per- 
fect roads.  On  the  other  hand,  the  close  correspondence  of  the  laws  of  varia- 
tion in  rolling  and  journal  friction,  together  with  the  laws  of  variation  in  jour- 
nal-friction only,  seem  to  indicate  quite  the  contrary.  Thus,  in  both  cases,  as- 
the  load  or  the  velocity  decreases  the  coefficient  of  resistance  increases,  and  at 
about  the  same  rates  (see  Appendix  B). 

648.  A  plausible  argument  may  be  made  to  show  that  no  theoretical  loss 
whatever  exists  from  the  compression  of  a  perfectly  elastic  substance,  such  as 

a  rail  may  be  ass^amed  to  be,  and  to  a  great 

Q  extent  the  permanent  way  as  a  whole,  under  a 
rolling  load.     In  Fig.  162,  the  compression  at 
any   point    of   the  surfaces  in   contact,    wher- 
C  ever  it  may  be,   is  proportional  to  ordinates 

Q-"-^^^i"Hjr^- O from  the  line  CC  to  the  periphery  of  the  wheel 

I  ^  *  P.     The  elastic  resistance  is  in  proportion  ta 

these    ordinates,    and   the  semi-segments  FF' 
'°"  ^  ^*  represent  in  magnitude  and  position  the  total 

elastic  forces  operating  to  retard  and  to  accelerate.  The  resultants  R  and  R' 
of  these  parallel  forces  must  pass  through  the  centre  of  gravity  of  these  semi- 
segments  F  and  F ,  and  must  each  be  equal  to  half  the  total  load  resting  on  the 
wheel.  It  appears  to  follow  clearly  from  the  figure  that  the  moments  of  these 
accelerating  and  retarding  forces  are  equal,  so  that  they  neutralize  each  other„ 

The  error  in  this  reasoning  is  in  part  that  at  high  speeds  the  element  of 
TIME  comes  in  to  modify  the  elastic  resistances,  increasing  that  in  front  of  the 
wheel  because  it  must  be  set  in  motion,  and  decreasing  that  behind  the  wheel 
because  the  elastic  resistance  requires  time  to  act,  and  hence  cannot  follow  up 
the  wheel  with  its  full  force.  In  part  the  error  is  that  any  irregularity  of  sur- 
face causes  an  irregularity  of  motion  which  is  known  to  very  seriously  affect 
both  wear  and  tear  and  friction. 

Any  attempt  to  determine  theoretically  the  amount  as  well  as  the  nature  of 
this  loss  would,  of  course,  be  impracticable. 

649.  The  work  of  Josef  Grossman,  Engineer  of  the  Austrian  Northwestern 
Railroad,  on  "  Lubricating  Materials  and  Metals  for  Bearings"  (Wiesbaden, 
1885),  treats  its  subject  with  a  good  deal  of  elaboration,  historically  and  ana- 
lytically, and  among  other  matters  discusses  quite  fully  the  question  of  train 
resistance,  although  not  always  with  correctness  and  good  judgment.  His 
results  indicate,  however,  that  the  axle-friction  is  at  any  rate  a  very  small 
element.  In  this  connection  he  cites  a  remarkable  result  of  some  Bavarian 
experiments,  in  which  by  greasing  the  rails  on  the  curve  of  100  metres  (337  ft.) 
radius  a  reduction  of  the  total  curve  resistances  of  q6  per  cent  was  attained:  61 
per  cent  of  the  total  resistance  due  to  the  curve  disappearing  when  the  inner 


:hap.  xiil— train  resistance— high  speed,      517 


^dge  of  the  head  of  the  outer  rail  was  greased,  and  31  per  cent  more  when  the 
other  rail  was  greased. 

The  striking  correspondence  of  these  experimental  results  with  those  de- 
duced theoretically  in  pars.  301-320  et  seq.  is  notable. 

THE   VELOCITY   RESISTANCES. 

650.  The  best  evidence  that  we  have  warrants  the  all  but  universal 
assumption  that  train  resistance  varies  as  the  square  of  the  velocity,  or 
that  its  equation  is  of  the  form 

R  =>»  +  c. 
This  is  still  merely  assumption,  not  only  as  respects  train  resistance  as 
a  whole,  but  as  respects  each  separate  constituent  element.  Air  resistance, 
for  example,  is  known  by  observations  on  projectiles  to  vary  more  nearly 
as  the  cube  of  the  velocity,  when  the  latter  is  very  great ;  but  at  all  ordi- 
nary velocities  it  appears  to  vary  very  nearly  as  the  square,  and  as  re- 
spects oscillatory  resistance,  we  know  absolutely  that  the  amount  of  de 
structive  work  (or  of  any  other  kind  of  work)  which  a  train  is  capable  of 
doing,  either  by  a  dead  or  glancing  blow,  is  directly  as  the  square  of  the 
velocity.  These  two  elements  constituting  together  the  ordinary  "  ve- 
locity resistance,"  it  is  but  natural  to  conclude  that  the  aggregate  also 
varies  as  the  square  of  the  velocity,  and  all  but  certain  that  it  does,  al- 
though it  may  very  easily  be  as  •^/^•^  or  7/^*S  or  even  v^-"^,  or  may  fluctuate 
between  these  powers  at  various  speeds  or  according  to  circumstances. 
There  have  been  various  formulae  put  forth,  and  some  of  them  on  very 
high  authority,  differing  widely  from  this  form,  some  of  them  giving  the 
velocity  resistance  directly  as  v,  and  others  (only  one  of  which  is  known 
to  the  writer)  as  v^,  but  both  of  these  assumptions  lead  to  absurd  results 
when  extended  to  very  high  speeds,  and  are  unquestionably  erroneous. 

651.  One  instance  of  the  former  (as  respects  the  train  behind  the  engine)  is 
given  in  par.  662.  On  the  other  hand,  a  formula  deduced  from  Bavarian  experi- 
ments in  1876,  on  a  large  and  costly  scale,  reported  by  the  late  Baron  von 
Weber  in  a  somewhat  informal  paper,*  led  to  the  most  absurd  results,  not 
necessary  to  detail  here. 

652.  As  a  rule,  no  attempt  is  made  in  train-resistance  formulae  to 
separate  the  aggregate  velocity  resistance  into  its  constituent  elements, 
although  in  some  cases  they  are  in  such  form  as  to  assert  or  imply  that 
the  velocity  resistance  is  either  all  oscillatory  or  all  atmospheric.  A 
formula  devised  by  Mr.  Wm.  H.  Searles,  which  has  been  adopted  as  the 

*  See  Railroad  Gazette,  June  ii,  25,  1880. 


5l8        CHAP,    XIII.— TRAIN  RESISTANCE— HIGH  SPEED. 

basis  for  the  computations  of  this  volume  as  having  a  truly  wonderful 
range  of  application  to  all  speeds,  conditions,  and  classes  of  trains,  even 
if  it  is  not  precisely  correct,  is  open  to  the  sole  serious  objection  (and 
that  chiefly  theoretical)  that  it  in  effect  assumes  all  velocity  resistance  ta 
be  oscillatory,  or  uniform  per  ton,  regardless  of  the  form  of  the  cars  (see 
pars.  657-8) ;  while,  on  the  other  hand,  formulae  proposed  by  Mr.  O. 
Chanute  (in  Haswell's  "  Pocket- Book ")  are  distinctly  based  on  the 
assumption  that  the  velocity  resistance  is  wholly  atmospheric.  Both 
of  these  assumptions  are  unquestionably  erroneous,  although  which  is 
most  so  must  remain  doubtful. 

653.  The  writer  has  conducted  the  only  tests  as  yet  made,  and  known 
to  him,  which  have  been  distinctly  directed  to  the  end  of  determining 
the  amoHut  of  each  element  of  train  resistance  separately,  and  owing  to 
the  delicacy  of  the  apparatus  by  which  they  were  made,  and  the  extreme 
care  used  in  computing  them,  he  believes  them  (with  perhaps  a  natural 
bias)  to  be  still  the  most  trustworthy  indication  in  that  respect.  These 
experiments  are  given  in  full  in  Appendix  A,  and  their  general  results  are 
shown  graphically  in  Fig.  163,  their  most  striking  feature  being  perhaps 
the  positive  evidence  that  atmospheric  resistance  is  at  least  a  less  pro- 
portion of  the  velocity  resistance  than  is  commonly  assumed,  and  that 
the  resistance  arising  from  oscillation  and  concussion,  whatever  its  exact 
cause  and  nature,  is  a  nraterially  more  important  element. 

654.  Nevertheless,  there  is  a  fact  tending  to  disprove  these  conclu- 
sions, viz.,  the  enormously  greater  indicated  power  of  locomotives  at 
high  speeds  than  that  transmitted  backward  to  the  train  as  determined 
by  a  dynamometer.  Table  164  gives  one  record  illustrating  this  fact — a 
test  trip  of  a  fast  express  train  on  the  New  York  Central  &  Hudson  River 
Railroad,  made  by  Mr.  P.  H.  Dudley,  in  which  it  will  be  seen  that  only 
some  55  per  cent  of  the  indicated  power  passed  back  of  the  dynamome- 
ter-car to  the  train  at  53  miles  per  hour.  Figs.  164,  165,  giving  the  re- 
sults of  some  elaborate  French  tests^  show  a  still  higher  proportion  of  en- 
gine-friction. Other  tests  of  the  kind  show,  according  to  the  speed,  from 
40  to  75  per  cent.  The  whole  subject  is  still  involved  in  much  obscurity 
and  doubt,  but  Figs.  164,  165  and  Table  165  will  illustrate  how  very  im- 
portant an  element  the  head  resistance  is  at  high  speeds. 

655.  According  to  the  best  evidences  which  the  writer  has 
been  able  to  secure,  the  ordinary  working  maximum  of  train  re- 
sistance, under  somewhat  adverse  conditions  as  respects  wind 
and  surfacing  of  track  and  rail,  may  be  considered  to  be  not  un- 


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D.  K.  Clark's  formula,  shown  hereon,  is  one  of  the  oldest  and  best  known  of  all  train-resistance  formute,  and  was  for  a  long  time  regarded  as  standard.     More 
modern  tests  indicate  that  it  is  far  too  high  at  low  speeds,  and  on  the  whole  somewhat  too  low  at  high  speeds,  although  the  latter  is  more  doubtful.     See  par.  655 


.zt. 


;:V8.0 


-^i\-<*.Cj *— 


CHAP.    Xlir.— TRAIN  RESISTANCE— HIGH   SPEED. 


519 


Table   164. 
Train  Resistance  of  Heavy  and  Fast  Passenger  Trains. 

Weight  of  Train. 

Engine  on  drivers 24.0 

"        on  truck 12.0 


Tons.   1 


Tender 

Three  day-coaches . . . 
Six  sleeping-coaches. 


65- 
185. 


250.0 
313.0 


Train  started  from  a 
state  of  rest.  Average 
speed  in  motion,  52  miles 
per  hour.  Slight  undu- 
lating grade  of  2  to  13 
ft.  per  mile,  the  effect 
of  which  is  corrected  be- 
low. 


Total  weight  of  train 

17  X  24  American  engine.    6  ft.  drivers,  135  lbs.  steam  pressure.      j 

[Deduced  from  records  of  dynamometer  tests  by  P.  H.  Dudley  on  New  York  Central  &  Hudson 
River  Railroad,  Kept.  Am.  Ry.  M.  M.  Assoc,  1882,  p.  132.] 


Aver- 
age 

Aver- 
age 
Speed. 

Vel.- 

Head 

(Table 

118). 

Wo;k 
repre- 
sented 

by 
Speed. 
Vert.  ft. 

Grade. 

Dyn. 
Work 

on 
Train. 
Vert.  ft. 

Do.  ± 
Effect 

of 
Grade. 
Vert.  ft. 

Do.  ± 

Effect 

of 
Speed. 
Vert.  ft. 

Aver- 
ages 
Vert.  ft. 
Per 
Mile. 

Equivalknt 
Resistance. 

Miles. 

Grade 
p.  c. 

Lbs. 
p.  ton. 

I 
2 

20.68 
38.31 

15 
52 

20 
10 

-I-15.20 
+36.90 

+  5-25 

48.23 
40.07 

48.23 
45-32 

33-03 
8.42 

3 
4 

43-90 
47-34 

68 
79 

42 
57 

+16.32 
+11. 15 

+  5-25 

35-53 
31.81 

40.78 
31-81 

24.46 
20.66 

20.72 

•393 

7.86 

% 

50.70 
49-31 
50.70 
52.89 

91 
86 
91 
99 

25 
32 
25 
3^ 

+11.68 
-  4-93 

—  13.0 
+18.0 
+13.0 

29-74 
30.57 
28.92 
26.44 

29.74 

17-57 
46.92 
39-44 

18.06 
22.50 
41.99 
31-38 

22.56 

•427 

8.56 

9 

10 
11 

53-70 
52.10 
52.89 

102 
96 
99 

t 

31 

+  3-07 
—  6.02 

4-  2.95 

+  8.0 

+  5.0 

23-13 

23-55 
23-55 

31-13 
28.55 
23-55 

28.06 

34-57 
20.60 

28.48 

-540 

10.80 

12 
13 
14 

52.10 
51.43 
51-43 
51-43 
51-43 

96 
93 
93 
93 
93 

36 
91 
91 
91 
91 

-  2.95 

-  2.45 

+  8.0 

25.61 
24.78 
25.61 
26.85 
26.60 

33 -61 
24.78 
25.61 
26.85 
26.60 

36-56 
27.23 
25.61 
26.85 
26.60 

27.74 

•527 

10.54 

17 
18 

19 

52.89 
52.89 
52.89 

99 
99 

99 

31 
31 
31 

+  5-40 

+  '6!o 
+  2.0 

27.68 
26.44 
26.44 

27.68 
32-44 
28.44 

22.28 
32.44 
28.44 

28.56 

-541 

10.82 

20 
21 
22 
23 

50.70 
49-31 
52.89 
53-70 

9'^ 
86 
99 
102 

25 
32 

38 

-  8.06 

-  4-93 
+  12.99 

+  3-07 

—  lO.O 

—  lO.O 

+10.0 

29.68 
28.92 
24.78 
24-37 

19.68 
18.92 
24.78 
34-37 

11.62 

13-99 
11.79 
31-30 

27.72 
17.18 

-525 
-337 

10.50 
6.74 

Mr.  Dudley  found  the  traction  in  starting  to  be  11,000  to  12,000  lbs.  for  the  first  100 
to  200  feet,  falling  to  2800  to  3000  lbs.  at  50  miles  per  hour.  The  consumption  of  steam 
and  water  per  mile  was  : 

At  135  lbs.  pressure,  300  to  333  lbs.  water, 
40  to    50  lbs.  coal. 
=  7.5  to  6.67  lbs.  water  per  lb.  coal. 
He  notes  that  Swiss  and  German  locomotives  carry  165  to  180  lbs.  as  a  rule ;  some- 
times as  high  as  225  lbs. 

The  total  horse-power  developed  by  the  engine  is  given  in  the  same  table  as  the 
dynamometer  record,  but  computed  and  not  observed.  The  computation,  however,  ap- 
pears to  be  one  based  on  Mr.  Dudley's  own  investigations.     It  shows  a  total  horse-power 


520        CHAP.   XIII.— TRAIN  RESISTANCE— HIGH  SPEED. 

developed  of  750  to  800  H.  P.-  and  taking  the  average  for  the  four  miles  13-16,  on  which 
the  grade  was  level  and  the  speed  uniform,  we  obtain  : 

Average  speed,  miles  per  Average  horse-power  expended  on— 

hour,  51.43.  Train.  Engine,  Total.  P.  c.  eng. 

340  426  766  55.61 

lbs.  lbs.  lbs. 

Equivalent  total  traction  resistance 2,479  3,106  5,585  (=  \  adhesion.) 

Ditto,  in  lbs.  per  ton     9.92  49-25  17.8 

This  is  considerably  lower  than  Table  166  indicates,  which  is  about  30  lbs.  per  ton; 
but  one  possible  explanation  of  this  discrepancy  is  that  Mr.  Dudley's  table  does  not  war- 
rant his  declaration  that  "at  50  miles  per  hour  the  traction  was  2800  to  3000  lbs.,"  but 
indicates  only  2500  lbs.  This  difference  alone  would  add  ij^  to  2  lbs.  per  ton  to  the 
resistance. 

Mr.  Dudley's  engine  and  head  resistance,  as  an  average  of  all  his  record  (not  all  given 
here),  amounts  per  engine  to  0.83  F^  lb.  The  writer's  tests  (see  Appendix  A  and  Fig. 
165)  give  a  somewhat  smaller  result  for  the  engine  resistances,  viz. : 

Lbs.  per  engine. 

For  head  resistance 0.28^2 

For  oscillation  and  concussion 0.35F8 

Total 0.63F2  +  4  to  8  lbs.  per  ton  constant. 

By  comparison  of  a  variety  of  evidences,  however,  the  writer  believes  that  0.83^2  lb. 
comes  very  close  to  giving  the  actual  total  velocity-resistance  of  the  engine  at  high  speeds, 
and  the  rapid  inroads  which  this  rate  makes  on  the  power  of  the  engine  is  shown  in 
Table  165. 

fairly  expressed  by  the  single  formula  of  Mr.  Wm.  H.  Searles 
just  referred  to  and  given  below.  For  the  more  favorable  con- 
ditions it  gives  unquestionably  far  too  high  resistance  ;  as  for 
example,  for  a  train  of  313  tons,  as  in  Table  164,  at  50  miles  per 
hour,  it  gives  a  tractive  resistance  of  30  lbs.  per  ton  for  the  en- 
tire train,  or  9390  lbs.  total  tractive  resistance,  equivalent  to  1280 
horse-power,  whereas  the  actual  horse-power,  as  given  beneath 
the  table,  was  less  than  800.  Further  evidences  to  the  same  ef- 
fect are  given  in  par.  659  et  seq.,  below  ;  but  the  ratios  of  the 
resistances  at  various  speeds  are  of  more  practical  importance 
than  their  absolute  amount,  and  these  will  not  be  affected  im- 
portantly by  any  reduction  in  the  latter.  Moreover,  nearly  all 
our  experimental  evidence  is  based  on  observations  taken  under 
the  most  favorable  conditions  for  low  resistance,  and  in  the  case 
of  European  tests  with  trains  of  much  smaller  cross-section  and 
with  cars  much  nearer  together.  The  bounding  rectangles  of  the 
average  American  and  European  passenger  cars  (a  fairer  basis  of 


CHAP.   XIII.— TRAIN  RESISTANCE— HIGH  SPEED.        $21 


Fig.  164.— Variation  in  Resistance  Per  Ton 
FOR  Various  Loads. 


.L-4 i U J.. 

20  30  40 

Mi  lesser  Hour. 


Engine  alone. 


50Tons  Load. 


Fig.  165.— Variation  in  Total  Traction  for 
Various  Loads, 


L -.i. 

iO  30 

Miles  per  Hour. 


French  Tests  of  Train  Resistance  at  Low  Velocities. 

[From  Annales  des  Fonts  et  Ckaussees,  May,  1886.  "  Etudes  Dynamometrique,"  par 
M,  Desdoint,  Ing,  de  la  Marine,  adjoint  a  I'lngenieur  en  Chef  du  Materiel  et  de  la  Trac- 
tion des  Chemins  de  Fer  de  I'Etat.] 


The  paper  showed  resistances  at  low  ordinary  speeds  of — 
Passenger  trains,  40^7^''  wheels,  3^  X  7"  axles,  4  tonnes  per  axle,  . 

Freight  "  "  "  5         "  **         • 


3-1 
3-2 


Lbs.  per  ton. 

.       .     -13.2' 

5         "  "         ....     -13.4 

^  •       •       •     1  3.0 

Temperature  of  axles  53.6"  Fahr. 

At  still  lower  velocities  of  5  ft.  per  second  (31^  miles  per  hour)  the  resistance  varied 
from  4.4  to  5.4  lbs.  per  ton,  this  being  in  fact  due  to  the  lower  journal  speed,  as  observed 
by  the  writer  in  his  tests  (par.  640  et  seq.  and  App.  A  and  B),  and  not  at  all  to  their  being 
"  valeurs  toutes  exagerees  comme  on  va  la  voir,"  as  suggested  in  M.  Desdoint's  paper. 

Trains  of  300  tonnes,  with  70-tonne,  4-coupled  engine,  showed  a  mean  resistance  of 
4.4  lbs.  per  ton. 


522        CHAP.   XIIL— TRAIN  RESISTANCE— HIGH  SPEED. 


Velocity  Resistances. 

The  following  grades  were  found  to  approximately  equalize  the  velocities  at  various 
speeds,  with  short  trains  : 

Miles  per  hour.  Grade  per  cent. 

o      to  i8i^  o  to  0.5 

185^  to  37  0.5  to  i.o 

37      to  50  1.0  to  1.5 

50     to  62  1.5  to  2.0 

See  also  par.  447. 


Equivalent,  lbs.  per  ton. 

10 

10  to  20 

20  to  30 

30  to  40 


comparison  than  the  precise  cross-section  area)  compare  about 
as  follows: 

American, 10  X  14  ft.  =  140  sq.  ft. 

European, 8  X  12  "     =     96     " 

656.  When  we  further  remember  that  the  car-bodies  of  Ameri- 
can cars  are  separated  by  over  six  feet  from  each  other  because 
of  the  platforms,  and  that  the  trucks  are  still  more  widely  sep- 
arated ;  and  when  we  remember  further  that  foreign  engines  have 
no  cabs,  and  a  smaller  cross-section  generally — the  foreign  evi- 


Table  165. 
Engine  Head-Resistance  at  High  Speed. 
[According  to  the  formula  ^  =  0.83  F'-f  (see  foot-note  to  preceding  table)  in  which  R  -. 
TOTAL  resistance  of  the  engine.] 


the 


Speed. 

Miles 

Per  Hour. 

Total  Head 

Resistance. 

Lbs. 

Horse- 
Power. 

Lbs. 

Per  Ton 

of  Train 

(313  Tons). 

.266 
1.06 
2.38 
4.25 
6.64 
9-58 
13-05 

lO 

83 
332 
747 
1328 
2075 
2988 
4067 

2.213 
17.71 
59-77 
141.67 
276.70 
478.20 
759-30 

20 

'XQ 

/1 0 

CO 

60 

70 

Since  the  resistance  in  pounds  increases  as  the  square  of  the  speed,  the  horse-power 
demanded  will  necessarily  increase  as  the  cube  of  the  speed.  It  takes  a  very  powerful 
engine  to  maintain  a  speed  of  70  miles  per  hour  on  a  level  for  any  distance,  and  no  engine 
can  do  it  long,  with  no  train  whatever  behind  it.  As  the  horse-power  corresponds  very 
correctly  to  the  conditions  at  this  maximum  speed  it  must  necessarily  correspond  very 
correctly  with  the  facts  at  the  lower  speeds.     See  end  of  par.  664. 


CHAP.    XIII.— TRAIN  RESISTANCE— HIGH  SPEED.        523 

dence  below  given  (par.  660  et  seq.)  seems  to  rather  support  than 
disprove  the  resistances  given  by  the  formulae  summarized  in 
Table  166  below,  although  nominally  smaller. 

657.  It  has  therefore  seemed  best  to  use  as  the  basis  for  all 
train-resistance  computations  in  this  volume  the  formula  above 
referred  to  (par.  652),  proposed  by  Mr.  Wm.  H.  Searles  in  his 
"  Field-Book,"  since  this  formula  in  a  single  simple  equation 
seems  to  approximate  very  closely  to  what  experiment  indicates 
to  be  an  ordinary  working  maximum  for  the  resistance  of  trains 
of  all  classes,  at  all  speeds,  and  with  all  forms  and  weight  of  cars. 
It  is  recommended,  with  justice,  by  Mr.  Searles  as  accomplisiiing 
this  end,  in  the  following  words: 

"  It  is  an  empirical  formula,  based  upon  a  careful  investigation  of  all 
such  records  of  experiments  on  the  subject,  several  hundred  in  number, 
as  have  come  under  the  author's  notice,  and  is  believed  to  give  results 
agreeing  closely  with  the  average  experience  and  practice  of  the  present 
day.  It  is  designed  to  give  the  resistances  per  ton  for  all  trains,  whether 
freight  or  passenger,  and  at  any  velocity,  under  ordinary  circumstances. 
Accidental  circumstances,  such  as  the  state  of  the  weather,  and  the  con- 
dition of  the  road-bed,  rails,  and  rolling-stock,  may  largely  modify  the  re- 
sistance, but  these,  of  course,  are  not  taken  account  of  in  the  formula." 

The  formula  (simplifying  its  form  somewhat)  is  as  follows 
for  velocities  in  miles  per  hour: 

Average  resistance  of  entire  train  in  lbs.  per  ton  of  2240  lbs.,  for 
all  weights  in  gross  tons, 
„  .        ^  T^2         I   -0006  V^  (wt.  ensf.  and  tender)' 

gross  wt.  of  train 
Average  resistance  of  entire  train  in   lbs.   per  net  ton,  for  all 
weights  in  net  tons, 
D         o     ^  jri  X   .0004783  F''(wt.  eng.  and  tender)2 

R—  4.82  +  .0015  3^7  F^H ^^^-^ ^ ^^ : '-  . 

^^^'         '  gross  wt.  of  tram 

This  formula,  with  a  comparison  of  others  below  it,  is  tabu- 
lated in  Table  166. 

658,  It  will  be  seen  that  this  formula  gives  the  same  result  whether 
a  given  weight  of  train  be  made  up  of  light  empty  box-cars,  weighing 
perhaps  9  tons  each,  or  loaded  coal  cars  weighing  three  or  four  times  as 
much  and  exposing  only  one  third  or  one  half  the  area  to  air  resistance; 


524       CHAP.   XIII.— TRAIN  RESISTANCE— HIGH  SPEED. 

Table  166. 

Train  Resistance  on  a  Level  as  Affected  by  Velocity. 

Giving  what  may  be  considered  as  the  ordinary  working  maximum,  as  computed  from  the 
general  formula  of  Wm.  H.  Searles,  coinciding  closely  with  the  apparent  indications 
of  the  most  recent  tests,  but  possibly  as  much  as  one  third  too  high  for  the  resistances 
at  high  speeds  under  favorable  conditions  (par.  655  et  seq.). 


Freight  Trains. 

Heavy 
Consolidation  Engine. 


Total  Weight 

OF  Tr.\in. 

Long 
Tons. 

Short 
Tons. 

70 
270 
470 

670 

78.4 
302.4 
526.4 
750-4 

870 
1070 
1570 
2070 

974-4 
1198.4 
1758.4 
2318.4 

Equation  of 

Resistance. 

Per  Short  Ton. 


Resistance  Per  Short  Ton,  for 
Velocities;  Miles  Per  Hour. 


10 


20        25 


30 


Engine  only 

"    and  10  loaded  cars. 


30 


4.82 


40 
50 
75 
100 


,0428/^2 
-t-  .ois-^V^ 
+  .0109F2 
4-  .00928^2 

+  .00837^2 

4-  .0078^2 
-1-  .00703^2 
+  .00653/^2 


9.10 
6.33 
5-91 

5-75 

5-66 
5.60 
5-52 
5-47 


14-47 
8.22 
7.17 
0.91 

6.70 
6.58 
6.40 
6.29 


21.94 
10.86 
9.18 
8.53 

8.17 
7-94 
7-63 
7-33 


31-59 
14.26 
11.53 
10.62 


10.05 

9.70 
9.21 
8.80 


43-34 
18.41 
14  63 
13-17 

12-35 
11.84 
II. 15 
10.70 


For  formula  of  resistances  for  trains  of  flat  cars,  subtract  about  .0012  from 
coefficient  of  V^.     For  resistances  and  formula  per  long  ton,  add  12  per  cent. 


Passenger  Trains. 

Total  Wt. 
OF  Train. 

Equation  of 

Resistance. 

Per  Short  Ton. 

Resistance  Per  Short  Ton  for 
Velocities;  Miles  Per  Hour. 

17  X  24 
Americ  nEngine. 

Long 
Tons. 

Short 
Tons. 

15 

20 

25 

30 

40 

50 

60 

70 

Engine  only 

"    and    2  cars. 

"  :'  4  r 

"      "      8     " 
"      "     12     " 
"      "     16     " 

50 
100 

150 
250 
350 
450 

56 
112 
168 
280 
392 
504 

4.82+  .03214F2 
"  +  .01875^2 

"  --  .0107^2 
"  +  .00918^2 
"  +  .00833  f^^ 

12.05 
9.04 
8.04 

r^ 

6.  JO 

17.68 
12.32 
10 -54 

i:« 

8.16 

24.91 
16.54 
13-75 
11.52 
10.56 
10.03 

33-75 
21.70 
17.68 
14.46 
13.09 
12.32 

56.25 
34.82 
27.69 
21.96 
19.51 
18.15 

85.18 
51.70 
40.53 
31.61 
27.78 
25.65 

120.54 
72.32 
56.25 
42.39 
37.88 
34.82 

162.32 
96.70 
74.82 
57-32 
49.82 
45-65 

For  resistances  and  formulae  per  long  ton,  add  12  per  cent. 
Weight  of  cars  taken  at  25  long  tons,  56,000  lbs.  each,  loaded. 

Any  of  the  formulae  compared  on  the  following  page  give  practically  identical  results, 
•except  that  Mr.  Chanute's  formulse  (extracted  from  the  new  edition  of  Haswell's  "Pocket- 
Book"),  although  correct  for  the  trains  probably  tested,  viz.:  passenger  trains  at  high 
velocities  and  freight  trains  at  low  velocities,  give  the  resistance  of  freight  trains  at  high 
velocities  at  only  }^  to  %  as  much  per  ton  as  passenger  trains. 


CHAP.   XIIL— TRAIN  RESISTANCE— HIGH  SPEED. 


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526        CHAP.   XIII.— TRAIN  RESISTANCE— HIGH  SPEED. 

in  othei:  words,  it  attaches  no  weight  whatever  to  atmospheric  resistance 
and  the  form  of  the  train.  The  writer's  experiments  (Fig.  163)  indicate 
positively  that  this  is  more  nearly  true  than  is  generally  suspected,  but  in 
going  to  such  an  extreme  the  formula  is  unquestionably  defective.  It 
would  seem  also  to  be  theoretically  defective — or  if  not  that,  certainly  to 
go  a  long  way  beyond  experimental  authority — in  multiplying  one  im- 
portant term  of  the  equation  by  the  square  of  the  weight  of  engine.  No 
theoretical  justification  for  this  is  apparent.  The  constant  for  rolling- 
friction,  4.8  lbs.  per  ton,  is  also  a  little  too  high  for  loaded  trains, 
although  fair  for  a  mean  between  loaded  and  empty. 

But  with  all  these  minor  imperfections  the  formula  is  certainly  one  of 
wonderfully  exact  application  to  a  wide  range  of  trains,  from  an  engine 
running  light  to  the  longest  freight  trains,  and  at  all  speeds.  The  writer 
maybe  overmuch  disposed  to  look  on  it  with  favor,  since,  as  examination 
of  Fig.  165,  Appendix  A,  and  Table  165  will  show,  it  could  hardly  agree 
better  with  all  the  conclusions  of  his  own  tests,  made  in  1879,  had  it  been 
based  on  them  alone;  yet  the  comparison  given  in  and  below  Table  166 
with  the  formulae  given  by  Mr.  O.  Chanute  in  Haswell's  "  Engineer's 
Pocket-Book"  shows  that  it  compares  equally  well  with  some  other 
modern  formulae.* 

A  variety  of  further  evidence  as  to  the  absolute  amount  of  train  re- 
sistance at  high  speed  is  given  below  : 

659.  The  tests  of  Mr.  J.  W.  Hill  on  an  American  freight  train  at  slow 
speeds,  given  in  Tables  146-7  and  Fig.  115,  check  very  closely  with  the  formula. 
Mr.  H  ill's  tests  were  on  a  freight  train  weighing  782. 94  tons  in  all,  with  an  engine 
and  tender  weighing  55.72  tons.  The  observed  and  computed  resistances  com- 
pare as  follows : 

Resistance  in  Lbs.  Per  Ton. 


ocity  in  Miles 
Per  Hour. 
17.23 

Observed. 
7.57 

Computed. 
6.97 

22.67 

7.27 

8.54 

23.00 

7.55 

8.66 

The  observed  resistances  should  be  reduced  5  to  10  per  cent  for  the  internal 
friction  of  the  locomotive.  They  indicate  that  the  formula  is  substantially  cor- 
rect at  slow  speeds,  but  increases  too  fast  with  speed. 

660.  Mr.  Stroudley's  tests  on  a  train  weighing  335.7  tons  of  2240  lbs.  gross, 

*  The  examples  of  the  application  of  these  formulae  to  various  trains  given 
in  the  above  "Pocket-Book"  contain  some  serious  errors  which  are  liable  to 
deceive. 


CHAP.    XIII.— TRAIN  RESISTANCE— HIGH  SPEED.        527 


with  an  engine  and  tender  weighing  60.05  tons  of  2240  lbs.  (Fig.  114)  should,  ac- 
cording to  Mr.  Searle's  formula,  have  had  the  following  resistance: 
R  —  l.^-^  .012445^2 

For  40  miles  per  hour  this  gives  25.3  lbs.  per  ton,  which  amounts  to  gc6 
horse-power,  whereas  the  average  horse-power  is  recorded  as  only  529  horse- 
power, and  the  maximum  shown  by  any  diagram  was  668;  but  then  the  draw- 
bar traction  on  the  same  train  is  given  as  an  average  of  4477  lbs.,  which  at  ihe 
average  speed  of  44.3  miles  per  hour  foots  up  528  horse-power  (13.36  lbs.  aver- 
age traction)  transmitted  through  the  draw-bar  to  the  train  alone,  excluding  all 
engine  and  head  resistance.  If  the  latter  bore  anything  like  the  ratio  to  the 
car  resistance  that  it  does  in  Fig.  165,  the  total  resistance  should  have  been 
fully  up  to  what  Mr.  Searle's  formula  gives. 

661.  The  Engineer  {K^xW  4,  1884)  states  it  to  be  a  figure  "accepted  by  lo- 
comotive superintendents,"  that  with  a  total  train-load  of  336  long  tons  the  train 
resistance  at  60  miles  per  hour  is  40  lbs.  per  ton,  which  corresponds  closely  to 
Table  131. 

662,  In  a  French  paper  on  the  subject  of  train  resistance  and  economy  of 
grades*  we  have  the  following  formulae  given, which  appear  to  have  been  deduced 
from  very  carefully  made  tests  : 

"  The  resistance  of  an  engine  and  tender  is  given  by  the  formula 

3-5^    ,    iVx^ 


^  ^^     1000  ~    \20  ) 


in  which 

E  =  Indicated  tractive  force  in  kilogrammes, 

R  =  Resistance  per  tonne  in  kilogrammes, 

V  =  Velocity  in  kilometres  per  hour. 

"  For  the  train  hauled  we  have 

V 
R  =  24-  --." 
^  40 

For  a  speed  of  80  kilos,  per  hour,  which  is  very  nearly  50  miles  per  hour, 

and  calling  2  lbs.  per  ton  =  i  kilo,  per  tonne,  as  it  is  almost  exactly,  we  have 

from  this  formula  for  the  train  tested  by  Mr.  Dudley  (Tables  146-7)  : 

Per  Ton.  Total. 

For  engine  resistance 60  lbs.  3, 780  lbs. 

For  train  resistance 8    "  2,000    " 

Total  (for  313  tons) 18.5  lbs.         5,780  lbs. 

*  "Notice  sur  les  Prix  de  Revient  de  la  Traction,  et  sur  les  Economies  reali- 
s6es  par  I'Application  de  Diverses  Modifications  aux  Machines  Locomotives. 
Par  M.  Ricour,  Ingenieur  en  Chef  des  Ponts  et  Chaussees,"  Annales  des  P.  et 
C,  Sept.,  1885. 


528        CHAP.   XIII.— TRAIN  RESISTANCE— HIGH  SPEED. 

This  corresponds  very  closely  to  what  we  have  just  deduced  (Table  164)' 
from  Mr.  Dudley's  tests. 

663.  Another  French  formula,  based  on  the  experiments  referred  to  beneath 
Figs.  164-165,  gives  still  lower  results,  indicating,  at  50  miles  per  hour, 

For  engine,  tender,  and  rear  car 31.0  lbs.  per  ton. 

For  interposed  cars 7.1   "  " 

It  is  stated  in  the  same  paper  that  at  about  18.6  miles  per  hour  the  resist- 
ance is  double,  and  at  31  miles  per  hour  triple,  what  it  is  at  6  to  9  miles,  and 
that  "at  still  higher  velocities  the  increase  is  rapid."  This  is  far  from  true 
for  American  rolling-stock,  and  probably  for  any  other,  up  to  30  or  40  miles 
per  hour,  and  the  exact  figures  given  may  be  rejected  as  untenable,  except  that 
they  may  serve  as  cumulative  evidence  that  the  resistances  at  high  speeds  are 
not  so  great  as  many  formulae,  including  those  of  Table  166,  give  them,  at  least 
for  European  trains  under  favorable  conditions. 

664.  A  test  was  made  in  1884,  upon  the  Bound  Brook  route,  between  Phila- 
delphia and  New  York,  to  ascertain  the  difference  in  the  consumption  of  coal 
between  an  express  train  running  on  schedule  time  and  the  same  train  run  at 
a  very  low  speed,  but  otherwise  under  the  same  conditions,  the  same  five  cars 
and  precisely  similar  engines  being  used.  The  trains  ran  in  each  case  from 
Philadelphia  to  Bound  Brook  and  back,  a  distance  of  119  miles.  The  slow  trip 
was  made  in  9  hours  and  23  minutes,  4420  lbs.  of  coal  being  consumed.  The 
train  stopped  at  the  same  places  as  the  regular  express  trains,  the  only  unusual 
feature  of  the  trip  being  the  funereal  pace,  averaging  a  little  over  \2\  miles  an 
hour. 

The  performances  compared  as  follows  : 

Speed.  Coal  burned. 

Slow  trip 12^  m.  per  h.     4,420  lbs. 

Fast  trip 50±  "     "  6,725   " 

Difference. . .     37^  m.  per  h.     2,305  lbs.  =  34.2  per  cent  saved. 

The  engine  and  tender  weighed  75  tons,  and  the  five  cars  126  tons. 

According  to  D.  K.  Clark's  formula,  R  = \-  8  (for  gross  tons),  the  com- 
parative resistances  at  these  speeds  should  have  been  about  31  to  \'i\  lbs.,  or 
more  than  double,  and  this  gives  a  much  less  rapid  increase  with  speed  than 
most  modern  formula.  (See  Fig.  163.)  By  Table  166  the  difference  should 
have  been  more  than  three  to  one.  This  appears  to  indicate  very  low  velocity 
resistances.  Coal  consumption,  however,  is  but  a  very  vague  guide  to  train  re- 
sistance, it  being  quite  certain  that  the  power  is  developed  more  economically 
at  the  higher  speeds.  Still  this  test  certainly  tends  to  show  that  the  resistances 
due  to  speed  are  not  as  great  as  supposed,  as  do  also  the  facts  presented  be- 
neath, Table  164,  Figs.  164,  165,  and  the  tests  already  referred  to  (par.  444)  as 


CHAP.   XIII.— TRAIN  RESISTANCE— HIGH  SPEED. 


529 


made  on  the  Lake  Shore  &  Michigan  Southern  Railvsray  ( Transactions  Am.  Soc. 
C.  E.,  Oct.,  1876,  p.  344,  "  Experiments  and  Tests,"  by  P.  H.  Dudley),  in  which 
tests  the  conclusions  reached  were  expressed  as  follows  : 

"  We  found  that,  with  the  long  and  heavy  trains  of  650  to  700  tons  it  re- 
quired less  fuel  with  the  same  engine  (Mogul)  to  run  trains  at  18  to  20  miles 
per  hour  than  it  did  at  10  or  12  miles  per  hour.  The  engine  at  the  highest 
rate  of  speed,  seems  to  produce  its  power  more  economically." 


Table  167. 

Speed  of  the  Fastest  Trains  in  England  and  America. 

[From  Mr.  E.  B.  Dorsey's  paper  on  "  English  and  American  Railroads  Compared,"  Trans. 
American  Soc.  C.  E.,  1885-6.] 

English  Railways. 


Line. 

Termini. 

Miles. 

Time, 

including 

Stops. 

Average 

Speed, 

incl.  Stops. 

London  &N.  W  .  ... 

London  to  Liverpool 

"          Glasgow 

"          Edinburgh  . . . 

Holyhead 

"          Glasgow 

«'          York 

201.75 

406 

401 

264 

444 

188.25 

397 

216 

118.5 

50 

76.5 
125 

h.    m. 

4    30 

10      CO 

9    55 
6    40 
10    20 

3     55 
9    00 
6    00 
2    36 
I    05 

1  47 

2  30 

44.8 
40.6 

«(             (( 

u                   u 

39-6 

Great  Northern 

u 

48.1 

u 

"          Edinburgh... 

"          Swansea 

"          Bristol 

"          Brighton 

"         Dover 

"          Nottingham  . . 

Great  Western 

36 
45-6 
46.15 
42.6 

London,  Br.  &  S.  Coast 

London,  Ch.  &  D 

Midland 

A  merica  n  Ra  ilways . 


N.  Y.,  N.  H.&H. 
Pennsylvania 


N.  Y.  Central  &  H.  R. 


Central  of  New  Jersey. 
Baltimore  &.  Ohio 


New  York  to  Boston 
Jersey  City  to  Phila. , 

"  Pittsburg 

"  Chicago. 

New  York  to  Albany  . . 

"  Buffalo.. 

"  Chicago. 

Jersey  City  to  Phila 

Baltimore  to  Washington 


443 
911 

143 
441 
980 
90 
40 


II 

45 

25 

15 

3 

30 

11 

00 

25 

30 

39 

44.9 

37-7 

36.1 

40.9 

40.1 

38.4 

45 

53-33 


These  runs  are  in  every  case/rom  te?'miftus  tc  terminus^  which  makes  a  difference  of 
5  to  8  miles  an  hour  from  the  speed  obtained  by  selecting  only  the  most  favorable  parts 
of  the  run.     See  summary  on  following  page. 
34 


530        CHAP.    XIII.— TRAIN  RESISTANCE— HIGH  SPEED. 

The  aggregates  of  the  preceding  tables  compare  as  follows : 

12  English  trains,  averaging  240%  miles  run  at  43.33  miles  per  hour. 
9  American     "  "  374/^      "  "     41.71     "  " 

Or,  omitting  the  two  long  runs  of  over  900  miles  from  Chicago  to  New  York : 
7  American  trains,  averaging  214  miles  run  at  42.90  miles  per  hour. 

While  this  table  correctly  indicates  that  the  fastest  trains  in  England  and  America 
make  substantially  the  same  time,  the  average  speed  of  all  trains  is  undoubtedly  consider- 
ably higher  in  England,  owing  chiefly  to  the  fact  that  there  are  almost  no  grade  crossings 
or  highway  crossings,  and  in  part  to  the  shorter  runs,  which  always  justify  and  require 
higher  speed  for  equal  convenience. 


665.  According  to  Table  165,  the  difference  in  the  horsei-power  demanded 
to  overcome  the  engine  resistances  only  in  the  Bound  Brook  test  just  mentioned 
would  have  been: 

Trip.  Time  X  Horse-power.        "Hour  Horse-powers." 

Slow,     ....     9.4  hours  X      5  H.  P         =47 
Fast,     ....     2.4  hours  X  271.7  H.  P.    =  652 

Total  difference  in  head  resistance,     .     .     .    605 

2305 


The  total  difference  in  coal  consumption  being  2305  lbs.,  we  have 


605 

3.62  lbs.  as  the  coal  burned  per  horse-power  per  hour,  without  making  any 
allowance  for  the  increased  car  resistance  due  to  speed  on  the  one  hand,  or  for 
the  greater  economy  with  which  steam  is  used  at  high  speed  on  the  other  hand. 
As  3.62  lbs.  is  about  a  fair  rate  of  coal  consumption  under  the  circumstances 
(rather  high),  these  two  latter  may  have  approximately  balanced  each  other. 

666.  Table  167  shows  the  fastest  regular  trains  in  England  and  America, 
every  train  on  the  list  probably  reaching  a  speed  of  60  miles  per  hour  on  short 
stretches  of  almost  every  run.  The  fastest  trains  do  not  haul  over  125  tons  to 
train,  but  even  then  they  could  not  probably  make  the  time  they  do  if  the 
resistances  were  quite  as  high  as  in  Table  166.  When  all  proper  allowances 
are  made,  however,  the  facts  do  not  necessarily  imply  any  materially  lower 
resistance. 

ENGINE-FRICTION. 

667.  In  computing  train  resistance  it  is  not  essential  to  assume  any 
different  rolling-friction  for  the  engine  than  for  the  cars.  The  tender- 
friction  should  of  course  be  the  same,  and  the  engine-truck  friction  sub- 
stantially the  same,  while  for  the  driving-wheel  base  we  have  only  to 


CHAP.   XIII.— TRAIN  RESISTANCE— ENGINE. 


531 


consider  the  rolling-friction  between  wheel  and  rail  only,  and  not  the 
journal-frictio7i,  since  the  latter  does  not  tax  the  adhesion  (par.  608). 
The  same  is  true  of  all  the  internal  machinery-friction  of  every  nature 
and  kind  ;  so  that,  as  we  have  plenty  of  steam-power  in  freight  service,  or 
can  have  by  reducing  the  speed,  and  only  lack  tractive  force  in  pounds, 
the  machinery  and  driving-journal  friction  is  of  slight  importance  for 
freight  service,  whether  much  or  little.  For  passenger  service  it  may  be 
of  more  importance,  and  it  will  at  least  be  profitable  to  summarize  the 
evidence  as  to  its  amount. 

668.  The  locomotive  is  a  simple  machine,  and  the  evidence  does  not 
make  it  probable  that  more  than  5  to  8  per  cent  of  its  indicated  power 
fails  to  reach  the  periphery  of  the  drivers.  Ten  per  cent  is  often  allowed. 
In  complicated  low-pressure  compound  engines  the  machinery-friction  is 
10  to  15  per  cent.  In  small  stationary  engines  (Table  168)  the  loss 
ranges  from  12  to  20  per  cent. 

In  16x24  American  locomotives,  the  tests  of  John  W.  Hill  (Tables 
146-7)  show  that  some  13  lbs.  per  ton  of  locomotive  and  tender  was  act- 
ually required  to  propel  it  without  load  at  speeds  of  17  to  23  miles  per 


Table  168. 
Estimated  Cost  of  Power  and  Efficiency  of  Stationary  Engines. 

[Abstracted  from  a  careful  and  detailed  paper  by  Charles  E.  Emery,  Ph.D.,  M.  Am.  So.  C.  E., 
Trans.  Am.  So,  C.  E.,  November,  1883.] 


H.P. 

Kind. 

Cost  in 
Mass. 

1874. 

Loss 
per 
cent  by 
Fric- 
tion. 

Indi- 
cated 
H.  P. 

Feed- 
Water, 

I  H^  P. 

Coal 
L  H.V. 

Evap. 
per  lb. 
Coal. 

Cost 

309 
days. 

5 

Portable  Upright 

$645 

20 

6.25 

42 

5.60 

7-5 

$176.46 

10 

"               "       

988 

20 

12.50 

38 

5-IO 

7 

5 

109.96 

15 

'*               "       

1,487 

18 

18.29 

36 

4.80 

7 

5 

90.14 

20 

"         Horizontal... 

1,981 

15 

23-53 

34 

4-25 

8 

73.28 

25 

"                   " 

2,441 

14 

29.07 

32 

4.00 

8 

67.28 

50 

Stationary  Non-cond'g. 

5,331 

12 

56.82 

27 

3-27 

8 

25 

52.15 

100 

Condensing  Single 

9,207 

II 

112.36 

23 

2.61 

8 

8 

36.02 

200 

li                         u 

16,785 

10 

220.99 

22.2 

2.52 

8 

8 

28.64 

300 

"             '••      . 

23,899 

9-5 

331-49 

22.2 

2.52 

8 

8 

26.82 

400 

((               (( 

29,958 

9-5 

441.99 

22.2 

2.52 

8 

8 

26.01 

500 



36,220 

9-5 

552.49 

22.2 

2.52 

8 

8 

25.66 

This  table  is  carried  out  in  the  paper  in  much  more  detail,  but  the  above  are  the  most 
important  data. 


532  CHAP.   XIII,— TRAIN  RESISTANCE— ENGINE. 

hour,  whereas  the  average  resistance  of  the  train  behind  it,  at  the  same 
speeds,  was  only  some  6f  lbs.  per  ton.  Assuming  that,  owing  to  the 
greater  weight  on  the  locomotive  drivers,  the  rolling-friction  proper,  be- 
tween rail  and  wheel,  was  at  least  as  much  as  the  rolling  and  axle  fric- 
tion combined  of  the  train  behind  it,  we  may  divide  up  this  i8  lbs.  ap- 
proximately as  follows : 

Lbs.  Per  Ton.    I'otal  Lbs. 

Taxing  adhesio7i :  Rolling-friction, 7  392 

"  Head  and  oscillatory  resistance,     .     .  2  112 

Not  taxing  adhesion  :  Friction  of  engine  running  light,  4  224 

"  "  Assumed  addition  due  to  load,     .  5  280 

Total 18  •  1,008 

Actual  average  tractive  pull  (nearly  \  load  on  drivers),     .     .     .      6,250 
Maximum  tractive  pull  in  ordinary  work  (i  weight  on  drivers),    11,200 

This  would  indicate  that  when  the  engine  is  working  fairly  hard  the 
internal  friction  consumes  about  9  per  cent  of  the  indicated  power,  but  it 
is  almost  certainly  too  high.  When  an  engine  is  working  light  and  run- 
ning fast  a  much  larger  proportion  of  the  energy  developed,  up  to 
nearly  \,  would  appear  to  be  used  up  by  internal  friction,  and  no  doubt 
is — a  waste  well  worthy  of  attention,  but  not  of  that  ruinously  injurious 
character  that  an  equal  tax  on  the  adhesion  would  be. 

669.  The  friction  of  the  slide-valve  is  one  of  the  chief  sources  of  loss 

by  machinery-friction;  but  by  the  rapid  introduction  of  "balanced  "  slide-valves, 

or  those  which  have  the  pressure  excluded  or  counteracted  on  the  top  side  of 

the  slide-valve,  this  loss  is  being  largely  eliminated.     The  slide-valve  exposes  an 

area  of  from  70  to  100  sq.  in.,  averaging  perhaps  90  sq.  in.,  to  the  steam-pres-^ 

sure  in  the  steam-chest,  which  may  be  taken  to  average  at  least  100  lbs.  per  sq. 

in.,  giving  some  9000  lbs.  pressure.     With  good  lubrication  this  pressure  would 

create  no  great  amount  of  friction,  but  with  the  imperfect  lubrication  which 

alone  is  possible,  it  is  far  more  serious.     The  coefficient  is  probably  in   the 

neighborhood  of  o.i  to  0.2  in  ordinary  working,  causing  a  resistance  to  motion, 

in  both  steam-chests,  of  900  to  1800  lbs.     With  5-in.  travel  of  valve  and  50-in. 

drivers  the  slide-valve  travels  about  y^g-  as  far  as  the  engine,  which  would  make 

,  .    ,               .     ,             goo  to  1800  ,,         .  . 

this  loss  equivalent  to  ~ =  say,  55  to  no  lbs.  of  tractive  resistance, 

amounting  to  something  like  i  per  cent  of  the  ordinary  work  done,  which  in 
starting  is  no  doubt  often  much  more. 

Direct  experiments  on  the  Boston  &  Albany  road  gave  a  resistance  to 
motion  of  2100  lbs.  in  starting  under  the  worst  conditions — full  stroke  with 
throttle  wide  open;  while  with  the  Richardson  balanced  slide-valve,  which  is 
one  of  the  most  approved,  325  lbs.  sufficed.     When  once  in  motion  it  is  prob- 


CHAP.    XIIL  — TRAIN  RESISTANCE— ENGINE.  533 

able  that  the  contrast  is  much  less  striking,  but  the  saving  in  wear  as  well  as 
resistance  is  so  great  that  balanced  slide-valves  promise  to  be  soon  practically 
universal. 

670.  Otherwise  than  this  it  is  difficult  to  account  for  any  great  loss  by  fric- 
tion at  any  one  part  of  the  machinery.  Therefore,  since  no  difficulty  is  found 
in  obtaining  correspondingly  favorable  results  with  stationary  engines  of  equal 
power  and  more  complication,  we  may  conclude  with  some  certainty  that  5  to  8 
per  cent  of  the  indicated  power  represents  the  full  extent  of  the  loss  by  ma- 
chinery-friction proper,  in  ordinary  cases. 

671.  Tests  at  the  works  of  Messrs.  Schneider  &  Co.,  Creusot,  reported  by 
Mr.  M.  F.  Delafield  in  a  notable  paper  published  in  the  Annales  des  Mines  (and 
most  other  scientific  journals  of  the  world),  1885,  made  on  a  22  X  44  in.  Corliss 
engine,  which  could  be  worked  either  condensing  or  non-condensing,  gave  the 
following  relation  of  indicated  and  effective  power: 

Condensing  engines,  effective  H.  P.  =  .902  I.  H.  P.  —  16 
Non-condensing  "  "  "       =  .945  I.  H.  P.  —  12 

This,  however,  is  not  known  to  apply  correctly  to  other  than  engines  ap- 
proximately similar  to  that  tested,  which  developed  140  to  250  H.  P.  with  about 
60  revolutions  per  minute,  according  as  it  was  condensing  or  non-condensing. 

672.  Tests  purporting  to  give  very  high  or  low  engine  friction  must  be 
looked  on  with  extreme  scepticism.  There  is  especial  danger  of  error  in  inter- 
preting the  apparent  results  of  such  tests  Thus,  tests  of  an  apparently  very 
accurate  character  by  the  Locomotive  Superintendent  of  the  Eastern  Railway 
of  France*  show  that  of  the  total  indicated  horse-power  only  42.5  and  41.6  per 
cent  was  delivered  to  the  draw-bar,  in  two  successive  tests,  out  of  which  it  was 
assumed  that  34.2  and  35.6  per  cent  was  consumed  by  the  bare  friction  of  the 
engine  mechanism,  after  deducing  the  assumed  resistance  of  the  engine  and 
tender  considered  as  vehicles.  The  error  lay  in  an  insufficient  allowance  for 
the  latter,  and  especially  in  an  insufficient  allowance  for  head  resistance,  which 
at  high  passenger  speeds,  such  as  that  of  the  tests,  consumes  a  large  part  of  the 
power. 

673.  An  investigation  by  the  writer  given  in  par.  128  shows  that  20  lbs.  X 
6:5  lbs.  per  car  gives  the  ordinary  consumption  in  passenger  service;  indicat- 
ing a  very  small  loss  by  internal  friction. 

674.  To  get  at  the  collective  resistance  of  the  bearings  of  a  locomotive 
under  steam,  and  to  separate  it  into  its  constituent  elements.  Messrs.  Vuillemin, 
Guebhard,  and  Dieudonne  made  some  experiments,  narrated  in  a  work  by  Josef 
Grossmann,f  showing  the  following  results: 


*  Eiigineenng  and  Engineer,  18S5. 

f  "  Die  Schmiermittel  und  Lagermetalle  fiir  Locomotiven,  Eisenbahnwagen, 
Schiffsmachinen,  etc."  Von  Josef  Grossmann,  Ingenieur  der  osterreichischen 
Nordwestbahn.     Wiesbaden,  C.  W.  Kreidels'  Verlag,  1885. 


534  CHAP.    XIIL— TRAIN  RESISTANCE— ENGINE. 

, Pounds  Per  Net  Ton. , 

Non-coupled  4-coupled  6-coupled 

pass,  engines.  engines.  engines. 

Total  resistance  per  ton  of  locomotive 16.0  25.2  3044 

Resistance  of  cold  engine  (connecting-rod 

removed) 6.0  10.44  12.30 

Percentage  of  latter  to  total  resistance 37-5  P-  c.  41-5  P-  c.     40-5  P-  c. 

These  figures  are  for  speeds  of  17  to  21  miles  per  hour. 

If  now  the  collective  resistance  of  the  axle  and  parallel-rod  bearings  and  of 
the  valve-gear  be  deducted  from  the  resistance  of  the  cold  engine,  as  above 
given,  the  remainder  ought  to  give  the  resistance  due  to  rolling-friction;  and  if 
this  be  deducted  from  the  total  resistance  of  the  above  table,  the  remainder 
should  be,  approximately,  the  total  resistance  of  all  bearings  in  the  engine  at 
work. 

The  axle-friction  coefficient  was  assumed  at  0.009  ^"^^  the  proportion  of  the 
diameter  of  axle-journal  to  that  of  the  wheels  at  yij  giving  for  the  axle-friction 
li  lbs.  per  ton  weight  of  engine.  The  friction  of  the  valve-gear  of  the  cold 
engine  was  taken  as  i  lb.  per  ton  of  engine,  and  the  crank-pin  friction  for  four- 
coupled  engines  at  0.2  lb.  and  for  six-coupled  engines  at  0.4  lb.  per  engine  ton. 
Adding  together  these  resistances,  and  deducting  them  from  the  resistances 
of  the  cold  engines  without  connecting-rods,  the  following  table  was  obtained. 

, Pounds  Per  Net  Ton. > 

Non-coupled  4-coupled  6-coupled 

pass,  engines.  engines.  engines. 

Total  resistances  per  ton  of  locomotive,  as 

above     . t6.o  25.2  30.44 

Resistance  of  rolling-friction  per  ton  of  lo- 
comotive          3.50  7.74  9.40 

Percentage  of  last  to  the  total 21.87  30.71P.C.     30.88p.c.. 

Resistance  of  oiled  parts  (in  steam)  per  ton 

of  locomotive 12.50  17.46  21.04 

Percentage  of  last  to  the  total 78.13  69.29  p.  c.     69. 12  p.  c. 

These  figures  were  assumed  to  show  how  large  a  portion  of  the  engine  re- 
sistances those  of  the  oiled  parts  constitute,  which  do  not  tax  adhesion. 

The  experimental  evidence  as  to  the  comparative  rolling  and  internal  fric- 
tion of  coupled  and  uncoupled  engines  is  interesting  and  possibly  correct,  but 
the  exact  figures  given,  as  with  all  such  single  statements,  must  be  received 
with  much  allowance. 

With  regard  to  the  increased  amounts  of  rolling  friction  indicated  for  four- 
and  six-coupled  engines,  the  author  reasonably  remarks  that  it  is  in  accordance 
with  what  might  be  expected,  since  the  coupled  wheels,  on  account  of  their 
slight  difference  of  form  and  of  imperfections  in  the  track,  cannot  roll  as  per- 
fectly as  the  uncoupled  ones,  and  must  slip  more  or  less. 


CHAP,   XIII.—  TRAIN  RESISTANCE— ENGINE.  535 


675.  The  following  record  of  some  other  French  tests  gives  very  different 
results  :  * 

For  determining  engine  resistance,  the  locomotive  to  be  tested  was  set  in 
motion  at  4  or  5  miles  per  hour,  and  change  of  velocity  determined  by  accurate 
apparatus,  from  which  the  following  resistances  were  computed: 

, Pounds  Per  Ton  of  Resistance. — ; ; — > 

Passenger  engine,       Locomotive  for  mixed      Freight  engine, 

3  axles,  2-coupled,    service,  3-coupled  axles,    4-coupled  axles, 

78-in.  drivers,  59-in.  drivers,  50-in.  drivers, 

52  tonnes.  48  tonnes,  70  tonnes. 

Engine  in  working  order. ..  6.4  7.2  8.0 
Eccentrics  and  connecting- 
rod  disconnected. 4.7                              4.5                           6.2 

Difference   1.7  2.7  1.8 

Coupling-rods  also  discon- 
nected   4.7  4-4  6.2 

In  all  these  tests  the  effect  of  disconnecting  the  coupling-rods  is  inappreci- 
able. The  tender  resistance  was  found  to  be  only  5.0  to  5.6  lbs.  per  ton.  All 
the  above  are  the  mean  of  a  number  of  tests,  not  differing  greatly  in  result. 
The  following  are  from  still  larger  averages: 

, Resistance  in  Pounds  Per  Ton. » 

Drivers.       No.  axles     Coned  tread.  Cylindrical  tread. 

coii.pled.  Link-  Link-  Walchaert's 

motion.  motion.  valve-gear. 

Passenger  engine..         78"  2  6.2  ..  5.2 

Mixed  engine 59"  3  7.2  7.2 

Freight  engine ..         51^"  3  9.4 

Freight  engine 50"  4  ...  ...  8.2 

The  tests  measured  the  resistances  between  velocities  of  2-^  to  5  miles  per 

hour.       The   resistances   include   machinery-friction,  and   the    very  low  speed 

would  tend  to  make  the  resistances  considerably  higher  than  at  working  speeds, 

notwithstanding  which  fact  it  would  appear  as  if  the  results  must  certainly  be 

too  low. 

*  "  Application de  la  Methode  rationale  aux  Etudes  dynamom6triques.  Par 
M.  Desdouits,  Ingenieur  de  la  Marine,  adjoint  a  I'lngenieur  en  Chef  du  Materiel 
et  de  la  Traction  des  Chemins  de  Fer  de  I'Etat,"  Annales  des  Fonts  et  Chausse'es, 
Mai,  1886. 


53^      CHAP.   XIV.— EFFECT  OF  GRADES  ON   TRAIN-LOAD. 


CHAPTER   XIV. 

THE    EFFECT    OF    GRADES    ON    TRAIN-LOAD. 

676.  The  absolute  effect  of  gradients  to  increase  the  load  on  the  engine 
is  constant  and  easily  determined.  Under  the  theory  of  the  inclined 
plane  (or  rather  under  the  general  theory  of  the  equilibrium  of  forces) 
any  body  W,  Fig.  167,  resting  on  such  an  inclined  plane,  is  acted  on  by  at 


Fig.  167. 


least  two  forces  :  the  force  of  gravity,  vertically  downward  ;  and  the  re- 
action of  the  supporting  plane  s,  acting  at  right  angles  thereto. 

Since  a  body  acted  on  by  two  forces  only  cannot  remain  at  rest  (see 
any  treatise  on  mechanics)  unless  the  forces  are  (i)  equal  in  magnitude, 
(2)  opposite  in  direction  to  each  other,  and  (3)  lie  in  the  same  right  line, 
motion  must  ensue  under  these  conditions  down  the  plane  s ;  and  the  force 
/  necessary  to  resist  motion  (or  impelling  the  body  down  the  plane,  if  equi- 
librium be  not  maintained)  is  represented  by  the  length  of  any  line  t,  which 
will  suffice  to  close  the  triangle  of  forces.  The  direction  of  this  force  is 
ordinarily  fixed  by  the  conditions,  and  in  the  case  we  are  now  considering 
it  must  lie  parallel  with  the  plane  s,  as  represented  in  the  cut ;  but  a  force 


CHAP.    XIV.— EFFECT  OF  GRADES  ON   TRAIN-LOAD.      537 

acting  in  any  other  direction,  as  ft".  Fig.  168,  will  suffice  for  the  same 
end,  provided  it  will  form  with  the  forces  g  and  w' , 
Fig.  167,  a  closed  triangle ;  the  magnitude  only  of  the 
force  /  required  varying  thereby. 

677.  If  the  body  W,  Fig.  167,  be  an  angular  body,  this 
necessary  force  t  will  be  supplied  by  the  friction  of  con- 
tact between  the  body  and  the  plane,  and  the  body  will 
remain  at  rest  until  the  angle  becomes  very  considerable, 
as  in  sliding  a  brick  down  a  board.  If  the  body  be  a 
wheeled  vehicle,  the  journal  and  other  rolling-friction 
subserves  the  same  purpose,  so  far  as  it  goes,  as  respects 
motion  down  the  plane ;  but  since  the  rolling-friction  is 
a  very  small  portion  of  the  total  weight  of  the  body,  the  angle  of  the 
slope  on  which  the  rolling-friction  alone  will  suffice  to  maintain  equi- 
librium must  be  very  small.  When  it  does  not  suffice  for  this  purpose, 
the  body  is  impelled  down  the  plane  by  the  difference  between  the  force  t 
of  gravity  and  the  retarding  force  of  friction. 

When  a  body  is  caused  to  move  up  the  plane  it  is  obvious  that  the 
resisting  friction,  whether  much  or  little,  plays  no  part  in  reducing  the 
force  /,  tending  to  cause  the  body  to  move  down  the  plane  ;  for  in  that 
case  the  two  forces  resisting  motion  coincide  with  each  other  in  direction, 
and  their  sum  instead  of  their  difference  has  to  be  overcome  by  the  im- 
pelling force,  whatever  it  may  be. 

678.  These  are  the  conditions  under  which  the  locomotive  acts  in 
hauling  a  train  up  a  grade ;  and  in  Fig.  167,  if  ^  be  made  to  represent  the 
weight  of  any  vehicle  W  or  of  all  the  vehicles,  W  will  represent  the 
force  with  which  they  press  against  the  rails ;  t,  the  "grade  resistance"  or 

force  impelling  them    downward,   or   resisting    motion  upward ;  — ,  the 

,     ,            ,           .                      1-1         2000/        2240^^  ,. 

ratio  of  the  grade  resistance  to  the  weight ;  or ,  according 

to  the  number  of  pounds  in  the  ton,  the  grade  resistance  in  pounds  per  ton, 

21/ 

— ,  the  ratio  of  the  reaction  ag^ainst  the  rails  to  the  actual  weight  of  the 

body,  which  is  given  numerically,  for  various  grades,  in  Table  119. 

679.  All  grades  are,  in  the  technical  work  of  American  and  Continen- 
tal engineers,  expressed  in  the  rate  percent,  although  in  common  American 
practice  the  words  "  per  cent"  are  (somewhat  unfortunately)  omitted,  the 
grades  being  known  as  a  0.5,  0.8,  or  i.o  grade.  A  grade  so  expressed  is 
independent  of  the  particular  unit  of  measure  employed,  whether  feet, 


538      CHAP.    XIV.— EFFECT  OF  GRADES  ON   TRAIN-LOAD. 

metres,  miles,  or  any  other.  In  popular  American  and  English  language 
grades  are  expressed  by  feet  per  mile,  which  (since  there  are  5280  feet  in 
a  mile)  is  52.8  times  the  rate  per  cent.  The  use  of  this  awkward  unit,, 
especially  among  engineers,  is  in  every  way  to  be  regretted.  English 
engineers  are  also  much  given  to  a  still  more  awkward  habit — expressing 
grades  as  rising  "  i  in  80,"  or  some  other  horizontal  distance.  (See  par. 
683.)  These  may  be  turned  into  grades  per  cent  with  a  table  of  recipro- 
cals.    In  Fig.  167  the  rate  of  grade  is  given  by  — .       If    we  let  ^=  100 

(whether  feet  or  any  other  unit),  then  r  will  give,  in  the  same  unit,  the 
rate  per  cent  of  the  grade. 

680.  Since  gravity,^,  in  the  diagram  of  forces  in  Fig.  167,  is  repre- 
sented by  the  hypothenuse  of  a  right-angled  triangle,  it  follows  that  the 
pressure  of  the  wheels  on  the  rails,  W,  can  never  be  quite  equal  to  the 
weight  of  the  body.  The  loss,  however,  is  not  on  any  ordinary  grade  a 
serious  or  even  an  appreciable  one.     It  may  be  determined  as  follows : 

Ratio  of  pressure  on  rails  to  real  weight  —  (Fig.  167)  =  — ;  but  s  =  ^d'^-\-h^y. 

exactly.     Or,  approximately  (i), 

id 
whence  (2),  s=^  —-  ■\-  d. 

681.  This  latter  is  determined  by  a  rule  of  great  convenience,  which  is  too 
little  known,  and  which  the  student  will  do  well  to  fix  indelibly  in  his  memory, 
for  the  multitudinous  uses  of  which  it  is  capable,  viz.  : 

To  SOLVE  A  RIGHT-ANGLED  TRIANGLE  OF  SMALL  ALTITUDE  :    Square  the  height 

or  rise  and  divide  by  twice  the  base  or  hypothenuse  (whichever  is  known).  The 
quotient  will  be  the  difference  between  the  base  and  hypothenuse,  whence 
the  unknown  side  is  obtained  from  the  known  by  direct  addition  or  subtrac- 
tion. Frequently,  however,  in  solving  such  triangles  the  difference  only  is 
required. 

Examples  showing  the  range  of  error  in  this  rule  are  given  in  Table  168^. 
The  extreme  examples  of  the  latter  part  of  the  table  are  intended  only  for  illus- 
trative purposes,  but  show  that  even  in  such  an  extreme  case  as  the  "3,  4,  and 
5  triangle"  the  error  is  only  -^  or  2|  per  cent.  For  a  multitude  of  engineering 
computations,  where  the  altitude  of  the  triangle  is  below  \  the  base,  the  formula 
is  sufficiently  approximate  for  all  purposes,  the  error  with  base  4  and  altitude 
I  being  less  than  half  of  one  per  cent  and  varying  as  the  square  of  the  alti- 
tude. 


CHAP.    XIV.— EFFECT  OF  GRADES  ON   TRAIN-LOAD.      539 


Table  168^. 

Examples  showing  Range  of  Error   in  the  Approximate   Formula    of 
Par.  681  for  Solving  Right-angled  Triangles. 


Given— 

Hypothenuse. 

Error 
Per  Cent. 

Base, 

Height. 

By  Approxi- 
mate Rule. 

Exact. 

10 

I 

10.05 

10.049 

O.OI 

10 

2 

10.2 

10.198 

0.02 

10 

4 

10.8 

10.770 

0.03 

10 

5 

11.25 

II. 180 

0.07 

10 

6 

II. 8 

11.662 

0.12 

10 

8 

13.2 

12.806 

0.39 

10 

10 

I5-0 

14.142 

0.86 

4 

3 

5^ 

5- 

^ 

(hyp.) 

(base.) 

5 

3 

4^ 

4- 

i^ 

All  these  examples  are  far  beyond  the  range  of  the  highest  rates  of  grade.     For 
pies  of  the  latter,  see  Table  119,  page  341. 


682.  Comparing  the  two  similar  triangles,  drs  and  W'tg,  Fig.  167,. 
we  have,  since  r'.dwt'.  W, 

^  _  W'r 

W  being,  as  we  have  seen,  not  the  true  weight  or  gravity  of  the  body, 
but  the  component  thereof  at  right  angles  to  the  plane,  or  the  force  with 
which  it  presses  against  the  plane. 

On  any  grade  practicable  for  locomotives,  however,  W  and  g  are 
practically  equal  to  each  other,  the  difference  even  on  a  10  per  cent 
grade  being  only  one  half  of  i  per  cent,  and  on  a  i  per  cent  grade  (52.8 
feet  per  mile)  only  -^  as  much,  or  gJ^  of  i  per  cent.  Therefore  it  is 
universally  customary  to  consider  that  for  all  practical  purposes  r'.dwt '.g, 
Fig.  167,  whence 

^~~d 
with  sufficient  exactness,  and  we  have  the  rule  already  given  in  par.  382 : 
The  rati  of  grade  in  ft.  per  100  =  the  grade  resistance  in  lbs.  per  100  lbs., 
whence,  evfdently, 


(=' 


540      CHAP.    XIV.— EFFECT  OF  GRADES  ON   TRAIN-LOAD. 

The  grade  resistance  in  lbs.  per  ton  =  the  rate  of  grade  pef 
cent  X  20,  OR  =  2  lbs.  per  o.i  per  cent. 

This  last  formula  should  likewise  be  indelibly  engraven  on  the  memory 
of  the  engineers  having  to  do  with  railway  work,  making  reference  to  a 
table  needless. 

683.  The  grade  resistance  in  lbs.  per  ton  on  a  grade  given  in  feet  per  mile 

grade  in  feet  per  mile\ 

smce  the  rate  per  cent  =  ■ ^r 1 

^  52.80  / 

srrade  in  feet  per  mile  grade  in  feet  per  mile 

equal  to  the  2 —^ X  20  =  2 -^l . 

^  52.80  2.64 

Or,  since  — 7-  —  0.3788,  we  have — 
2.04 

Grade  resistance  in  lbs.  per  ton  =  grade  in  ft.  per  mile  X  0.3788  =  grade  in 

ft.  per  mile  -v-  2.64. 

For  the  long  ton  of  2240  lbs.  we  obtain,  in  the  same  way, 

Grade  resistance  in  lbs.  per  ton  =:  grade  in  ft.  per  mile  X  .4242. 

For  a  grade  expressed  in  a  horizontal  distance  for  a  rise  of  i,  as  i  in  80,  i  in  100, 

or  I  in  d,  the  total  grade   resistance  is  — -,  ■ — -,  or  —  of  the  weight  ;  or  in  lbs. 
*  80   100         d 

2000        224.0 

per  ton, or  — - — ,  for  the  short  and  long  ton  respectively.    This  method  of 

d  d 

expressing  grades  is  used  nowhere  in  the  world  but  by  English  engineers,  and 
has  nothing  to  commend  it. 

684.  From  the  preceding  it  follows  that  the  effect  of  grades  UPON 
the  grade  resistance  is  directly  as  the  rate  of  grade.  On  a  grade  of 
i.o  per  cent,  the  grade  resistance  is  just  twice  as  much  as  on  a  grade  of 
0.5  ;  and  by  whatever  percentage  the  rate  of  grade  be  reduced  the  grade 
resistance  will  be  reduced  as  much. 

To  determine  the  effect  of  the  grade  resistance  ON  THE  power  of 
engines,  the  rolling-friction,  a  constant  element  per  ton  on  both  grades 
and  levels,  must  first  be  considered,  in  addition  to  the  grade  resistance. 

685.  Assuming,  for  reasons  already  stated  (par.  623),  that  the  rolling- 
friction  at  ordinary  freight  speeds  of,  say,  15  miles  per  hour  is  8  lbs.  per 
ton  (=0.4  per  cent  grade),  which  is  a  high  resistance  to  assume,  and 
much  higher  than  the  ordinary  resistance  of  the  train  behind  the  engine 
only,  the  total  train  resistance,  and  hence  gross  weight  of  trains  on  any 
two  rates  of  grade,  will  be  as  the  rate  of  grade  per  cent  +  0.4,  or  as 

^  +  0.4 
^'+0.4- 

On  grades  of  0.5  and  i.o  per  cent,  adding  0.4  to  each,  we  have  0.9 and 
1.4  as  the  equivalent  gradient  in  each  case,  including  the  rolling-friction. 


CHAP.   XIV.— EFFECT  OF  GRADES  ON   TRAIN-LOAD.      54 1 

The  gross  weight  of  trains  on  these  grades,  consequently,  will  be  as  0.9: 
1.4  or  I  to  1.556,  and  not  as  0.5  :  i.o  or  i  to  2.00. 

With  grades  of  0.3  and  0.6  per  cent,  we  have  for  the  comparative 
gross  weight  of  trains  0.7:  i.o  or  i  to  1.43,  instead  of  i  to  2.00.  With 
grades  of  1.0  and  2.0  per  cent  we  have,  similarly,  1.4  :  2.4,  or  i  to  1.714  for 
the  comparative  gross  weight ;  whereas  in  this,  as  in  the  two  form^er  ex- 
amples, the  grade  resistance  only  is  as  i  to  2. 

686.  It  will  be  seen  from  these  examples  that  as  the  grades  are  higher 
the  comparative  gross  weight  of  trains  comes  nearer  and  nearer  to  the 
ratio  of  the  grade  resistance  only,  as  is  but  natural,  since  the  rolling-fric- 
tion becomes  a  less  and  less  important  fraction  of  the  total  resistance. 
Thus,  in  grades  of  2.00  and  3.00  per  cent,  the  comparative  gross  loads  are 
as  2.4  :  3.4  or  2  :  2.833.  But  on  the  lower  gradients  this  is  far  from  being 
the  case. 

687.  So  far,  we  have  considered  only  the  gross  weight  of  train,  in- 
cluding engine ;  but  it  is  apparent  that  the  true  measure  of  the  cost  of 
gradients  is  their  effect  upon  the  net  or  revenue-earning  load 
of  cars  and  freight,  and  the  ratio  of  the  net  loads  on  any  two  gradients 
depends  upon  an  additional  variable,  viz.,  the  ratio  of  the  gross  weight 
of  engine  and  tender  (or  rather,  of  engine,  tender,  and  caboose)  to  the  trac- 
tive power  of  the  engine.  Whatever  the  absolute  weight  of  the  engine,  if 
its  ratio  to  the  tractive  power  be  the  same,  the  ratio  of  the  net  loads  will 
be  the  same  on  any  two  given  grades,  whether  the  engine  be  light  or 
heavy. 

For  the  gross  weight  of  train  on  any  given  grade  is  directly  as  the 
tractive  power,  and  if  the  ratio  of  the  weight  of  engine  to  the  tractive 
power  be  the  same,  the  resulting  net  loads,  as  well  as  gross  loads,  will  be 
to  each  other  directly  as  the  tractive  power. 

688.  The  ratio  of  the  tractive  power  to  the  total  weight  of  engine  is 
not  a  constant,  but  varies,  yfrj-/,  with  the  pattern  of  engine,  and,  secondly y 
with  the  ratio  of  adhesion,  which  is  itself  a  variable  quantity  ;  but  assum- 
ing the  constant  ratio  of  adhesion  of  ONE  fourth,  which  we  have  seen 
(par.  530)  to  be  that  justified  by  ordinary  American  experience,  the  ratio 
is  readily  determined  for  any  pattern  of  engine,  and  will  be  seen  from 
the  following  Table  169  to  vary  from  i  to  10^  to  i  to  4,  according  to  the 
pattern  of  engine,  the  ratio  for  the  more  usual  patterns  of  freight  engines 
being  about  i  to  7. 

In  the  former  edition  of  this  treatise  it  was  assumed  as  i  to  10,  the  average 
ratio  of  adhesion  being  taken  at  \,  but  conditions  have  greatly  changed  since 
then  (1872-6). 


542      CHAP.   XIV.— EFFECT  OF  GRADES  ON  TRAIN-LOAD. 


Table  169. 
Ratio  of  Weight  of  Engine  and  Tender  to  the  Tractive  Power,  for 

Various  Types  of  Engines, 
As  assumed  in  the  headings  of  Table   170,  substantially  in  accordance  with  the  data  of 

Tables  127-131. 


Kind  of  Engine. 

Tractive  Power. 

(J4  Weight  on 

Drivers.) 

Total  Weight 

of  Engine  and 

Tender 

in  Service. 

Ratio  of  Weight 
to  Tractive  Power, 

Light  Americati 

tons. 
5 
6 

7 

8 

9 
10 
II 
12 

13 

tons. 
52 
58 
60 

64 

67 
70 

75 
80 

87 

trac.  power  =  i.o. 
10.4 
9.67 

8.57 

Average  American 

L/ight  Ten-wheel   

Average  Ten-wheel 

Ticrht  Mogul     

8.0 

Average  Mogul 

7-44 
7.0 
6  82 

Light  Consolidation 

Average         "            , 

St'nd(i887)   "            

6.67 
6.69 

Heavy  Mastodon 

Tank  Consolidation 

TankSwitch-engine  (all  weight 
on  drivers) 



about  4.50 
4.00 

If  any  one  of  these  constant  ratios  be  subtracted  from  the  fourth  column  of  the  long 
Table  170,  it  will  give  a  column  of  ratios  of  net  loads  to  tractive  power  which,  when 
multiplied  by  the  tractive  power  of  any  engine  whatever  of  the  same  proportion  of  weight 
on  drivers  to  total  weight,  will  give  its  hauling  power. 

689.  From  the  preceding  it  u^ill  be  clear  that  if  we  know  merel}^  the 
RATIO  of  the  net  load  to  the  tractive  power  we  can  determine  by  what 
per  cent  a  given  increase  or  decrease  of  grade  will  modify  the  necessary 
tractive  power,  without  determining  the  absolute  amount  of  either  the 
one  or  the  other,  and  this  method  was  followed  in  the  first  edition  of  this 
treatise.  It  obliges  us  to  assume,  however,  that  this  ratio  is  constant  ;  and 
as  it  is  commonly  the  case  that  with  every  considerable  variation  in  the 
weight  of  engine  the  ratio  of  its  power  to  its  weight  will  also  vary,  it  is  prac- 
tically much  better  to  study  the  effect  of  gradients,  and  of  the  changes 
therein,  directly  from  a  table  showing  the  tons  of  net  load,  exclusive  of 
engine,  tender,  and  caboose,  which  various  patterns  of  engine  can  handle 
on  various  grades.  Such  a  table  is  given  in  the  following  long  Table  170, 
in  which  the  net  load  in  tons  for  nine  different  patterns  of  engines,  varying 
from  light  American  to  the  heaviest  Mastodon  engines,  is  shown  for  every 
0.02  per  cent  of  grade  up  to  4.0  per  cent,  and  from  that  to  10  per  cent  at 
wider  intervals. 


CHAP.    XIV.-^EFFECT  OF  GRADES  ON   TRAIN-LOAD.      543 

690.  Table  170  is  computed  under  the  following  assumptions  : 

Rolling-friction, 8  lbs.  per  ton. 

Adhesion  or  tractive  power ^  weight  on  drivers. 

Weight  of  tender  (about  two-thirds  loaded),  as  noted 

in  the  heading  to  the  table, 21  to  25  tons. 

It  gives  also,  in  addition  to  the  grade  per  cent,  the  corresponding 
grade  in  feet  per  mile,  the  resistance  in  pounds  per  ton  on  each  grade  due 
to  gravity  only,  and  to  gravity  and  rolling-friction  (8  lbs.)  combined,  and 
the  ratio  of  the  gross  load  to  the  tractive  power,  or 

2000 
total  resistance  in  lbs.  per  ton* 
This  ratio  x  tons  of  tractive  power  of  each  engine  (=  \  weight  on 
drivers)  =  gross  weight  of  train  in  tons  which  the  engine  can  haul.  Sub- 
tracting from  it  the  total  weight  of  each  engine,  as  given  in  the  first  line 
of  each  heading,  we  have  the  net  load  of  train  in  tons,  as  given  in  the 
nine  columns  which  constitute  the  body  of  the  table. 

691.  This  Table  170  we  shall  make  the  basis  of  our  ensuing  study  of 
the  effect  of  gradients  on  net  loads.  Experience  has  clearly  shown  that 
only  by  the  aid  of  such  tables  or  by  diagrams  can  the  effect  of  gradients 
be  comprehended,  since  the  number  of  variables  entering  into  such  a 
table  is  so  great  that  formulae  become  very  intricate  in  form,  and  carry  no 
impression  to  the  mind.  The  weight  of  the  caboose  at  the  rear  of  the 
train,  which  is  practically  only  another  tender,  and  almost  universally  used, 
might  well  have  been  included  as  a  part  of  the  gross  weight  of  the  engine 
and  tender  in  Table  170;  but  there  are  two  styles  of  caboose  in  use, 
4-wheel  and  8-wheel,  differing  considerably  in  weight,  and  for  other  rea- 
sons it  seemed  better  not  to  include  it. 

692.  In  Table  138  a  variety  of  records  of  actual  performances  of  en- 
gines has  already  been  given,  which  justify  the  claim  made  at  the 
head  of  Table  170,  that  it  represents  the  fair  working  capacities  of  the 
various  engines  on  the  given  grades  in  good  American  practice.     The 

CAUTIONS  AT  THE  HEAD  AND  FOOT  OF  THE  TABLE  MUST  BE  FULLY 

REMEMBERED,  however,  that  the  grades  must  be  the  de-facto  or  virtual 
grades,  not  increased  in  effect  by  unreduced  curvature  or  by  stops  on  or 
near  the  grade,  nor  decreased  in  effect  by  the  assistance  of  momentum 
(see  par.  41$  et  at.),  either  of  which  contingencies  may  make  the  nominal 
grades  of  the  profile  anything  but  the  true  governing  gradients.  Fig. 
169  with  its  accompanying  note  will  serve  better  than  Table  170,  perhaps, 
to  make  the  effect  of  grades  on  train-load  clear  to  the  eye. 


544      CHAP.   XIV.— EFFECT  OF  GRADES  ON  TRAIN-LOAD. 


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CHAP.    XIV.— EFFECT  OF  GRADES  ON   TRAIN-LOAD.      553 


Notes  to  Fig.  169. 

Regarding  the  bottom  of  the  page  as  the  base-line  of  the  diagram,  or  axis  of  x,  as  ex- 
plained beneath  the  title  to  it : 

1.  The  lower  heavy  line  represents  the  progressive  increase  of  train-load  (behind  ten- 
der) as  the  grade  is  reduced,  for  the  lightest  A7nerican  engine  given  in  Table  170,  which 
begins  at  o  at  a  grade  of  480  ft.  per  mile,  and  ends  at  1198  tons  on  a  level,  just  beyond  the 
limits  of  the  diagram, 

2.  The  tipper  heavy  line^  marked  A,  represents  the  same  thing  for  the  heaviest  Mas- 
todon engifte  given  in  Table  170,  so  nearly  that  it  is  not  in  error  by  more  than  its  own 
width  at  any  point.  It  was  not  plotted  for  that  purpose,  however,  but  was  one  of  the 
lines  of  the  original  diagram,  as  below,  made  blacker  to  correspond  with  line  i. 

Similar  lines  for  all  the  other  nine  engines  whose  tractive  capacities  are  given  in  Table 
170  would  fall  between  these  two  Hnes  at  approximately  regular  intervals.  It  has  not 
seemed  necessary  to  plot  them. 

The  remaining  lines  of  the  diagram  give  the  cylinder  and  adhesion  tractive  powers  sep- 
arately for  the  three  different  engines  below  detailed,  as  computed  by  Mr.  G.  W.  CUSH- 
ING,  Supt.  M.  P.  No.  Pac.  Ry.,  on  the  following  assumptions  : 

Rolli7ig-friction,  6}4  lbs.  per  ton  in  place  of  8  lbs.  per  ton,  as  in  this  volume. 

Ratio  0/ adhesion,  >4,  as  in  this  volume. 

The  difference  in  the  rolling-friction  makes  the  train-loads  somewhat  greater  than 
those  given  in  Table  170,  especially  as  a  level  is  approached,  but  makes  no  great  differ- 
ence on  the  higher  grades.     The  three  engines  are  as  follows  : 


Cylin- 
ders. 

Drivers. 

Trac.  Pr. 
in  Lbs., 
Per  Lb.  of 
Effective 
Pressure. 

No. 
Drivers. 

Weights. 

Engine, 

On 
Drivers. 

Total       Tender, 
Eng-ine.      Loaded. 

Total. 

.  A 
B 

c 

22" X  26" 
22" X  26" 
20" X  24" 

49" 
49" 
49" 

256.8 
256.8 
196 

8 
10 

8 

100,000 
110,000 

96,000 

112,000 
112,000 
108,000 

65,000 
65,000 
65,000 

177,000 
177,000 
173,000 

The  lines  marked  A,  B,  C  indicate  the  loads  corresponding  to  the  adhesion  tractive 
power  of  these  three  engines,  computed  on  the  basis  of  one  fourth  the  weight  on  drivers. 

The  remaining  lines  indicate  the  cylinder  tractive  powers  for  the  same  engines  at 
various  points  of  cut-offs,  as  follows  : 

Engine  C,  2o"x24",  Consolidation,  48  tons  on  drivers.  At  half-stroke  the  cylinder 
power  is  somewhat  less  than  the  adhesion,  and  at  70  per  cent  very  slightly  over.  Only  at 
very  slow  speed  can  such  an  engine  furnish  steam  for  running  at  70  per  cent  cut-off. 

Efigine  A,  22"  x  26",  Consolidation,  50  tons  on  drivers,  or  5  tons  less  than  B,  but  iden- 
tical in  cylinder  capacity,  showing  that  the  latter  is  in  excess. 

Engifie  B,  22"  x  26",  Mastodon,  55  tons  on  drivers.  The  two  lines  for  cylinder  tractive 
power  apply  alike  to  engines  A  and  B. .  In  both  of  these  engines  the  cyhnder  power  is 
much  greater  in  proportion  than  in  engine  C,  and  cannot  be  fully  utilized  at  one  fourth 
adhesion.     As  the  working  adhesion  on  a  good  rail  often  rises  much  higher  than  one  fourth  ' 


554      CHAP.    XIV.— EFFECT  OF  GRADES  GN   TRAIN-LOAD. 

THE   PERCENTAGE   OF   CHANGE   IN   THE   NET    LOAD   RESULTING   FROM   A 
CHANGE   IN   THE   RATE   OF   ANY   GRADE. 

693.  Assuming  Table  170  as  a  basis,  we  can  readily  determine 
from  it,  in  the  manner  below  outlined,  the  two  following  laws, 
which  are  the  foundation  for  a  correct  estimate  of  the  value  of 
reducing  grade: 

First.  Whe7i  the  rate  of  any  otie  given  ruling  grade  is  increased  or 
decreased,  the  corresponding  percentage  of  increase  or  decrease  in  the 
engine-tnileage  required  to  handle  any  given  tonnage  varies  ahnost  di- 
rectly as  the  change  in  rate  of  grade,  however  much  or  little  the  change 
may  be,  slightly  iiicr easing,  however,  as  the  increase  is  greater  and  de- 
creasing as  the  decrease  is  greater. 

For  example,  if  a  0.6  per  cent  grade  be  increased  to  0.8  the  increase  in  en- 
gine-tonnage required  is,  for  Consolidation  engines,  J^^  —  21,73  per  cent  in- 
crease, or  10.9  per  cent  per  o.i  per  cent  of  grade  ;  but  if  it  be  increased  to  1.5 
percent,  the  increase  is  ^Vt"  =  i03-37  per  cent  increase,  or  11.48  per  cent  per 
0.1  per  cent  of  grade  ;  being  about  5i  per  cent  more  per  o.i  per  cent  of  grade 
than  for  the  smaller  increase. 

If  the  entire  weight  of  the  engine  be  on  the  drivers,  or  if  only 
the  load  on  the  drivers  be  considered,  the  engine,  and  the  re- 
mainder a  part  of  the  train,  this  law  is  exact,  and  the  engine-ton- 
nage varies  precisely  with  the  change  in  rate  of  grade,  as  may 
be  seen  in  Table  172. 

Second.    The  amount  of  this  percentage  of  increase  or  decrease  in 


however,  this  surplus  cylinder  power  is  likely  to  be  very  useful  in  handling  heavy  trains 
easily,  and  indicates  that  engine  B  at  least  is  better  designed  than  engine  0  for  the  most 
efficient  freight  service. 

W/m-e  and  why  tajik  engines  are  advantageous  may  be  very  clearly  seen  from  this 
diagram  as  follows : 

Referring  to  the  head-hnes  to  Table  170,  it  will  be  seen  that  the  total  weight  of  the 
Hghtest  American  engine  and  the  weight  on  drivers  of  the  heaviest  Mastodon  are  the 
same,  52  tons.  A  tank  engine  of  the  same  total  weight,  all  of  it  on  drivers,  while  it  will 
be  a  much  lighter  and  cheaper  machine  than  the  Mastodon,  and  be  equal  to  much  lower 
speeds  only,  will  have  a  greater  net  tractive  power  on  all  grades  by  the  constant  amount 
of  35  tons  (saved  in  dispensing  with  a  tender  and  leading  truck).  Therefore,  plotting  on 
Fig.  169  a  Hne  for  35  tons  greater  loads  than  for  the  upper  heavy  black  line,  we  find  that 
on  the  higher  grades  it  makes  an  enormous  difference  in  the  percentage  of  net  load 
hauled,  but  as  the  lower  grades,  below  2  per  cent  (106  ft.  per  mile),  are  reached  the  two 
lines  become  almost  coincident. 


CHAP.    XIV— EFFECT  OF  GRADES   ON   TRAIN-LOAD.      555 

the  engifie-tonnage  required  varies  cofisiderably  with  each  grade^  being 
nearly  five  times  as  i?iuch  07i  a  level  as  on  a  3  per  ce7it  grade  j  and  is 
about  as  given  in  the  following  Table  171,  where  these  percentages 
are  given  for  all  grades,  determined  in  a  manner  we  will  shortly 
review. 

964.  These  two  facts  being  definitely  ascertained,  we  have,  in 
order  to  determine  the  effect  of  any  change  of  grade  upon  the 
engine-mileage  required  to  handle  a  fixed  tonnage,  simply  to 
multiply  the  percentage  given  in  Table  171  (which  see)  by  the 
nun\b&v  oi  tenths  per  cent  change  of  grade  to  obtain  the  total  in- 
crease in  engine-mileage  which  will  be  required  for  any  given 
change  of  grade  ;  or,  the  same  fact  may  be  still  better  deter- 
mined directly  from  the  actual  load  on  each  grade,  given  in 
Table  170.  This  percentage,  multiplied  by  the  proportion  of  the 
expenses  which  varies  with  the  number  of  trains  or  engine-ton- 
nage (the  car-mileage  and  traffic  remaining  constant),  i.e.,  by  the 
portion  of  the  expenses  which  would  be  doubled  if  the  engine- 
tonnage  were  doubled,  will  give  the  annual  cost  of  a  proposed 
increase  of  grade,  or  the  annual  saving  of  a  proposed  decrease. 

695.  Table  171  (see  p.  556)  is  determined  from  Table  170  in  the  fol- 
lowing simple  manner : 

Taking  only  three  types  of  engines,  the  lightest  "  American,"  heaviest 
Consolidation,  and  a  tank  engine  of  the  same  weight  on  drivers  as  the 
latter,  but  with  no  tender  nor  truck,  and  comparing  the  net  loads  given 
for  grades  of  Level,  0.5,  i.o,  1.5,  and  2.0  per  cent,  we  have  the  following 
net  loads  hauled  : 

Light  American,  .    .     . 
St'nd  Consolidation, 
Heavy  Tank  Engine,     . 

Then  it  is  evident  that,  whatever  the  total  tonnage  to  be  moved,  the 
percentage  of  increase  in  the  engine-mileage  required  to  move  it  will  be,, 
with  a  1.5  per  cent  instead  of  i.o  per  cent  ruling  grade, 

American.  Consolidation.  Tank. 

i^^^.^6,  ^7^  =  1.408,  z^^  =  ..357. 

211  ^^  552    —  ^  632    —  ^-J^/' 

times  that  required  on  a  i  per  cent  grade,  or 

44.55  per  cent,  40.8  per  cent,  35.7  per  cent. 


Grades  of 

Level. 

0.5. 

I.O. 

1.5. 

2.0. 

1 198 

504 

305 

211 

156 

2920 

1253 

777 

552 

420 

3000 

1333 

857 

632 

500 

55^      CHAP.   XIV.— EFFECT  OF  GRADES  ON   TRAIN-LOAD. 


Table  171. 
Percentage  of  Increase  (or  Decrease)  in  the  Engine-Mileage  required 

WHICH   RESULTS   FROM    ANY    CHANGE   IN   THE    RaTE   OF   ANY    GrADE. 
[Deduced  from  the  long-  Table  170  in  the  manner  explained  in  Table  172.] 


INCREASE  Per  Cent  in  E 

NGINE- 

Grade 

DECREASE  Per  Cent  in  Engine-      | 

Mileage 

Per  0.1  of  Change 

in  Grade 

to  be 

Mileage 

Per   0.1  of  Change 

in  Grade 

RESULTING  FROM  A  TOTAL  ChANGE  OF— 

Changed 

resulting  from  a  Total  Change  of— 

79.2 

52  8 

26.4 

5.28   -j 

Ft.  Per 

Mile. 

[    5.28 

26.4                 £ 

2.8 

79.2 

+  1.5 

+  1.0 

+  0.5 

+  0.1 

Per  cent. 

-  0.1 

-0.5 

1.0 

-  1.5 

28 

68 

27 

62 

26.64 

25-9 

Level. 

23 

16 

22 

30 

21.46 

20.9 

.10 

20.6 

1 

19 

43 

18 

73 

18.02 

17-5 

.20 

17-3 

16 

80 

16 

15 

15-54 

I5-I 

.30 

14.9 

... 

■ 

... 

14 

84 

14 

25 

13-72 

13-3 

.40 

13-1 

... 

13 

30 

12 

76 

12.26 

II. 9 

.50 

II. 8 

11.42 

... 

12 

05 

II 

58 

II. 16 

10.8 

.60 

10.6 

10.36 

• 

... 

II 

05 

10 

60 

10.22 

9.8 

.70 

9-7 

9.48 

10 

24 

9 

81 

9.44 

9.2 

.80 

9.0 

8-74 

■ 

... 

9 

50 

9 

13 

8.76 

8.5 

.90 

8.4 

8.14 

8 

93 

8 

56 

8.22 

8.1 

1.00 

7.8 

7.60 

^34 

7 

91 

7 

59 

7.26 

7.0 

1.20 

6.9 

6.76              ( 

5.52 

7 

18 

6 

86 

6.60 

6.3 

1.40 

6.3 

6.10 

5.88 

6 

58 

6 

27 

6.02 

5-8 

1.60 

5.8 

5-56 

5-37 

517 

6 

09 

5 

80 

5.60 

5-5 

1.80 

5-4 

5-14 

)--95 

4-77 

5 

67 

5 

38 

5.20 

5-1 

2.00 

5-0 

4.80 

t.62 

4.44 

5 

35 

5 

01 

4.86 

4.8 

2.20 

4-7 

4.50 

^•3I 

4.14 

5 

05 

4 

79 

4.66 

4.6 

2.40 

4.4 

4.22 

\.a^ 

3-92 

4 

85 

4 

58 

4.44 

4-4 

2.60 

4.2 

4-00 

3.85 

3-71 

4 

68 

4 

39 

4.24 

4.2 

2.80 

4.0 

3-8o 

5.67 

3-55 

4 

50 

4 

23 

4.06 

4.0 

3.00 

3.8 

3-62 

5-50 

3-37 

4 

03 

3 

80 

3.66 

3-6 

3.50 

3-5 

3.38 

5.19 

3-07 

3 

79 

3 

57 

3-34 

3-4 

4.00 

3-3 

3.10             5 

2.97 

2.83 

3 

51 

3 

30 

3-14 

3-2 

5.00 

3-0 

2.80             : 

2.63 

2.51 

These  perceiitages  are  computed  for  an  average  Consolidation^  having  11  tons  trac- 
tive power  or  88,000  lbs.  on  drivers,  but  they  are  substantially  the  same  for  all  freight 
engines.     See  par.  698. 

By  interpolation  any  desired  percentage  can  be  determined  from  the  above  very  ap- 
proximately.    Thus  for  an  increase  of  0.75  in  a  0.75  grade  we  have 

_o-4   -t-  9-  o  _  jQ  Q2  X  7.5  =  7-5  +  per  cent  increase  in  engine-mileage. 
2 

Exactly,  it  is  (Table  170)  —  -  -  74.64  per  cent,  increase. 
552 


CHAP.    XIV.— EFFECT  OF  GRADES  ON   TRAIN-LOAD.      557 


1.850, 


857 


total  increase  of  engine-mileage,  equivalent  to  an  average  increase /^r 
o.i  of  mcrease  of  grade  of 

8.91  per  cent,  8.16  per  cent,  7.14  per  cent. 

For  an  increase  from  a  i.o  per  cent  to  a  2.0  per  cent,  we  have 

American.  Consolidation.  Tank. 

a  total  increase  per  cent  ot 

95.5  per  cent,  85.0  per  cent,  71.4  per  cent, 

or  an  increase  per  o.i  per  cent  of  increase  of  grade  of 

9.55  per  cent,  8.50  per  cent,  7.14  per  cent. 

696.  Proceeding  similarly  for  other  changes  of  grade,  viz.,  o.i,  0.3, 
0.5,  and  1.0  per  cent  of  increase  from  a  i  per  cent  grade  (making  the 
maximum  change  considered,  from  a  i.o  per  cent  to  a  2.0  per  cent),  and 
computing  also  the  comparative  engine-tonnage  required  for  correspond- 
ing decrease  in  a  i  per  cent  grade,  this  extreme  reduction  being  to  Level, 
we  obtain  the  following  Table  172,  in  which  the  computations  in  the  last 


Table  172. 

Showing  the  Effect  of  Various    Changes    in  a  One  Per- Cent  Grade 
ON  the  Engine  Tonnage  required  for  Three  Patterns  of  Engines. 


For  a  Decrease  in 

A  1. 00  Per  Cent 

Grade  of — 

Making 

the 
Grade 

The  Per  Cent  of  Change  in 
Engine  Tonnage  needed  is— 

And  the  same  Per  o.i  Per 
Cent  of  Change  in  Grade  is — 

Light 
Ameri- 
can 

Heavy 
Cons'n. 

Heavy 
Tank. 

Light 
Ameri- 
can. 

Heavy        Heavy 
Cons'n.        Tank. 

I  0  per  cent      

Level. 
0.3 
0-5 
0.7 
0.9 

1.00 

i.i 
1-3 
1-5 
1-7 
2.0 

74-5 
53-9 
39-5 
24-3 
8.4 

8.5 
26.0 
44.6 
64.0 
95-5 

73-4 
52.4 
38.0 
23.1 
8.8 

7-9 
24.1 
40.8 
58.2 
85.0 

71.4 
50.0 

35-7 
21.4 
7.14 

7.14 
21.4 
35-7 
50.0 
71.4 

7.45 
7.70 

7.90 
8. II 
8.41 

8.53 
8.68 
8.91 
9.14 
9-55 

7^1                           1     T  A 

7-o4 
7.49 
7.60 
7.71 
7.83 

7.92 
8.04 
8.16 
8.31 
8.50 

7.14 
7.14 
7.14 
7.14 

7.14 
7.14 
7.14 
7.14 
7.X4 

0  ■?     "     "          .     . 

0.1     "     " 

And  for  an  Increase 

of.... 

0  I  per  cent  ... 

01     "     '*     ...   

0  <;     "    " 

10    "     "     

Computed  from  Table  170 
lar  computations  for  all  rates 


m  the  manner  explained  in  par.  695.     The  results  of  simi- 
of  grade  are  condensed  in  Table  171. 


558      CHAP.   XIV.— EFFECT  OF  GRADES  ON   TRAIN-LOAD. 

column  but  one  correspond  substantially  with  one  line  (that  for  a  i.o 
grade)  of  Table  171.  All  the  other  lines  of  Table  171  were  computed  in 
the  same  way  from  Table  170,  the  figures  only  differing. 

697.  It  will  be  seen  in  Table  172  that  a  tank  engine  which  has  all  its 
weight  on  drivers  gives  exactly  the  same  per  cent  of  change  in  motive- 
power  per  unit  of  change  of  grade,  whether  it  be  great  or  small.  In  pro- 
tion  as  the  dead  weight  of  the  engine  becomes  a  larger  proportion  of  the 
w^eight  on  drivers,  the  absolute  per  cent  of  change  in  motive-power  in- 
creases, and  likewise  the  irregularity  of  the  percentage. 

698.  By  interpolation  in  Table  171,  the  percentage  for  almost  any 
kind  of  a  change  of  grade  can  be  readily  determined.  These  percentages 
do  not  vary  to  any  important  extent  with  the  pattern  of  engine,  within 
the  range  likely  to  be  used  for  freight  service,  nor  even  for  considerable 
differences  in  the  assumed  ratio  of  adhesion.  Moreover,  as  it  is  now  well 
established  that  \  is  the  proper  ratio  to  assume,  for  American  practice 
at  least,  no  other  should  be  assumed. 

699.  Ordinarily  the  changes  of  grade  which  the  engineer  is  called 
upon  to  consider  are  not  very  great.  The  typical  percentage  for  any  or- 
dinary change  in  any  grade,  for  use  in  estimating  the  value  of  a  reduc- 
tion or  the  cost  of  an  increase,  may  therefore  be  taken  to  be  that  due  to 
a  change  of  o.i  per  cent  in  it,  as  shown  in  Table  178,  which  is  practically 
the  same  for  either  an  increase  or  a  decrease  of  grade.  For  extreme  dif- 
ferences of  conditions,  of  any  kind,  the  actual  percentage  of  change  in 
engine-tonnage  should  be  directly  computed  from  the  relative  train-loads 
given  in  Table  170. 

We  are  now  prepared  to  consider  the  cost  of  changing  the  hauling 
power  of  engines  by  changes  of  grades. 

700i  Table  173  will  illustrate  how  enormously  the  virtual  gradient  as  well 
as  the  work  of  the  engine  may  be  increased  by  frequent  stops  and  quick  starts. 
On  the  New  York  Elevated  Railway  the  stops  are  so  close  together  that  it  is  ab- 
solutely essential  that  speed  should  be  gotten  up  very  quickly  indeed  if  reason- 
ably fast  time  is  to  be  made.  Accordingly  we  find  that  the  work  done  in  get- 
ting up  speed  is  equivalent  to  an  addition  to  the  actual  grade  of  2.63  per  cent, 
or  139  feet  per  mile — an  addition  so  great  that  whether  the  actual  grade  be  i 
per  cent  up  or  i  per  cent  down  makes  comparatively  little  difference  in  the 
working  of  the  engine.  Table  173  gives  an  extreme  example  of  conditions 
which  obtain  very  largely  in  passenger  service,  and  which  make  frequent  stops 
a  very  serious  disadvantage.  Due  allowance  for  this  effect  should  never  be 
forgotten  in  attempting  to  determine  what  the  actual  grades  are. 


CHAP.    XIV.— EFFECT  OF  GRADES  ON   TRAIN-LOAD.      559 


Table  173. 

Handling  of  Trains  on  Manhattan  (Elevated)  Railway  (Third  Avenue 

Line). 
[From  a  paper  by  Mr.  Frank  J.  Sprague  before  the  Boston  Society  of  Arts,  1886.] 


Length  of  line 8.48  miles. 

Total  lift,  up  track 144.42  ft. 

Lineal  distance  for  same 13,160        ft. 

Total  lift,  down  track 137 .  60  ft. 

Lineal  distance  of  same 16,510        ft. 

Level  on  each  track 15,100        ft. 

Number  of  stations 27 

Number  of  stoppages 26 

Average  Times  : 

Single  trip 42  min. 

Per  station 97  sec. 

Under  way 80    " 

Stop 17    " 

Time  due  to  a  run  without  stop  at 
max.  speed  of  19.2  m.  per  hour.,  26.56  min. 

Total  time  standing  still  at  sta- 
tions, at  17  sec.  each — 7.37    " 

Time  lost  in  slowing  up  and  get- 
ting under  way 8.07    " 


Total 42.00  min. 


Average  distance  between  stations.     1,722  ft. 

Divided  nearly  as  follows  : 
Getting  up  to  10  miles  per  hour. . . .        130  ft. 
Thence  to  full  speed  (19.2  miles  per 

hour) 495  ft. 

Full  speed 808  ft. 

Slowing  to  stop 289  ft. 

Average  Speed — miles  per  hour : 

Getting  under  way 13.4 

Full  speed 19.2 

Slowing  to  stop 9.6 

Mean  between  stations 14.7 

Daily  Work  of  One  Engine  : 

Round  trips  made 9 

Coal  used 5,760  lbs. 

Hours  on  duty 20 

Hours  steam  on 6 

Av.  consumption  of  coal  per  trip 640  lbs. 

Total  horse-power  per  round  trip 


Horse-power  per  pound  of  coal 


6184 
640 
60 


Pounds  of  coal  per  H.  P.  p.  h. .  — —  = 


9.66 


6,184 
9.66 

6.21 


For  a  speed  in  miles  per  hour  of. 
The  velocity-head  (Table  118)  is  . 


10. o 
3-55  ft. 


19.2 
13.10  ft. 


Divided  by  distance  to  acquire  that  speed 135  ft.  495  ft. 

Gives  as  the  virtual  gradient  due  to  that  acceleration,  in  excess 

of  the  actual  grade 2.63  p.  c.  2.64  p.  c. 

If  the  actual  grade  be  i  per  cent  up,  the  same  speeds  will  be 

acquired  in  a  distance  of 218  ft.  800  ft. 

Or  if  I  per  cent  down,  in 98  ft.  360  ft. 

Even  so  extreme  a  difference  in  grade  makes  comparatively  little  difference,  therefore,  in 
practical  operation. 


Getting  up  speed  to  19.2  miles  an  hour  26  times  is  equivalent  to  lifting  the  train  ver- 
tically 13.10  X  26  =  340.6  ft.  in  a  run  of  8.5  miles,  or  40  ft.  per  mile,  whereas  the  total 
tractive  resistance  in  motion  at  that  speed,  at  10  lbs.  per  ton,  is  equivalent  to  some  26  ft. 
per  mile  only. 


ci6o   CHAP.  XV.— TRAIN-LOAD   ON  OPERATING  EXPENSES. 


CHAPTER  XV. 

THE    EFFECT    OF    TRAIN-LOAD    ON    OPERATING    EXPENSES. 

701.  The  increase  in  train  resistance  which  results  from  an  increase 
of  ruHng  grade  can  be,  and  is,  overcome  in  either  of  two  ways:  (i)  By  an 
increase  in  the  weight  and  power  of  engines  ;  (2)  by  decreasing  the  weight 
and  increasing  the  number  of  trains. 

The  first  of  these — increasing  the  weight  of  engines — is  by  much  the 
cheapest,  but  is  only  possible  to  a  limited  extent  and  under  special  cir- 
cumstances. Ordinarily,  it  is  not  fair  to  assume  that  heavier  engines 
are  used  on  one  alternate  grade  than  on  another,  because,  whatever 
advantage  may  be  gained  by  using  heavier  engines  on  one  grade  may  be 
equally  well  gained  on  the  other  grade.  It  is  far  more  frequently  possi- 
ble to  fairly  assume  the  use  of  heavier  engines  on  heavier  grades  with 
passenger  than  with  freight  service,  but  passing  (until  par.  732)  the  ques- 
tion of  when  it  is  or  is  not  possible  to  adopt  the  cheaper  expedient,  we 
will  estimate  the  cost  of  each  separately. 

THE  COST   OF   INCREASING  THE   WEIGHT  OF   ENGINES. 

702.  The  following  items  will  not  be  increased  at  all  by  an  increase  of 
weight  of  engines  to  suit  the  requirements  of  a  higher  grade,  the  weight 
of  train  remaining  the  same :  The  cost  of  (i)  repairs  of  cars ;  (2)  train- 
wages  ;  (3)  general  expenses  ;  (4)  maintenance  of  way  and  works,  exclusive 
of  rail  and  tie  renewals  and  lining  and  surfacing;  (5)  that  portion  of  the 
inaintenance-of-way  expenses  last  excepted  which  is  caused  by  the  cars 
and  not  by  the  engines. 

The  most  reasonable  estimate  which  can  now  be  made  of  the  relative 
etfect  of  engine  and  cars  upon  the  track  is  (pars.  115,  116)  that  consider- 
ably over  half  of  the  deterioration  of  track  comes  from  the  passage  of  en- 
gines over  it,  and  the  remainder  only  from  the  passage  of  cars,  which  may 
weigh  ten  or  twenty  times  as  much.     Assuming  one  half  only,  we  are  led 


CHAP.  XV.— TRAIN-LOAD   ON  OPERATING  EXPENSES.    561 

to  the  conclusion  (see  Table  175)  that  more  than  three  quarters  of  the 
total  expenditure  is  unaffected  by  an  increase  of  the  weight  of  engines  in 
any  visible  and  direct  way. 

703.  The  effect  on  cost  of  maintenance  of  track  of  increasing 
the  weight  of  engines  has  been  greatly  modified  and  much  reduced  since 
the  publication  of  the  first  edition  of  this  volume  (prepared,  as  it  neces- 
sarily was,  from  records  which  were  some  years  old  in  1876)  by  the  now 
universal  use  of  steel  rails  in  place  of  iron.  The  causes  and  extent  of  the 
changes  thus  brought  about  have  been  already  summarized  in  par.  109 
et  seq.  The  most  important  of  all,  as  respects  the  use  of  heavy  engines, 
is  that  the  nature  of  the  wear  of  rails  has  changed.  With  iron  rails,  the 
wear  took  the  form  of  a  crushing  or  lamination,  which  destroyed  their 
surface  long  before  the  direct  abrasion  had  become  a  serious  matter.  This 
crushing  was  very  greatly  hastened  by  heavy  loads  per  wheel,  and  in- 
creased in  much  faster  ratio — to  the  extent  that  iron  rails  which  would 
sustain  the  passage  of  light  engines  for  many  years  would  be  crushed  out 
by  heavy  engines  in  a  few  months.  On  the  other  hand,  with  steel  rails 
(excluding  those  of  inferior  quality,  of  which  far  too  many  have  been  and 
are  laid)  the  wear  is  merely  direct  abrasion,  which  is  not  materially  in- 
creased per  ton  of  train  either  by  load  per  wheel  or  speed.  As  respects 
the  last  at  least,  there  is  very  good  reason  to  believe  that  it  increases  in 
much  less  than  direct  ratio. 

704.  For,  as  respects  speed,  when  the  question  is  one  merely  of  abrasion 
and  not  of  destruction  impact,  the  less  the  time  to  which  the  rail  is  exposed  to 
load  the  less,  undoubtedly,  the  normal  crushing  effect,  for  the  same  reason 
that  journal  and  other  (i.e.,  brake)  friction  is  less  at  high  speeds  or  that  it  takes 
more  force  to  rupture  a  specimen  in  a  test- 
ing-machine quickly  than  slowly.      Impacts 

proper  play  their  part,  no  doubt,  in  the  wear  "  '       '         ^ 

of  steel  rails  as  of  iron  rails,  but  so  long  as  the  Fig.  170. 

surface  remains  tolerably  good  (as  it  does  almost  indefinitely  with  the  best  steel 
rails)  it  is  a  small  part.  When  the  surface  becomes  seriously  impaired  steel 
rails  go  almost  as  quickly  as  iron;  but  either  with  steel  or  iron  the  effect  of  the 
impacts  is  not,  as  is  often 
assumed,  as  Mv^.  This  is 
true  of  a  body  impinging 
directly  upon  another;  but 
one     caused     to     impinge  Fi<^-  ^yi- 

upon  another  in  jumping  from  .4  to  B  under  conditions  outlined  clearly  enough 
in  Fig.  170  impinges  at  a  different  angle,  which  has  the  effect  of  reducing  the  im- 
pact communicated  to  B  to  the  approximate  ratio  Mv  ;  and  when  we  assume  a 
36 


562    CHAP.  XV.— TRAIN-LOAD   ON  OPERATING  EXPENSES. 

case,  as  in  Fig.  171,  still  more  closely  approaching  average  practical  conditions, 
the  communicated  impact  becomes  more  nearly  in  the  ratio  M  ^v. 

That  this  is  so  follows  clearly  from  experience  on  tracks  where  the  varia- 
tions of  speed  are  considerable,  as  notably  on  the  four  tracks  of  the  New  York 
Central  &  Hudson  River  Railroad,  two  of  which  are  used  for  passenger  ser- 
vice only,  and  two  for  freight  only.  The  observed  rate  of  wear  per  ton  is  nearly 
constant  on  these  tracks,  in  spite  of  the  fact  that  the  proportion  of  engine-ton- 
nage is  several  times  greater  on  the  passenger  tracks. 

As  respects  effect  of  increase  of  load,  abrasion,  other  things  being  equal, 
I  I      should  be  in  some  approximately  exact  ratio  to  the 

\  /       maximu77i  fibre-strain.     If  we  assume  an  elastic  cyl- 

\  /        inder  or  sphere  to  be  rolling  on  a  plane,  a  distor- 

^N^^^^^^._?__^£_^>^  tion  of  form  will   result   from   compression,  rudely 

'A      ~~(^'      °  outlined  in  Fig.   172.     The   volume    of    this    solid, 

—  shown  in  plan  in    Fig.    173,  will  be  in  direct  ratio 
to  the  total  load,  but  the  maximum  fibre-strain  will 
be  in  proportion    to    the  maximum    ordinate   CC , 
Fig.  173.  which  varies  more  nearly  as    \fL  or  even    \/ L,  ac- 

cording to  the  assumptions  as  to  the  surfaces  in  contact. 

The  subject  is  too  obscure,  and  too  unimportant  for  our  immediate  purpose, 
to  consider  further. 

705.  The  observations  of  the  Pennsylvania  Railroad  on  the  wear  of 
rails  on  grades  (par.  457)  also  tend  to  show  that  not  more  than  half,  or  at 
most  two  thirds,  of  the  total  cost  of  rail  wear  can  be  considered  to  vary 
directly  with  the  engine-tonnage,  the  car-tonnage  remaining  constant; 
whereas  in  the  first  edition  of  this  treatise,  based  in  the  main  on  iron- 
rail  statistics,  the  whole  cost  of  rails  was  assumed  (and  the  writer  be- 
lieves with  substantial  correctness)  to  vary  as  the  square  of  the  weight 
on  drivers,  or  at  the  rate,  for  small  increments,  of  200  per  cent.*  This 
change  is  one  small  evidence  of  the  immense  advantages  which  have  re- 
sulted from  the  introduction  of  steel  rails. 

706.  Of  the  remaining  items  of  the  cost  of  track,  lining  and  sur- 
facing, in  spite  of  apparent  reasons  to  the  contrary  (discussed  in  par. 
125),  is  affected  by  increased  weight  of  engines  in  a  considerably  greater 
ratio  than  the  rail  wear,  and  tie  renewals  to  a  very  considerable  extent, 
although  not  quite  so  largely.  We  may  not  improperly  take  half  the  total 
cost  of  rails,  ballast,  ties,  adjusting  track,  and  switches,  frogs,  and  sidings, 
as  varying  directly  with  the  average  weight  on  drivers,  car-tonnage  being 

*  For  the  reason  (to  those  familiar  with  the  elements  of  the  calculus)  that 
dx^  =  2xdx.     See  p.  90,  old  edition. 


CHAP.  XV.— TRAIN-LOAD   ON  OPERATING  EXPENSES.    563 

constant.  With  inferior  steel  rails  it  may  be  much  more,  but  with  such 
rails  as  may  be  had  at  the  same  cost  by  adequate  care  in  inspection  this 
estimate  is  a  sufficient  one. 

707.  The  remaining  items  of  maintenance  of  way,  for  bridges  and 
BUILDINGS,  are  very  slightly  affected,  certainly  by  not  more,  in  ordinary 
cases,  than  \  ct.  per  train-mile,  the  whole  being  an  allowance  for  interest 
and  maintenance  charges  on  heavier  bridges. 

708.  Repairs  of  engines  are  affected  much  less  than  would  be  sup- 
posed by  the  weight  of  engines.  Renewals  constitute,  as  per  Table  55  and 
others,  from  40  to  50  per  cent  (under  normal  conditions,  which  can  hardly 
be  said  as  yet  to  exist  on  account  of  the  rapid  growth  of  traffic)  of  what  ap- 
pears charged  to  "repairs."  Table  174  affords  the  means  for  estimating 
that  considerably  less  than  50  per  cent  of  \S\q.  first  cost  of  engines  varies 
directly  with  weight,  the  remainder  being,  within  moderate  limits  of 
variation,  a  constant. 

Of  the  remaining  cost,  repairs  proper,  it  is  indicated  in  Table  ^\etseq. 
and  a  number  of  others,  that  between  50  and  60  per  cent  is  for  labor  only  : 
an  item  which  will  be  somewhat,  but  very  slightly,  affected  by  the  weight 
of  engines.  The  remaining  expenditures,  for  raw  materials  and  for 
wheels,  axles,  and  tires,  will  vary  nearly,  but  not  quite,  directly  as  the 
weight. 

It  would  appear  from  these  facts  that  50  per  cent  of  the  cost  of  repairs 
may,  with  sufficient  exactness,  be  assumed  to  vary  directly  with  weight 
of  engines,  the  remainder  iDeing  constant,  as  has  been  already  stated  in 
par.  134. 

709.  The  cost  of  fuel  for  heavier  engines  hauling  the  same  train 
behind  them  will  not  be  largely  increased.  In  not  a  few  cases  there 
would  be  an  actual  decrease.  It  is  to  be  remembered  that,  even  if  heavier 
engines  are  used  to  overcome  a  somewhat  higher  grade,  it  is  only  for  a 
short  distance  that  the  extra  power  is  required.  On  all  up  grades  below 
the  maximum,  and  in  descending  all  grades,  the  power  required  and  ex- 
erted will  be  no  greater  than  with  the  smaller  engine,  except  the  slight 
addition  due  to  the  weight  of  the  engine  itself,  and  this  power  will  be 
somewhat  more  economically  exerted  (par.  579),  owing  to  the  heavier  en- 
gine being  less  pushed.  The  constant  wastage  from  radiation,  stopping 
and  starting,  etc.,  estimated  in  par.  344  et  seq.,  at  50  per  cent  of  the  fuel 
consumption,  will  remain  for  the  most  part  constant. 

For  all  these  reasons  together,  on  something  like  two  thirds  of  the 
length  of  ordinary  railways  the  fuel  burned  per  mile  would  be  but  slightly 
if  at  all  affected  by  moderate  (not  over  20  per  cent)  differences  in  weight 


564  CHAP.  XV.— TRAIN-LOAD   ON  OPERATING  EXPENSES. 


Table  174. 

Comparative  Cost   Per  Ton  of  Various  Sizes  of  Engines,  Broad  and 

Narrow  Gauge. 

[Compiled  from  information  furnished  by  the  Baldwin  Locomotive  Works.] 
American   Type — Standard  Gauge. 


Weight  (net  tons). 

Cost,  1886. 

Cylinders. 

Total. 

On  Drivers 

Engine. 

Tender, 

Per  Ton  on 
Drivers. 

12    X    22 

24. 

15- 

$5,750 

$950 

$383 

13   X  24 

27 

18. 

6,000 

1,000 

333 

14  X  24 

29 

5 

19.5 

6,250 

1,050 

321 

15   X  24 

32 

5 

22. 

6,500 

1,100 

295 

16  X  24 

36 

24-5 

6,750 

1,150 

276 

17  X  24 

38 

25.5 

7,000 

1,200 

275 

18  X  24 

41 

27-5 

7,250 

1,250 

264 

Mogul  Type— 

Standard  Gauge. 

16  X  24 

37. 

32.5 

$7,250 

$1,150 

$223 

17  X  24 

39- 

34.5 

7,500 

1,200 

217 

18   X  24 

42. 

37- 

7,750 

1,300 

209 

19  X  24 

45. 

40. 

8,000 

1,350 

200 

Consolidation    Type — Standard  Gaug 


20  X  24 

21  X    24 

53. 

59- 

46. 

52. 

$9,250 
9,750 

$1,400 
1,400 

$201 
188 

Narrow-Gauge  Engines. 
At7ierican    Type. 


10  X  16 

16.5 

II. 

$4,750 

$750 

$432 

II  X   16 

18. 

12. 

5,000 

775 

417 

12    X    16 

19-5 

13. 

5,250 

800 

404 

13  X   16 

22.5 

15.5 

5,500 

850 

355 

14  X  16 

24. 

16.5 

5,750 

900 

357 

Mogul  Type. 


II   X   16 

17.5 

14-5 

$5,250 

$800 

$362 

12    X    16 

20. 

16.5 

5,500 

850 

334 

13   X   16 

23- 

19-5 

5,750 

900 

295 

14  X   16 

25. 

21.5 

6,000 

950 

278 

15   X   16 

28. 

24.5 

6,250 

1,000 

255 

CHAP.  XV.— TRAIN-LOAD   ON  OPERATING  EXPENSES.    565 

Table  174. — Continued. 
Consolidation   Type. 


Weight  (net  tons). 

Cost,  1886. 

Cylinders. 

Total. 

On  Drivers. 

Engine. 

Tender, 

Per  Ton  on 
Drivers. 

15  X   18 

16  X   18 

28. 
34- 

24. 
29. 

$6,750 
7.250 

$950 
1,000 

$282 
250 

Comparison  of  the  above  table  shows  that  the  cost  of  engines  increases  at  about  the 
rate  of  $250  per  inch  of  cyHnder  diameter,  about  $750  per  extra  driving-axle,  and  $250 
per  extra  truck-axle;  which  are  builders''  approximate  rz^/^i',  starting  from  the  17x24 
American  engine  as  the  standard  or  unit  type. 

Comparitig  the  lightest  and  heaviest  engines  of  each  type,  we  find  that  the  cost  per  ton 
on  drivers  of  extra  weight  is  but  little  over  $100  per  ton,  viz. : 

Standard    Narrow 
Gauge.       Gauge. 

American, $120  $182 

Mogul, 100  100 

Consohdation, 125  100 

These  figures  indicate  that,  on  an  average,  the  first  cost  of  additional  power  in  engines 
is  considerably  less  than  half  the  average  cost. 

Messrs.  Burnham,  Parry,  Williams  &  Co.,  proprietors  of  the  works,  state  in  an  ac- 
companying letter  : 

"  Respecting  the  relative  cost  of  narrow-  and  standard-gauge  locomotives  of  the  same 
w^eight  and  pattern,  we  have  long  believed  that  in  many  cases  where  narrow-gauge  rail- 
roads have  been  contemplated  it  would  be  more  economical  and  desirable  to  lay  light 
Tails  561^  inches  apart,  and  use  rolling-stock  of  the  weight  usual  on  narrow-gauge  roads. 
We  have,  therefore,  given  much  attention  to  the  subject  of  your  question.  Our  ex- 
perience indicates  that  for  engines  of  similar  weight,  dimensions,  and  pattern,  differing 
only  in  gauge,  there  is  no  appreciable  difference  in  cost.  What  extra  expense  is  in- 
volved by  the  greater  cross-measurements,  is  quite  compensated  for  by  the  reduced  length, 
as  the  greater  distance  between  the  frames  permits  of  widening  and  shortening  the  fire- 
box, with  corresponding  reduction  in  length  of  frames  and  wheel-base.  The  shorter 
wheel-base  enables  the  engine  to  curve  more  readily,  removing  in  a  measure  one  of  the 
objections  urged  against  the  standard  gauge.  For  these  reasons  we  have  been  led  to  de- 
sign a  series  of  standard-gauge  locomotives,  precisely  similar  in  all  except  gauge  and  the 
details  of  construction  dependent  thereon,  to  equivalent  narrow-gauge  engines,  and  which 
are  offered  at  the  same  price." 


of  engines,  and  on  the  remaining  distance  not  more  than  50  per  cent  of 
the  fuel  burned  would  vary  directly  with  the  weight  and  power  exerted. 
As  an  average  of  entire  runs,  it  is  entirely  adequate  to  assume  that  25  per 


566    CHAP.  XV.— TRAIN-LOAD   ON  OPERATING  EXPENSES. 

cent  of  the  total  fuel  consumption  varies  directly  with  the  weight  of  engines 
hauling  the  same  train  over  for  the  most  part  the  same  grades,  and  that 
the  remaining  75  per  cent  is  unaffected.  On  this  basis,  an  engine  20  per 
cent  heavier  would  average  for  entire  runs  not  over  5  per  cent  more  fuel 
to  haul  the  same  trains.  The  cost  of  supplying  oil  and  water  would  vary 
in  about  the  same  proportion. 

710.  These  various  items  are  summed  up  in  the  following; 
Table  175.  As  already  stated,  however,  it  is  only  under  very 
exceptional  circumstances  and  on  a  limited  scale  that  it  is  proper 
to  assume  that  differences  of  grade  can  or  will  be  overcome  in 
practice  by  the  cheap  and  apparently  simple  expedient  of  in- 
creasing the  weight  of  engines  for  freight  service,  and  on  roads 
enjoying  a  moderately  large  passenger  traffic  the  same  is  very 
nearly  true  of  passenger  trains.  The  engines  will  in  any  case  be 
made  as  powerful  as  is  deemed  feasible  or  expedient,  for  conveni- 
ence in  stopping  and  starting,  and  for  occasional  exigencies,  if  for 
nothing  else;  and  anything  w^hich  reduces  their  hauling  capacity  at 
the  requisite  speed  between  stations  will  be  apt  to  result  directly 
or  indirectly  in  running  shorter  trains  and  more  of  tfiem.  This  is 
far  from  an  unmixed  disadvantage  under  many  circumstances- 
(par.  89),  but  nevertheless  it  is  a  real  disadvantage. 

711.  Table  175  itself  makes  clear  wh}^  it  is  entirely  improper 
to  assume  the  use  of  heavier  engines  to  meet  the  demands  of 
heavier  grades,  by  indicating  that  there  is  always  a  great  econ- 
omy in  using  the  heaviest  engines  which  the  traffic  will  warrant. 
To  double  the  weight  of  engine  to  haicl  the  same  train  will  only 
add  some  14  per  cent  to  expenses,  according  to  Table  175.  If  by 
doubling  the  weight  of  engine  we  can  also  halve  the  number  of 
trains,  we  immediately  effect  an  immense  economy  in  train-wages, 
engine  repairs,  fuel,  and  maintenance  of  way,  exceeding  more 
than  threefold  (Table  176)  the  increased  expense  per  train-mile 
due  to  the  heavier  weight  of  engine.  It  is  only  when  the  grades 
are  so  very  low  (approximating  closely  to  a  level)  that  even  a 
light  engine  can  haul  the  fifty  or  sixty  loaded  cars,  which  are 
as  many  as  can  be  conveniently  handled  with  the  present  bad 
style  of  coupling,  that  heavier  engines  can  be  legitimately  assumed 
to  meet  the  requirements  of  a  heavier  grade;  if  even  then. 


CHAP.  XV.  — TRAIN-LOAD    ON   OPERATING   EXPENSES.    567 


Table  175. 

Estimated  Average  Cost  Per  Train-Mile  of  Doubling  the  Weight  of 
Engines  to  Haul  the  Same  Train. 

[The  percentage  by  which  any  given  change  of  grade  will  require  the  weight  of  engines 
(or  number  of  trains)  to  be  increased  is  given  in  Table  171.] 


Item. 
(As  per  Table  80,  page  179.) 


Average 

Cost  of  Item. 

Cents  or 

Per  Cent. 


Per  Cent  Added  by 

Doubling  Weight 

of  Engine. 


Added 

Cost. 
Cents  or 
Per  Cent. 


Fuel 

Oil,  wraste,  and  water 

Engine  repairs 

Switching-engines 

Train  wages  and  supplies 

Car  maintenance  and  mileage 

Renewals,  rails 

Adjusting  track 

Renewals,  ties , 

Earthwork,  ballast,  etc 

Switches  and  sidings 

Bridges  and  buildings , 

Station,  terminal,  and  general 

Total 


6 
.1 

6 
,2 

■4 
.0 
.0 
6.0 
3.0 
4.0 
2.5 
5-5 
30.0 


25  per  cent. 

50  per  cent. 
Unaffected. 


1.9 

0.3 

2.8 


50  per 


cent. 


100.  o 


14. 1  per  cent. 


14. 1 


Perhaps  one  further  exception  should  be  made — when  the 
traffic  is  so  very  light  that  it  is  not  practically  convenient  to  run 
very  heavy  trains,  as  when  it  is  less  than  three  to  five  freight  trains 
per  day. 

712.  Table  175  also  explains  why  there  is  so  great  a  tendency 
to  increase  the  weight  of  passenger  trains  by  supplying  more 
luxurious  accommodations.     It  is  because — 

1.  A  very  powerful  engine  costs  but  little  more  to  run  than  a 
light  one  (Table  175). 

2.  Coal  consumption  is  but  little  increased  by  material  differ- 
ences in  the  weight  of  cars  (par.  129). 

3.  Grades  have  but  little  influence  upon  passenger  trains 
until  they  become  very  long  (par.  397  et  seq.),  and  by  slight  re- 
ductions of  velocity  on  up  grades  only  the  effect  of  increased  weight 
can  be  equalized  if  necessary  (Table  120),  running  somewhat 
faster  down  hill. 


568  CHAP.  XV.  — TRAIN-LOAD    ON  OPERATING  EXPENSES. 

4.  It  encourages  traffic  to  run  more  passenger  trains  (par.  89), 
and  discourages  it  materially  to  attempt  to  crowd  the  traffic  upon 
a  few  trains. 

5.  And  more  important  than  all,  the  increased  luxury  is  a 
great  attraction  to  travel,  and  added  travel  thus  secured  is  of 
immense  value  to  the  property  (pars.  37-41). 

713.  The  cost  of  increasing  the  number  of  engines  to  haul 
THE  SAME  TRAFFIC,  OH  accouHt  of  a  heavier  grade,  may  be  estimated  as 
follows : 

The  number  of  trains  is  supposed  to  be  increased  by  a  change  of  maxi- 
mum grade  only,  which  will  not  ordinarily  extend  over  one  third  of  the 
distance.  While  running  over  the  remaining  distance,  the  work  done  on 
the  train  behind  the  engine  will  vary  according  to  the  v/eight  or  number 
of  cars.  While  running  on  the  maximum  grade  the  power  exerted  by  the 
engine  will  be  the  same,  since  in  each  case  the  engine  is  supposed  to  be 
fully  loaded  on  that  grade. 

714.  Fuel. — For  reasons  already  enumerated  (par.  344),  about  one 
half  of  the  consumption  of  fuel  will  vary  directly  with  the  tonnage  of  the 
train;  the  other  half,  consisting  of  the  fuel  burned  in  stopping  and  start- 
ing (in  part),  getting  up  steam,  loss  by  radiation,  loss  by  head  resistance, 
etc.,  making  up  in  the  aggregate  the  50  per  cent  which  is  unaffected  by 
the  length  of  the  train. 

If,  therefore,  the  maximum  grade  be  increased  on  about  one  third  the 
length  of  the  road,  while  on  the  remainder  the  grades  remain  about  the 
same,  about  half  the  consumption  on  two  thirds  of  the  distance,  equal  to 
all  the  consumption  on  one  third  of  the  distance,  or  33  per  cent  of  the 
entire  consumption  will  vary  directly  with  the  net  weight  of  the  train  ;  so 
that,  if  the  grade  were  so  increased  as  to  take  two  locomotives  instead  of 
one  to  handle  the  same  traffic,  the  fuel  consumption  would  be  as  i.o  to 
1.67  at  most,  and  not  as  i.o  to  2.0,  as  might  be  over-hastily  assumed. 
The  aggregate  cost  of  oil,  waste,  and  water  will  vary  in  about  the  same 
proportion. 

715i  Train-wages  will  of  'course  vary  directly  with  the  number  of 
trains,  unless  the  change  of  grade  in  contemplation  were  so  great  as  to 
shorten  up  trains  so  as  to  dispense  with  one  brakeman,  which  can  rarely 
happen. 

716.  Station,  terminal,  and  general  expenses  will  remain  unaf- 
fected by  any  moderate  change,  but  there  is  nothing  b)^  which  they  are 
so  quickly  affected  as  by  a  decided  increase  in  the  number  of  trains,  and 


CHAP.  XV.— TRAIN-LOAD    ON   OPERATING  EXPENSES.   569 

a  full  20  per  cent  of  their  aggregate  may  be  considered  as  varying  directly 
therewith. 

717.  Of  the  COST  OF  MAINTENANCE  OF  WAY  we  Cannot  directly  account 
for  an  increase  of  more  than  one  half  to  two  thirds  as  a  result  of  doubling 
the  engine-mileage,  the  car-mileage  remaining  constant ;  but  the  facts  given 
in  par.  125  and  its  accompanying  Tables  41-44  indicate  that  there  is  an  in- 
direct effect  from  multiplication  of  the  number  of  trains  which  seems  to 
cause  all  expenses  for  maintenance  of  way  to  increase  pari  passu  there- 
with, including  some  items,  such  as  those  for  policing,  maintenance  of 
ballast,  road-bed,  and  ties,  etc.,  etc.,  which  should  be  affected  but  little, 
if  any,  apparenth^  by  the  precise  number  of  trains  over  the  road.  It  is  to  be 
remembered,  in  considering  the  tables  referred  to,  that  during  the  years 
which  they  cover  the  weight  as  well  as  the  number  of  trains  has  increased 
enormously,  which  should  naturally  tend  to  keep  maintenance  of  way  per 
train-mile  at  a  high  figure  ;  but  after  making  all  allow^ances  for  this  differ- 
ence, tlie  chief  cause  for  the  singularly  constant  ratio  of  increase  in  main- 
tenance of  way  and  maintenance  of  rolling-stock  is  probably  this  :  A  con- 
tinually advancing  standard  of  maintenance  is  indispensable  as  the  volume 
of  traffic  increases,  and  the  cost  of  each  step  toward  perfection  increases 
about  as  the  square  of  the  number  of  steps.  A  very  slight  expenditure 
suffices  to  make  track  good  enough  for  the  passage  of  one  train  a  day. 
A  slight  addition  suffices  for  two  or  three  trains  a  day,  and  makes  a  great 
improvement  in  the  condition  of  the  track.  A  much  greater  expenditure 
is  necessary  to  fit  the  track  for  ten  trains  a  day,  and  yet  the  visible  ad- 
vance in  condition  is  much  less ;  and,  finally,  as  we  get  up  to  thirty  or 
forty  or  fifty  trains  a  day,  a  very  great  additional  expenditure  is  found 
necessary — or  at  least  expedient — although  the  visible  advance  of  condi- 
tion is  very  small.  At  any  rate,  the  fact  seems  to  be  that  even  in  so  ex- 
treme an  advance  as  from  six  trains  a  day  to  sixty  (see  top  of  page  128), 
the  cost  of  maintenance  of  way  per  trai7i-mile  does  not  decrease,  but 
rather  the  total  cost  per  mile  of  road  increases  tenfold  with  the  number 
of  trains. 

718.  Investigation  clearly  indicates  this  to  be  the  fact.  We  are 
therefore  not  justified  in  going  behind  it,  to  see  whether  we  can  explain 
it,  but  must  take  it  as  it  is.  If  we  do  so,  we  are  compelled  to  estimate 
that  if  by  a  change  of  grade  we  should  double  the  engine-mileage  needed 
for  handlmg  the  same  tonnage,  we  should  also  double  the  entire  cost  of 
maintenance  of  way.  Making  a  concession  of  somewhat  doubtful  pro- 
priety to  the  fact  that  the  car-mileage  would  remain  the  same,  we  may  ex- 
clude, the  cost  of  bridges  and  buildings  as  unaffected  ;  but  this  is  the  most 


570  CHAP.  XV.— TRAIN-LOAD   ON  OPERATING  EXPENSES. 

which  can  be  done.  Statistics  do  not  seem  to  indicate  that  the  total  cost 
per  train-mile  on  roads  which  handle  light  trains  is  sensibly  less  than  on 
roads  which  handle  heavy  trains. 

719.  Engine  repairs  should  apparently  vary  directly  with  the  miles 
run  ;  but  the  indications  are  (Table  42  et  al.)  that  as  a  matter  of  fact  it  is 
much  less  likely  to  do  so  than  maintenance  of  way,  owing  in  part  to  the 
large  proportion  of  incidental  expenses  (see  Table  57),  which  are  not  by  any 
means  doubled  to  maintain  a  double  number  of  engines.  There  will  also 
be  a  certain  diminution  of  wear  and  tear  from  stopping  and  starting,  etc. 
(see  Table  85,  page  203),  from  the  fact  that  the  trains  to  be  handled  are 
shorter.  Taking  both  of  these  causes  together,  it  is  not  probable  that 
doubling  the  number  of  engines  to  move  the  same  number  of  cars  would 
increase  engine  repairs  in  the  ratio  of  more  than  i.oo  to  1.75,  and  prob- 
ably somewhat  less. 

720.  Car  repairs  are  certainly  affected  beneficially  by  having  a  less 
number  of  cars  to  a  train.  By  referring  to  Table  86  (page  203)  it  will  be 
seen  that  more  than  one  third  of  the  total  cost  of  car  repairs  can  be  di- 
rectly traced  to  the  concussions  of  stopping  and  starting  and  making  up 
trains.  Much  of  this  expense  may  disappear  with  the  introduction  of 
better  couplers ;  but  even  this  is  doubtful,  as  an  automatic  coupler  will 
permit  of  much  more  violence  in  running  cars  together,  since  a  brake- 
man's  life  between  the  cars  will  no  longer  have  to  be  considered.  A 
diminution  of  at  least  10  per  cent  may  fairly  be  estimated  as  a  result  of 
running  only  half  as  long  trains. 

721.  To  these  expenses,  properly  so  called,  is  to  be  added  an  inter- 
est charge  on  the  cost  of  the  additional  motive-power  re- 
quired by  the  higher  grade,  unless  the  first  cost  of  these  engines  be  in- 
cluded in  the  estimated  cost  of  constructing  the  higher  grade-line,  before 
determining  the  difference  in  the  capital  investment. 

This  should  be  done  because  the  addition  of  the  required  number  of 
engines  is  really  so  much  added  to  the  original  investment.  Before  the 
line  is  ready  to  handle  the  required  traffic  it  is  as  necessary  to  have  them 
as  it  is  to  have  the  track  laid  on  the  high  grade-line  and  not  on  the 
other.  In  considering  differences  of  distance  (if  not  too  great),  or  curva- 
ture, or  rise  and  fall,  this  is  not  so.  The  total  amount  of  equipment  will 
be  the  same  whatever  the  differences  in  that  respect.  We  therefore  es- 
timate the  expenses  regardless  of  interest  on  the  plant,  and  only  consider 
differences  in  the  cost  of  construction.  Of  the  car  equipment  the  same 
is  true  in  the  case  of  gradients.  Whatever  the  grades,  the  number  of 
cars  will  be  the  same  ;  but  as  the  number  of  engines  is  increased  because 


CHAP.  XV.— TRAIN-LOAD    ON  OPERATING  EXPENSES.   571 

of  the  grades,  and  not  for  any  difference  of  traffic,  we  must  either  include 
the  difference  in  the  cost  of  equipment  as  a  part  of  the  cost  of  construc- 
tion, or  add  an  interest  charge  to  expenses.  On  the  whole,  it  is  more 
convenient  to  add  the  interest  charge. 

722,  Putting  together  all  these  items  which  have  been  just 
considered,  we  obtain  the  summary  given  in  Table  176,  as  the 
effect  on  operating  expenses  of  so  increasing  the  rate  of  grade 
as  to  double  the   number  of  engines  required  to  handle  a  given 


Table  176. 

Estimated  Average  Cost  Per  Train-Mile,  of  Doubling  the  Number  of 
Trains  to  Handle  a  Given  Traffic;  or  Proportion  of  Expenses 
WHICH  Varies  Directly  with  the  Number  of  Trains,  the  Car-Ton- 
nage remaining  Constant, 

[The  percentage  by  which  any  given  change  of  grade  will  require  the  number  of  trains 
(or  weight  of  engines)  to  be  increased,  is  given  in  Tables  171  and  178.] 


Item. 
(As  per  Table  80,  page  179.) 


Average 

Cost  of  Item, 

Cents  or 

Per  Cent. 


Per  Cent  Added  by 

Doubling  Number 

of  Trains. 


Added 

Cost. 
Cents  or 
Per  Cent. 


Fuel... 

Oil,  waste,  and  water , 

Engine  repairs , 

Switching  engines 

Train  wages  and  supplies 

Car  maintenance  and  mileage. 

Renewals,  rails 

Adjusting  track 

Renewals,  ties .  . 

Earthwork,  ballast,  etc 

Switches  and  sidings 

Bridges  and  buildings 

Station,  terminal,  and  general 

Total  of  operating  items. . 


7.6 
1.2 


30.0 


67  per  cent. 

75  per  cent. 

Unaffected. 
100  per  cent. 

10  p.  c.  less. 
100  per  cent. 


Unaffected. 
20  per  cent. 


6.0 


47.8  per  cent. 


47.8 


To  this  is  to  be  added  the  interest  on  the  cost  of  one  extra  locomo- 
tive for  one  train-mile.  Estimating  the  cost  of  the  locomotive 
at  about  10  000  times  the  cost  of  a  train-mile,  and  the  interest 
thereon  at  6  per  cent  as  about  600  times  the  cost  of  a  train-mile; 
and  estimating  the  average  passenger-engine  mileage  to  be 
40,000  miles  per  year,  we  have,  as  the  interest  charge,  per  mile, 


Making  the  grand  total, 


1.7 
49.5 


572  CHAP.  XV  — TRAIN-LOAD    ON  OPERATING  EXPENSES. 


traffic.  When  and  if  it  can  fairly  be  assumed  that  the  weight  of 
engines  can  be  increased  instead  (par.  711),  Table  175  gives  the 
percentage  of  increase  in  expenses. 

723.  In  the  former  edition  of  this  work,  this  summary  was  materially  dif- 
ferent, especially  as  respects  the  effect  of  increasing  the  weight  of  engines,  as 
shown  in  the  following  Table  177.  The  cause  of  the  discordance  is  simply  the 
change  in  conditions,  in  the  writer's  view,  and  not  that  either  is  essentially  in- 
correct. 

Table  177. 

Estimated  Cost  of  Doubling  the  Engine-Tonnage  for  the  same  Car- 
Tonnage  USED   IN  THE   FORMER   EDITION   OF  THIS   TREATISE. 
[For  statistics  based  for  the  most  part  on  iron-rail  track.] 


Total 

Cost. 

Cts.  or 

Per  Cent. 

For  a  Double  Number 
OF  Engines. 

For  a  Double  Weight 
OF  Engines. 

Items. 

Percent  increas- 
ing with  Number 
of  Engines. 

Added 
Cost. 

Per  cent  increas- 
ing with  Weight 
of  Engines. 

Added 
Cost. 

Fuel  

lO.O 

2.0 

9.0 

12.0 

13.0 
7.0 
7.0 

30.0 

90  per  cent. 

90    "      " 

90    "      " 

90    "      " 
100    "      " 
100    "      " 
Included  above. 

Unaffected. 

9.0 

\  21.0 

13.0 
7.0 

50  per  cent. 

r  so  "    " 
\  33  "    " 

t   Unaffected. 

200  per  cent. 

100    "      " 
Included  above. 

Unaffected. 

5-0 
I  0 

Oil   waste    etc 

Engine  repairs  

3-0 

Track  repairs      

26  0 

7.0 

Yards  and  structure 

General  and  station 

Totals  

100. 0 

50  per  cent. 

50.0 

42  per  cent. 

42.0 

Assumed  average.,  48  cents  per  train-mile,  or  48  per  cent  of  operating-  expenses. 

724.  Assuming  that  under  all  ordinary  circumstances,  for 
moderate  changes  of  grade,  any  increase  must  be  met  by  an  in- 
crease in  the  number  and  not  in  the  weight  of  engines,  we  have 
49.5  cents  per  train-mile,  or  49.5  per  cent  of  operating  expenses, 
as  the  portion  of  the  total  expenses  which  will  vary  with  increase 
of  engine-mileage  to  handle  the  same  business,  which  is  not  far 
from  the  cost  of  running  an  engine  light,  as  it  should  be. 

Multiplying  this  amount  by  365  X  2,  we  have 
$0,495  X365  X  2  =$361.35 
as   the  yearly  sum  per  daily  train  per  mile  of  road  which  varies  di- 
rectly with  an  increase  of  engine-tonnage  for   the  same  traffic. 


CHAP.  XV.—  TRAIN-LOAD    ON   OPERATING  EXPENSES.   S73 

If,  now,  we  multiply  this  sum  by  the  percentage  of  the  in- 
crease IN  engine-mileage    resulting    from  an    increase    of    O.I 

PER  CENT  in  any  ruling  grade,  we  shall  obtain  the  cost  per  daily 
train  per  mile  of  road  of  such  increase.  In  other  words,  we  ob- 
tain the  cost  per  train  of  increasing  the  number  of  trains  to  han- 
dle the  same  fixed  tonnage,  or  the  saving  per  train  by  decreasing 
that  number;  i.e.,  we  obtain  the  cost  of  using  i.i,  1.2,  1.5,  or 
2.0  trains,  instead  of  one,  to  handle  a  given  tonnage,  or  the  sav- 
ing by  using  0.9,  0.8,  or  0.6.  That  cost  or  saving  is  given  in 
Table  178,  and  when  multiplied  by  the  estimated  number  of  the 
trains  on  the  grade  for  which  the  traffic  was  estimated,  it  gives 
the  total  cost  or  saving. 

725.  The  cost  thus  obtained  is  not  an  absolute  value,  inde- 
pendent of  the  length  of  the  road,  as  in  the  case  of  the  similar 
values  deduced  for  distance  (Tables  88,  89),  curvature  (Table 
115),  or  rise  and  fall  (Table  124),  but  varies  with  the  length  of 
the  road  or  division,  inasmuch  as  the  ruling  grade  increases  the 
cost  of  operating  the  entire  road,  whatever  the  length  of  the  rul- 
ing grade  itself  may  be.  Hence,  to  obtain  the  true  value  of  re- 
ducing grade,  it  must  be  multiplied  by  the  length  of  the  road. 
It  may  appear  that  it  should  be  multiplied  by,  not  the  actual 
but,  the  equated  length,  according  to  pars.  195-9,  since  we  have 
there  seen  that  10  per  cent  more  distance  does  not  by  any 
means  add  10  per  cent  to  operating  expenses.  But  while  this 
view  is  in  a  sense  correct,  yet  the  items  w^hich  vary  with  a  change 
of  grade  vary  so  nearly  with  distance  likewise,  that  it  would  lead 
us  too  far  to  attempt  any  more  accurate  process  of  equating. 

726.  The  cost  per  year  in  Table  178,  divided  by  the  rate  of 
interest  on  capital,  0.06,  0.07,  etc.,  will  give  the  capitalized 
value  per  daily  train  of  avoiding  an  addition  of  o.i  per  cent  to 
the  ruling  grade.  Thus,  to  avoid  an  increase  of  o.i  per  cent  in 
a  i.o  ruling  grade,  at  6  per  cent  on  capital,  and  for  a  division  100 
miles  long,  we  have 

^^^  =  $48,873  per  daily  train, 


574  CHAP.  XV  — TRAIN-LOAD    ON  OPERATING  EXPENSES. 


Table  178. 

Estimated   Value  per   Daily   Train    of  Avoiding  an  Addition  of  0. 
Per  Cent  (5 .  28  Feet  Per  Mile)  to  the  Rate  of  any  Ruling  Grade. 

[Cost  per  train-mile  assumed  at  $1.00.] 


Per  Cent  of 
Increase  in 
Eng.  Mileage 
for  Each  o.i 

Per  Cent 

Added  to  the 

Grade  (from 

Table  171). 

Cost  Pep  Year  Per  O.I  Per 
Cent  Increase  in  Grade. 

Relative  No.  of 

Trains  to 

Haul  Same 

Trafi&c. 

Rate  of 

Grade  to 

BE  Changed. 

Per  Daily  Train 

=  Preceding 
Per  Cent 

X  $361.35 
X  100  Miles. 

Per  Tooo  Ton- 
Miles  Daily  of 
Cars  and   Load 

as  per 
Table  170. 

Relative 
Net  Load. 

Level 

25-9 

$9,359 

$17.50 

1. 00 

100.00  * 

0.1 
0.2 
0.3 

20.9 
17-5 
I5-I 

7,552 
6.353 
5.456 

17.77 
18.03 
18.23 

1.26 
I-52 
1.79 

79-44 
65.72 
55-93 

0.4 

0.5 
0.6 

13-3 
II. 9 
10.8 

4,806 
4,300 
3,903 

18.48 
18.75 
19.03 

2.06 

2.33 
2.61 

48.60 
42.88 
38.32 

0.7 
0.8 
0.9 

9.8 
9.2 

8.5 

3,541 
3.324 
3,072 

19-34 
19.74 
20.12 

2.89 

3.18 

3-47 

34.58 
31.48 
28.82 

I.O 

8.1 

2.927 

20.38 

3.76 

26.58 

1.2 
1.4 
1.6 

7.0 
6.3 

5.8 

2,530 
2,277 
2,096 

20.87 

21-43 
22.26 

4-37 
4-99 
5-63 

22.88 
20.04 
17.76 

1.8 
2.0 
2.2 

5.5 
5-1 
4.8 

1,987 
1,843 
1,734 

23.18 
24.26 
25.22 

6.29 
6.98 
7.69 

15.89 
14.32 
13.01 

2.4 
2.6 

2.8 

4.6 
4.4 
4.2 

1,662 
1.590 
1,518 

26.23 
27.22 

28.21 

8.41 
9.16 
9.94 

11.89 
10.92 
io.o6 

3-0 

4.0 

1,445 

29.02 

10.74 

9-31 

3-5 
4.0 
5-0 

3-6 
3-4 

3-2 

1,301 
1,229 
1,156 

31.42 

35- 10 
44-82 

12.92 
15.29 
20.74 

7.74 
6.55 
4.82 

Comparison  of  the  third  and  fourth  columns  will  show  that  while  the  cost 
per  daily  train  of  a  g:iven  increase  of  grade  is  much  less  on  the  higher  grades,  because 
the  number  of  trains  is  so  much  greater,  yet  that  the  cost  per  unit  of  traffic  is  gjeater  as 
the  grades  are  higher,  as  it  naturally  should  be. 


CHAP.  XV.—  TRAIN.LOAD   ON   OPERATING  EXPENSES.   575 

The  third  column  in  this  table  is  computed  for  a  division  ioo  miles 
LONG.  For  a  greater  or  less  length,  increase  in  direct  ratio  with  the  length.  Letting 
C  =  the  sum  thus  obtained,  we  have 

C  X  number  daily  trains  (each  way)  x  tenths  per  cent  of  change  of  grade  _ 
rate  of  interest  on  capital  (0.06,  0.07,  etc.)  ~ 

capitalized  value  of  any  increase  or  decrease  in  the  rate  of  the  given  ruling  grade,  approx- 
imately. For  greater  exactitude,  determine  the  correct  percentage  for  the  given  change 
of  grade  from  Table  171  ;  or,  for  still  greater  exactitude  compute  the  percentage  from  the 
train-loads  given  in  Table  170  for  the  two  given  grades  and  the  given  type  of  engine. 

The  fourth  column  is  independent  of  the  length  of  the  division,  and  may  be  de- 
duced from  the  third  column  by  dividing  it  by  the  total  weight  of  train  as  given  in  Table 
0:70,  X  200. 

or,  for  the  moderate  traffic  of  10  daily  trains  per  da}'  (each  way, 
in  all  cases),  $487,833. 

If  the  division  be  no,  i>b,  or  150  miles  long,  this  sum,  multi- 
plied by  1. 10,  1.20,  or  1.50,  will  give  the  capitalized  value,  as 
nearly  as  may  be.  If  the  change  in  grade  be  0.2  or  0.3  per  cent, 
the  capitalized  value  will  be  again  increased  in  proportion. 
Thus,  if  the  division  be  150  miles  long,  and  the  comparison  be 
between  a  i.o  and  1.5  grade,  we  have 

$487,833  X  1.5  X  5  =  $3,658,750 

as  the  approximate  justifiable  expenditure  for  avoiding  the  in- 
crease, for  10  trains  per  day  and  at  $1.00  per  train-mile.  For 
greater  exactness  see  note  to  Table  178,  above. 

727i  Several  recent  French  and  German  estimates  of  the  value  of  reducing 
grades  might  be  given,  which  do  not  differ  radically  from  the  preceding  except 
in  the  constants  assumed;  in  which  latter  respect  they  do  differ  radically. 
Table  179  gives  one  of  the  most  recent  and  most  nearly  correct  of  such  esti- 
mates. There  are  no  estimates  in  English  known  to  the  writer,  of  an  at  all 
reliable  character. 

72 8i  The  greatly  inferior  loads  hauled  on  foreign  railways  compared  with 
American  practice  is  conspicuously  brought  out  in  this  table.  An  American 
■engine  with  40  tons  on  the  drivers  will  haul  in  daily  practice  (Table  170), 

Tons.  Tonnes. 

On  a  0.5  grade, 1041  )  Against  French  (  487 

On  a  1.0  grade, 644  V         practice,        •]  274 

On  a  2.0  grade, 347  )    by  Table  179,    (  131 

The  French  loads  are  explicitly  stated  to  be  based  on  velocities  of  25  kilos. 
per  hour,  and  indicate  to  an  American  eye  very  bad  administration. 


57^  CHAP.  XV.^TRAIN-LOAD   ON  OPERATING  EXPENSES. 

Table  179. 
Estimate  of  the  Value  of  Reducing  Grades  on  French  Railways. 

[By  M.  Ricour,  Ing.  en  Chef,  Corps  des  Fonts  et  Chaussees.      Abstracted  from  the  paper 

referred  to  in  par.  662.] 


Grade. 

Gross  LoadI    Price  per 
C.           1  Train  Kilo. 
Tonnes.          Francs. 

i 

Price  per 

1000  tonnes  gross, 

per  Kilo. 

Francs. 

•4 

568                 1.546 

2.72           Diffs. 

•5 

487     !     1.465 

3 . 00              .28 

.6 

•7 
.8 
•9 

425         1.403 

375         :         1-353 
335                  1.313 
302                   1 .  280 

3-30               -3° 
3.60              ,30 

3-91               -31 
4.23               .32 

I.O 

274                  1-252 

4-56               .33 

1.2 
1.4 
1.6 
1.8 

230 
196 
169 
T47 

1.208 
1. 174 
1. 147 
1. 125 

5-25               .36 
5-98               .37 
6.78               .39 
7-65               .46 

2.0 

131          1         1. 109 

8.46               .43 

The  last  column  of  this  table  x  ii7-5  (1.61  X  0.20  X  365)  will  give  a  column  corre- 
sponding to  the  fourth  column  of  Table  178.  No  close  correspondence  can  be  expected, 
because  the  French  loads  are  so  much  less  and  decrease  so  much  more  rapidly  with  grade. 

This  table  was  computed  for  a  6-driver  engine,  36  tonnes  (39.67  tons)  on  drivers  ; 
mean  total  weight,  50  tonnes  (55.10  tons).  The  values  in  the  last  column  are  of  a  more 
general  character.  They  are  independent  of  the  weight  of  the  engine — at  least  within 
the  limits  of  usual  French  practice. 


THE    PROPORTION    OF     TRAFFIC    AFFECTED     BY    THE    RATE    OF 
RULING    GRADE. 

729.  According  to  the  character  of  the  road,  this  may  vary- 
under  certain  conceivable  circumstances  between  the  extreme 
limits  of  o  and  loo  per  cent,  for  both  passenger  and  freight 
traffic.  Freight  traffic  is  by  far  the  most  affected,  but  there  are 
at  least  occasional  instances  in  which  the  freight  traffic  is  so 
light  and  so  little  liable  to  grow  that  no  appreciable  value 
whatever  can  be  assigned  to  reduction  of  grades  below  a  cer- 
tain limit.  For,  as  the  whole  objection  to  gradients,  properly 
so  called,  lies  in  their  effect  to  limit  the  length   of  trains,  a   re- 


CHAP.  XV.—  TRAIN-LOAD   ON  OPERATING  EXPENSES.    577 

duction  of  their  rate  has  value  only  for  such  trains  as  they  do  in 
fact  so  limit.  One  train  at  least,  the  "  way  freight,"  is  very 
often  not  so  limited  on  all  railways,  and  many  minor  railways 
are  not  so  fortunate  as  to  run  anything  else  but  way  freights 
over  their  lines. 

730.  Nevertheless,  as  a  rule,  both  the  way  freight  and  all  other 
freight  trains  vary  in  length  directly  with  the  de-facto  gradients, 
and  should  be  assumed  to  do  so.  This  does  not  at  all  assume 
that  all  trains  will  be  fully  loaded,  for  that  is  not  a  practicable 
result,  but  simply  that  the  percentage  of  power  wasted  to 
power  utilized  will  be  sensibly  the  same  for  all  grades  and 
lengths  of  trains,  or  nearly  enough  so  for  all  practical  purposes. 
If  so,  it  necessarily  results  that  the  percentage  of  increase  in 
trains  will  be  much  the  .same,  whether  they  are  fully  loaded  or 
not. 

731.  As  respects  passenger  business  (see  par.  ^Z\  although 
it  is  much  less  directly  and  immediately  affected  by  a  change 
of  grade  than  freight  traffic,  because  of  the  higher  speed,  and 
the  large  surplus  of  motive-power  required  therefor  and  for 
stopping  and  starting,  yet  in  the  long-run,  whenever  the  pas- 
senger business  becomes  considerable  in  volume  or  largely  com- 
petitive, either  the  number  or  the  weight  of  passenger  engines 
must  be  materially  affected  by  the  rate  of  grade.  The  effect  in 
the  case  of  passenger  traffic  is  far  more  irregular,  but  not  there- 
fore the  less  certain.  A  train,  for  example,  might  haul  an  extra 
car  or  two  over  any  given  grades,  or  haul  the  same  cars  over  a 
heavier  grade,  as  well  as  not,  when  the  addition  of  yet  another 
car  to  the  train  of  say  ten  cars  might  require  it  to  be  cut  in  two, 
and  so  immediately  double  the  moiive-power  required  by  in- 
creasing the  load  hauled  only  ten  per  cent.  It  is  certain,  more- 
over, that,  whatever  the  margin  of  power  deemed  necessary  for 
emergencies,  if  we  reduce  our  grades  and  train  resistance  by 
any  fixed  amount,  the  weight  of  engines  may  always  be  re- 
duced, or  the  weight  of  train  increased,  in  the  same  proportion, 
and  yet  leave  the  same  margin  for  emergencies  or  anticipated 
growth  of  traffic  as  before,  however  much  or  little  that  may  be. 

37 


578    CHAP.  XV,— TRAIN-LOAD   ON  OPERATING  EXPENSES. 

Hence  a  reduction  of  ruling  grade  has  a  positive  and  present 
cash  value,  even  if  every  passenger  train  on  the  road  v^^ill  habit- 
ually run  light  for  an  indefinite  number  of  years. 

732.  But  this  value  will  be  but  small  when  the  passenger 
traffic  will  be  light  during  the  first  few  years  after  construction 
(par.  84)  or  when  the  traffic  is  not  exacting  as  respects  speed,  or 
both,  for  the  reason  that  the  effect  of  any  ordinary  increase  of 
grade,  not  sufficient  to  imply  pushers  for  passenger  as  well  as 
freight  trains,  may  frequently  be  eliminated  by  a  moderate  re- 
duction of  speed  between  stations.  The  limits  within  which 
this  is  certainly  and  readily  possible  may  be  determined  as 
follows  : 

733.  In  Table  180  are  given  the  grades  of  repose  for  various 
passenger  trains  at  various  speeds,  determined  from  the  com- 
puted resistances  in  pounds  per  ton  in  Table  166  by  simply 
dividing  them  by  twenty.  The  limits  of  ordinary  passenger 
trains  are  from,  four  to  twelve  cars,  but  the  table  extends  from 
no  cars  at  all  to  sixteen. 

These  so-called  "grades  of  repose"  (see  definition  in  par.  384) 
-are  grades  equivalent  to  the  addition  which  the  train  resist- 
ance makes  to  the  actual  plus  or  minus  grade  resistance.  Sub- 
tracting them  one  from  another,  as  is  done  in  Table  180  B,  we 

have  THE  AMOUNT  BY  WHICH  THE  GRADE  IS  IN    EFFECT  REDUCED  BY 

REDUCING  SPEED  bv  a  Certain  number  of  miles  per  hour.  If, 
then,  it  be  admissible  to  consider  the  speed  of  a  4-car  train  to 
be  reduced  from  thirty  miles  per  hour  to  fifteen  or  twenty  miles, 
we  can  (Table  181)  use  a  grade — 

0.19  -I-0.16  +0.13  =  0.48  per  cent, 

or  0.19  -|-  0.16  =  0.35  per  cent  higher  than  if  a  speed  of  thirty 
miles  per  hour  were  essential  on  the  grade  as  well  as  elsewhere. 
We  shall  shortly  see  (Table  183)  that  the  loss  of  time  in  so  do- 
ing is  less  than  is  often  supposed.  When  to  this  is  added  the 
relief  gained  by  momentum  if  the  foot  of  the  grade  can  be  ap- 
proached at  thirty  or  forty  or  fifty  miles  per  hour  (Table  118 
and  par.  408)    we  have  considerable  lee-way  in  respect  to  pas- 


CHAP.  XV.  —  TRAIN-LOAD   ON  OPERATING  EXPENSES,    5/9 


Table  180. 

Grades  of  Repose  for  Passenger  Trains  of  Various  Lengths  at 
Various  Speeds. 

[17  X  24  American  engine — cars  averaging  25  tons  each.    According  to  the  formulas  given 

in  Table  166.] 

[For  grades  of  repose  of  freight  trains,  see  Table  120.] 


Weight 
Tons. 

Grades  of  Repose,  Per  Cent,  for  Velocities  in  Miles  Per  Hour. 

Kind  of  Train. 

15 

20 

25 

30 

40 

50 

60 

70 

Engine  only 

"    and  2  cars.. 
"      "     4  cars.. 
"      "     Scars.. 
"      "  12  cars.. 
"      "  16  cars.. 

56 
112 

168 
280 
392 

504 

0.60 
0-4S 
0.40 
0.36 
0.34 
0-33 

0.88 
0.62 
0.52 
0.46 
0.42 
0.41 

1.24 
0.83 
0.69 
0.58 
0.53 
0.50 

1.69 
1.08 
0.88 

0.73 
0.65 
0.62 

2.81 
1.74 
1.38 
1. 10 
0.98 
0.91 

4.26 
2.58 
2.02 
I.S8 
1-39 
1.28 

6.03 
3.62 
2.81 
2.12 
1.89 
1.74 

8.12 
4.83 
3-74 
2.87 
2.49 
2.28 

Table  180  B. 

Increase  of  Grade  which  will  be  Compensated  for  by  a  Reduction 
OF  Train  Speed  from  each  of  those  given  in  Table    180    to   the 

NEXT   LOWER. 

[Deduced  by  subtracting  each  of  the  grades  of  repose  from  the  next  higher.] 


Reduction  of  Eq#ivalent  Grade  by  Reducing  Speed  from — 

Kind  of  Train. 

20  to  15 

25  io  20 

30  to  25 

40  to  30 

50  to  40 

60  to  50 

70  to  60 

Engine  only 

0.28 

0.46 

0.45 

1. 12 

I-4S 

1.77 

2.09 

"      and  2  cars. .. 

0.17 

0.21 

0.2s 

0.66 

0.84 

1.04 

I -.21 

"        "     4  cars... 

0.13 

0.16 

0.19 

0.50 

0.65 

0.78 

0.93 

"        "     Scars... 

O.IO 

0.12 

o.xS 

0.37 

0.48 

0.54 

0.75 

"        "   12  cars... 

0.08 

O.II 

0.12 

0.33 

0.41 

0.50 

0.60 

"        "  16  cars... 

0.08 

0.09 

0.12 

0.29 

0.37 

0.46 

0.54 

While  it  is  probable  that  these  differences  represent  somewhat  more  than  the  actual 
differences  in  the  resistance  to  be  overcome  (par.  655),  it  is  quite  certain  that  they  are  not 
nearly  large  enough  to  fully  represent  the  combined  effect  of  the  lower  resistance  and 
greater  cylinder  and  boiler  power  of  the  engine  at  lower  speeds  (par.  557). 


580   CHAP.  XV.— TRAIN-LOAD   ON  OPERATING  EXPENSES. 

senger  trains  before  certain  differences  of  grade  may  materially 
affect  them. 

734.  This  assumes  that  there  are  ho  stops  made  or  to  be  made  on  the  grade 
without  ample  reduction  of  grade  at  the  stopping  point,  the  train  which  can  be 
started  promptly  being  for  the  most  part  the  limiting  cause  to  the  length  of 
passenger  trains.  The  ultimate  limits  of  the  possibility  of  eliminating  the  effect 
of  grades  by  reduction  of  speed  must  be  determined  a  little  differently  from  the 
above,  and  may  be  more  appropriately  given  in  Chapter  XX. 

735.  Keeping  all  these  considerations  in  view,  the  effect  of 
change  of  grade  on  passenger  traffic  may  be  summarizes  as  fol- 
lows: 

For  roads  having  considerable  passenger  traffic,  say  over 
four  or  five  trains  per  day  each  way,  the  passenger  trains  will  be 
affected  essentially  as  freight  trains  are,  unless  the  ruliug  grades 
are  short  and  undulating,  and  the  estimated  number  of  each 
class  of  trains  should  be  added  together. 

For  roads  having  only  one  or  two  light  passenger  trains  per 
day  run  at  no  very  exacting  speed,  the  passenger  traffic  may 
not  be  affected  at  all  by  a  moderate  change  of  grade.  Whether 
it  is  likely  to  be  or  not,  must  be  determined  by  Tables  i8o  and 
i8i. 

For  such  ordinary  passenger  traffic  as  most  new  American 
roads  look  forward  to  in  the  near  future,  say  from  two  to  five 
trains  per  day,  half  the  estimated  number  of  passenger  trains 
may  be  added  to  the  freight,  for  estimating  the  value  of  reduc- 
ing grade,  for  the  reason  that  at  least  half  the  trains  are  liable 
to  be  affected  by  the  gradients. 

736.  The  tendency  to  increasing  luxury  in  first-class  passenger 
travel  has  been  already  alluded  to  in  par.  712.  An  opposite  ten- 
dency has  begun  to  show  itself,  which  will  tend  to  still  further 
increase  the  effect  of  grades  on  passenger  traffic — a  kind  of  third- 
class  traffic  carried  at  low  rates  but  in  large  numbers.  It  is 
probable  that  before  many  years  the  mutual  interests  of  the  rail- 
ways and  the  public  will  compel  a  large  extension  of  this  class  of 
traffic,  and  favorable  grades  for  passenger  service  will  then  be  a 
factor  of  great  importance. 

737.  As  an  example  of  the  great  comparative  importance  of 


CHAP.  XV.— RULING   GRADE  AND  MINOR  DETAILS.     58 1 

low  grades,  we  may  now  profitably  refer  back  to  Chap.  X.,  the 
assumptions  made  in  which  we  have  just  substantiated.  While 
such  estimates  as  are  here  made,  as  has  been  often  stated,  cannot 
be  regarded  as  positive  and  exact,  even  when  carefully  revised  to 
suit  individual  lines,  the  possible  margin  of  error  is  too  small  to 
seriously  modify,  if  corrected,  the  moral  which  they  are  calculated 
to  convey,  which  is  that  wrongly  directed  expenditure  is  at  the 
root  of  much  of  the  financial  difficulties  of  railways. 

In  the  example  referred  to  one  detail  of  occasional  importance 
has  been  neglected,  viz.: 


THE   EFFECT    OF   A    DIFFERENCE    IN    RULING    GRADE   ON    THE    COST    OF 
DISTANCE,   CURVATURE,  AND   RISE  AND    FALL. 

738.  While  we  have  seen  in  Chap.  X.  that  ordinarily,  when  two  lines 
differing  in  ruling  grade  are  to  be  compared,  the  importance  of  the  differ- 
ence in  gradients  and  in  traffic  advantages  combined  will  be  so  great  that 
such  differences  as  may  exist  in  any  or  all  the  minor  details  may  be  neg- 
lected without  affecting  the  decision,  yet  when  the  comparison  between 
two  lines  differing  in  ruling  grade  is  so  close  that  it  is  desirable  to 
determine  accurately  the  effect  of  differences  in  the  minor  details  also, 
the  difference  in  the  rate  of  the  ruling  grades  of  the  two  lines  makes  it 
necessary  to  treat  the  minor  details  somewhat  differently  from  merely 
subtracting  the  amount  of  distance,  curvature,  or  rise  and  fall  on  the  two 
lines  from  each  other,  and  computing  the  value  of  the  difference  only,  as 
we  have  done  heretofore. 

739.  Suppose  the  case  of  two  lines,  each  100  miles  long,  and  with  pre- 
cisely the  same  amount  of  curvature  and  rise  and  fall,  but  with  a  ruling 
grade  on  one  line  of  0.8  per  cent  and  on  the  other  of  1.6  per  cent.  It 
appears  at  first  sight  as  if  in  this  case,  whatever  the  amount  of  curvature 
or  rise  and  fall,  they  might  be  balanced  against  each  other  and  neglected  ; 
but  consideration  shows  this  to  be  so  far  untrue  that,  inasmuch  as  more 
trains  will  be  run  over  one  line  than  the  other,  the  cost  of  each  degree  of 
curvature  and  each  foot  of  distance  or  rise  and  fall  will  be  greater  on  one 
line  than  the  other,  so  that  the  line  having  the  heavier  gradients  will  be 
more  objectionable  in  proportion  to  the  amount  of  curvature  or  rise  and 
fall  which  there  fnay  be  on  both  lines  alike.  In  other  words,  just  as  there 
is  a  certain  cost  of  operating  each  train-mile  of  distance,  so  there  is  a 


582     CHAP.  XV.— RULING   GRADE  AND  MINOR  DETAILS. 

certain  cost  of  operating  what  we  may  call  each  train-degree  of  curvature 
and  each  train-foot  of  rise  and  fall. 

If,  therefore,  in  such  an  instance  as  that  supposed,  the  two  lines  had 
much  curvature  and  rise  and  fall,  the  money  value  in  favor  of  the  lower 
grade  would  be  considerably  greater  than  if  both  lines  alike  were  nearly 
straight  and  had  very  little  rise  and  fall. 

740.  This  difference  of  value  should  properly  find  expression  in  a 
different  assumed  cost  per  train-mile ;  and  in  estimating  the  value  of  a 
projected  improvement  to  a  line  already  in  operation  it  would  be  so  ex- 
pressed, since  the  curvature  and  rise  and  fall  would  already  have  had  its 
effect,  much  or  little  as  the  case  might  be,  to  increase  the  operating  ex- 
penses by  which  we  gauge  the  value  of  reducing  grade. 

But  in  the  case  of  a  new  road  we  have  not  this  advantage,  inasmuch 
as  we  cannot  foresee  the  exact  cost  of  each  item  of  operating  expense. 
The  most  feasible  method  therefore  for  approximating  to  what  we  really 
desire,  the  difference  in  operating  expenses  per  train-mile  on  the  two 
lines,  is  this: 

741.  First.  Estimate  the  cost  per  year  of  all  the  curvature  and  rise 
and  fall  on  the  low-grade  line  for  the  estimated  number  of  daily  trains, 
according  to  Tables  115  and  124. 

Secondly.  Make  the  same  estimate  for  all  the  curvature  and  rise  and 
fall  on  the  high-grade  line,  for  the  estimated  increased  number  of  trains 
required  to  handle  the  same  traffic,  as  determined  by  Tables  170, 171,  and 
178. 

Thirdly.  Subtract  one  from  the  other  for  the  net  difference. 

Similarly  for  any  difference  of  distance  :  If  the  high-grade  line  be  the 
longer,  the  cost  of  operating  the  extra  distance  on  the  high-grade  line 
must  be  estimated  for  the  number  of  trains  on  it ;  while  if  the  low-grade 
line  be  the  longer,  by  the  same  amount  the  cost  of  operating  the  extra 
distance  must  be  estimated  for  its  smaller  number  of  trains,  and  hence 
will  be  somewhat  smaller  than  for  a  similar  excess  on  the  high-grade 
line. 

742.  There  is  this  further  caution  :  Inasmuch  as  the  traffic,  and  hence 
number  of  cars  per  day  or  per  year,  is  supposed  to  be  the  same  by  either 
]'ne,  the  only  difference  being  that  shorter  trains  and  more  of  them  are 
run  over  the  high  grade,  the  same  cost  per  train-mile  cannot,  strictly 
speaking,  be  assumed  the  same  for  both  lines.  We  have  estimated  in 
Table  176  that  the  cost  of  doubling  the  number  of  trains  for  the  same 
traffic  is  49. 5  cts.  per  extra  train-mile,  or  49.5  per  cent  of  the  average  cost. 
For  a  change  of  grade  so  considerable  as  to  halve  the  number  of  cars  per 


CHAP.  XV.— RULING   GRADE  AND  MINOR  DETAILS.     583 

train,  therefore,  the  relative  cost  per  train-mile  in  the  two  lines  would  be 
as  1. 00  to  — '—,  or  I.  to  0.74,  and  proportionately  for  less  consider- 
able differences  of  grade.  In  other  words,  whatever  wear  and  tear  results 
from  the  number  of  cars  moved  over  the  line,  as  well  as  the  expense  of 
loading  and  billing  the  freight  in  them,  etc.,  is  unaffected  by  the  change 
of  grades.  Whatever  is  due  to  the  engine  increases  pro  rata  with  the 
number  of  trains. 

743.  For  still  another  reason  than  those  just  mentioned,  it  can 
rarely  be  essential  to  enter  into  minutely  accurate  calculations  as 
to  the  minor  details  to  decide  on  one  line  or  the  other.  When 
the  comparison  between  two  lines  becomes  so  close  that  it  would 
otherwise  be  necessary,  the  possible  effect  of  the  two  lines  on 
volume  of  traffic  ought  alone  to  outweigh  it,  and  the  prudent  rule 
becomes — 

1.  When  the  company  is  or  soon  may  be  poor  (and  it  is  no 
more  than  common  prudence  to  assume  that  it  will  be  embar- 
rassed for  means  at  some  time  in  the  near  future,  when  it  is  not 
backed  by  a  great  system  of  profitable  lines  in  operation),  take  the 
line  of  lowest  first  cost. 

2.  When  immunity  from  financial  embarrassment  is  assured, 
take  the  line  which  offers  the  most  promising  co7iditions  for  future 
growth  of  traffic. 

3.  Only  w^hen  the  two  lines  are  substantially  equal  in  both  these 
respects  enter  into  such  minute  calculations  as  these  just  sug- 
gested, and  whichever  line  be  selected  no  serious  harm  can  then 
result. 

744.  Having  determined  the  justifiable  expenditure  to  obtain 
low  grades,  we  have  only  taken  the  first  step  toward  their  proper 
adjustment.  Some  of  the  worst  sacrifices  of  gradients  are  made 
without  effecting  any  saving  of  cost  whatever,  simply  from  inat- 
tention to  its  importance,  or  from  attaching  exaggerated  impor- 
tance to  losses  of  distance  or  curvature,  or  from  insufficient  study 
of  the  topography,  leading  to  a  too  hasty  conclusion  that  all  has 
been  done  which  can  be  done,  when  in  fact  a  very  little  study 
would  lead  to  far  better  results.^ 

"  It  is  an  invidious  and  unpleasant  thing  to  say,  but  the  importance  of  the 


584    CHAP.  XV.— RULING   GRADE  AND  MINOR  DETAILS. 

, . ■ — •— • — 

This  question  of  how  to  get  the  lowest  grade  which  the  region 
admits  of,  at  a  given  cost,  is  discussed  in  Part  V.  and  Appendix  C. 
The  four  following  sub-departments  of  the  general  problem  of 
gradients  yet  remain  to  be  considered: 

1.  The  use  of  assistant  engines  with  high  "bunched"  grades. 

2.  The  balance  of  grades  for  unequal  traffic. 

3.  Limiting  curvature,  and  the  proper  compensation  therefor. 

4.  The  limit  of  maximum  curvature. 

These  questions  we  will  consider  in  their  order. 

caution  thereby  conveyed  seems  to  justify  saying  it:  Out  of  a  hundred  men 
putting  a  line  through  either  easy  or  difficult  country,  but  especially  through  easy 
country,  the  writer's  observation  is  that  all  but  four  or  five  of  them  will  adopt 
rates  of  grade  from  ten  to  fifty  or  even  a  hundred  per  cent  higher  than  the  other 
five  will  obtain  at  the  same  cost;  and  the  same  holds  true  as  to  amount  of  curva- 
ture. 


CHAP.  XVI.— ASSISTANT  ENGINES.  585 


CHAPTER   XVI. 

ASSISTANT     ENGINES. 

745.  The  general  use  of  assistant  engines,  commonly  called 
PUSHERS,  is  a  comparatively  modern  innovation.  So  recently  as 
1873,  Gen.  Herman  Haupt,*  in  a  paper  on  gradients,  felt  com- 
pelled to  say  that  he  was  making  "an  attempt  to  prove,  contrary 
to  the  generally  received  opinion,"  that  undulating  gradients 
below  the  limits  of  the  maximum  do  not  necessarily  increase  ex- 
penses materially,  and  "that  the  use  of  higher  gradients  for  part 
of  a  given  distance  will  often  result  in  greater  economy  of  opera- 
tion than  a  lower  and  uniform  gradient  for  the  whole  distance." 

This  statement  has  now  become  a  truism.  Driven  to  econ- 
omy by  the  necessities  of  competition,  the  use  of  assistant  en- 
gines, even  on  lines  ill  adapted  to  their  most  advantageous  use, 
has  become  very  general  in  recent  years  and  is  constantly  ex- 
tending, although  they  are  even  yet  not  used  on  more  than  a 
proportion  of  the  lines  which  might  use  them  with  advantage 
and  economy,  so  that  their  use  is  one  of  the  most  hopeful  direc- 
tions in  which  further  economy  may  be  sought,  especially  on 
low-grade  lines,  where  the  trains  hauled  even  by  one  engine  are 
of  fairly  profitable  length,  but  might  be  readily  increased  by 
help  at  a  few  points. 

What  has  been  accomplished,  however,  is  that  whereas  assist- 
ant engines  were  formerly  used  only  in  exceptional  instances  on 
very  heavy  grades,  their  use  has  now  multiplied  many-fold,  and 
the  expediency  of  using  them  when  possible,  even  at  quite  fre- 
quent intervals,  is  universally  admitted  by  skilled  railway  offi- 
cers. Some  of  our  earliest  and  greatest  engineers,  as  notably 
the  engineers  of  the  Baltimore  &  Ohio,  Pennsylvania,  and  Erie 
railways,  distinctly  contemplated  the  use  of  pushers  and  adapted 
*  See  Railroad  Gazette,  July  5,  1S73, 


586  CHAP,  XVI.— ASSISTANT  ENGINES. 

their  lines  thereto;  no  doubt  in  part  because  of  the  topo- 
graphical conditions  in  passing  the  AUeghanies,  but  in  part  also 
because  of  the  singular  foresight  and  sagacity  which  the  great 
engineers  who  laid  out  those  lines  showed  in  many  ways.  But 
these  precedents  have  not  been  generally  recognized  as  estab- 
lishing a  general  principle  until  very  recently,  nor  can  it  be  said 
to  be  yet  established  as  fully  as  it  should  be. 

746,  The  presumption  is  strong  in  laying  out  every  line,  that 
advantage  can  be  derived  from  laying  out  the  grades  for  the 
use  of  assistant  engines,  because  of  the  fact  that  topographical 
conditions  always  require  more  or  less  irregularity  of  gradients. 
The  usual  law  is  that  the  grades  will  be  for  long  distances  very 
low  and  easy,  or  can  be  made  so  at  slight  cost,  but  that  for 
much  shorter  distances  much  higher  gradients  will  be  unavoid- 
able. By  adapting  the  line  to  the  use  of  assistant  engines  on 
these  higher  grades  we  are  enabled  to  utilize  the  full  advantage 
of  the  lower  grades,  by  making  up  our  trains  to  correspond  to 
them,  so  that  long  trains  can  be  handled  over  the  entire  line  by  a 
single  crew,  without  breaking  it  up  into  sections,  and  the  full 
power  of  the  motive-power  actually  in  use  at  all  points  on  the 
line  be  more  nearly  utilized. 

747.  The  adoption  of  the  opposite  policy,  attempting  to  get  a 
line  of  a  low  uniform  gradient  through  a  country  of  any  diffi- 
culty whatever,  is  very  apt  to  be  enormously  expensive,  and  to 
be  possible  at  all  only  by  frequent  undulations,  considerable  de- 
tours, and  much  higher  gradients  over  most  of  the  line  than 
than  there  is  any  necessity  for  using.  This  results  from  the  fact 
that  it  sets  at  defiance  one  of  the  broadest  and  most  nearly 
universal  laws  of  physical  geography, — to  which  there  are  few 
and  rare  exceptions  on  the  whole  face  of  the  globe, — that  long 
stretches  of  easy  plains  or  gently  sloping  valleys  penetrate  at 
intervals  to  and  into  the  very  heart  of  even  the  roughest  regions, 
leaving  short  sections  only  over  which  high  gradients  are  un- 
avoidable. By  following  these  easy  routes  as  long  as  we  can  we 
accomplish  over  most  of  our  line  three  desirable  ends  at  once: 

1.  We  get  the  cheapest  line. 

2.  We  get  the  lowest  through  grades  ;  and. 


CHAP.  XVI.— ASSISTANT  ENGINES. 


587 


3.  More  than  all  else,  we  concentrate  the  resistances  into 
the  remaining  more  difficult  section,  so  that  the  motive-power  on 
it  can  be  accurately  adapted  to  the  work  required  and  kept  fully 
at  work  over  the  distance  where  it  is  used,  thus  making  it  almost 


Fig.  175 


Table  181. 

Comparative  Work  accomplished  by  an  Engine  in  running  100  Miles 
FROM  X  TO  Y,  Fig.  175,  and  making  a  Rise  of  2640  Feet  thereon  over 
THE  Various  Grades  shown. 


Line, 
Fig.  175. 

Distance 
Miles. 

Grade  p.c. 

Net  Load. 

Tons. 

Net 
Load. 
Tons. 

Total  Ton-Miles 
Hauled  by  one  Trip 
of  Through  Engine. 

Total  Engine- 
Miles  to  Haul 
2675  Tons  100 
Miles. 

Per  Cent 
of  Effici- 
ency. 

A 

B 

C 

D 

E 

100 

i     50 
i     50 

1    33i 
i    75 
]    25 
j    80 
\    20 

0.5 
Level. 

1.0 
Level. 

1-5 
Level. 

2.0 
Level. 

2.5 

II47 
2675 

711 
2675 

504 
2675 

383 
2675 

304 

114,700 

'^^;^-^a,..5o 

214.000                ^„ Q^ 

t  ^0^    f  220,080 

6,080 

233 

100. 0 

102. 1 

104.7 
106.4 
109.9 

The  fifth  column  indicates  that  a  single  through  engine,  which  drops  cars  to  corre- 
spond to  its  hauling  capacity  at  the  foot  of  the  grades  B,  C,  D,  E,  Fig.  175,  will  make 
vastly  more  ton-miles  on  the  high  grades  than  the  low.  This,  however,  is  unfair.  The 
true  test  is  :  Hozu  much  motive-power  will  it  take  to  carry  a  whole  train-load^  or  a  thou- 
sand train-loads,  through,  the  tj^Dical  train  weighing  by  assumption  above  2675  tons.  The 
two  last  columns  show  that,  from  this  more  correct  point  of  view,  there  is  a  certain  dis- 
advantage in  the  higher  grades,  but  a  most  trifling  one,  so  long  as  the  resistances  are 
concentrated^  so  that  engines  can  be  at  all  times  fully  loaded.  But  if  scattered,  so  that  it 
is  necessary  to  run  short  trains  from  X  TO  F,  because  of  the  occasional  steep  grades,  the 
disadvantage  becomes  enormous. 


588 


CHAP.  XVI,— ASSISTANT  ENGINES. 


a  matter  of  indifference  what  rate  of  ascent  we  adopt  on  our 
more  difficult  sections — a  fact  which  powerfully  tends  to  still 
further  reduce  the  cost  of  construction  over  those  more  difficult 
sections.  Table  i8i  and  Fig.  175  illustrate  fully  how  and  why 
this  advantage  arises,  and  should  be  carefully  studied. 

748.  Even  where  we  are  unable  for  any  reason  to  follow  the 
valley  lines  which  usually  penetrate  far  into  hilly  or  mountainous 
regions,  as  for  instance  when  the  valleys  are  impracticable,  or  are 
less  practicable  than  the  ridges,  it  is  still  true  that  pusher  gradi- 
ents will  almost  invariably  fit  the  country  better.     The  all  but 

universal  law  of  topography 
B^^-~^_  is  that,   when  the  ground  is 

not  a  dead  level,  transitions 
from  one  level  to  another, 
whether  on  a  large  scale  or  on 
a  small  scale,  are  of  the  form 
shown  in  Figs.  176  and  177.  If  on  a  small  scale,  we  may  simply 
adopt  the  dotted  profile  AB,  and  make  the  fill  at  C  or  cut  at  B.  If 
on  a  larger  scale,  say  for  a  total  rise  of  50  or  60  or  80  feet,  it  be- 
comes impossible  to  do  this,  especially  if  the  necessity  occurs  at 
many  points,  and  we  are  reduced  to  adopting  the  profile  ACB, 
making  BC  the  ruling  grade  of  the  line,  or  else  to  one  of  the  two 
expedients  shown  in  plan  in  Fig.  177 — either  to  run  right  over 
^  the  obstruction  with  almost  a 

tangent  line,  giving  the  dotted 
profile  AB,  in  Fig.  178,  or  to 
sacrifice  curvature  and  dis- 
tance and  obtain  the  full-line 
profile.  The  first  has  been 
done  to  a  most  unfortunate 
extent  in  the  prairie-lines  of 
the  West  ;  the  last  is  almost 
always  the  proper  course,  if  it 
saves  an  increase  of  ruling 
grade,  even  when  necessary  at 
many  points  on  the  line. 

749.  But  when  the  rise  to  be  overcome  becomes  more  consid- 


'^vf  '%\rf 


CHAP.  XVI.— ASSISTANT  ENGINES.  589 

erable,  as  100  or  200  feet,  even  this  course  is  rarely  convenient. 
To  obtain  an  equivalent  for  the  full  line  AB,  Fig.  177,  we  are 
then  compelled,  usually,  to  adopt  a  costly  line  hanging  upon  the 
slopes  of  such  supporting  ground  as  can  be  had  in  order  to  ob- 
tain the  dotted  profile  AB,  Fig.  176,  or  the  solid-line  profile  AB, 
Fig.  178.  When  we  have  got  it — assuming  that  we  can  and  do 
get  it — we  have  even  then,  in  all  probability,  been  compelled  to 
use  a  higher  grade  than  it  is  at  all  necessary  to  use  on  the  re- 
maining and  easier  portions  of  the  line.  If  so,  we  have  not  only 
spent  a  great  deal  of  money  where  we  have  difficulties,  but  have 
injured  our  line  where  we  have  no  difficulties. 

750.  The  alternative  is  to  treat  the  difficult  ground  as  a  sep- 
arate feature  ;  to  maintain  the  lowest  grades  we  can,  on  the 
ground  where  we  have  no  difficulties  ;  to  push  these  low  grades 
as  far  as  possible  to  some  point  C,  Fig.  176,  as  near  as  may  be  to 
the  rise;  and  then  to  adopt  some  entirely  different  and  much 
higher  grade  BC,  conforming  as  closely  as  possible  to  the  natu- 
ral surface,  with  a  view  of  using  auxiliary  power  or  "pushers" 
on  it,  thus  not  only  saving  our  money  on  the  parts  of  the  line 
which  are  naturally  most  costly,  but  retaining  all  our  natural 
advantages  elsewhere  which  cost  us  nothing. 

751.  In  other  words,  the  secret  of  the  vast  economies  which 
may  often  be  realized  by  the  skilful  use  of  assistant  engines  is 
this — that  as  respects  construction  we  work  with  Nature  instead 
of  against  her,  and  that  as  respects  operation  we  gain  a  like  ad- 
vantage by  keeping  every  engine  while  running  fully  at  work, 
the  greater  portion  of  the  hard  work  in  foot-pounds  being  done 
on  a  small  portion  of  the  division,  with  such  favorable  through 
grades,  in  many  cases,  that  there  is  little  more  need  for  an  en- 
gine on  the  remainder  of  it,  than  to  keep  the  longest  trains 
moving  and  under  control.  It  is  a  truth  of  the  first  impor- 
tance, that  the  objection  to  high  gradients  is  not  the  work  which 
engines  have  to  do  on  them  (see  Table  181),  but  it  is  the  work 
which  they  do  not  do  when  they  are  thundering  over  the  track 
with  a  light  train  behind  them,  from  end  to  end  of  a  divi- 
sion, in  order  that  the  needed  power  may  be  at  hand  at  a  few 


590  CHAP,  XVI.— ASSISTANT  ENGINES. 

scattered  points  where  alone  it  is  needed.  But  if  we  may  give 
this  additional  motive-power  its  work  to  do  once  for  all,  and 
have  done  with  it,  high  summits  cost  very  little,  and  an  increase 
of  the  rate  of  grade  costs,  practically,  nothing  whatever.  At  the 
points  of  greatest  difficulty  we  are  independent  of  the  rate  of 
ascent  and  in  a  great  degree  of  the  elevation  attained,  and  are 
therefore  at  liberty  to  concentrate  our  efforts  and  expenditure  on 
the  more  tractable  portions  of  the  line,  where  a  few  feet  per 
mile  reduction  in  grade  (see  Table  170  and  Fig.  169)  may  be  of 
enormous  value. 

752.  In  this  way  it  is  in  every  way  practicable  to  secure  lines 
over  tolerably  high  summits  and  through  difficult  country  which 
shall  approximate  closely  in  operating  value  to  the  most  favor- 
able existing  examples  of  low-grade  lines.  On  the  other  hand, 
BY  SEEKING  FOR  WHAT  WE  DO  NOT  REQUIRE,  by  defying  the  ob- 
stacles of  nature  and  forcing  them  to  conform  throughout  to  the 
Procrustean  standard  of  a  uniform  ruling  gradient,  we  shall 
enormously  increase  the  cost  of  construction,  and  in  the  end  find 
that  we  have  a  far  more  costly  line  to  operate  than  if  we  had 
"stooped  to  conquer"  by  boldly  conforming  to  the  topographical 
conditions  and  then  skilfully  forcing  them  to  serve  our  purpose. 
This  goes  so  far  that  it  is  true  policy  in  very  many  instances  in 
difficult  country  to  make  boldly  for  the  "meeting  of  the  waters" 
at  the  summit,  even  at  the  cost  of  a  higher  summit,  rather  than 
to  zigzag  up  and  down  and  from  side  to  side  in  a  costly  effort  to 
avoid  a  continuous  succession  of  transverse  valleys  and  other 
petty  obstacles,  each  of  which  has  us  at  great  disadvantage. 

753.  The  advantage  of  the  use  of  pusher  grades  are  not  at  all 
confined  to  high  grades,  but  on  the  contrary  are  even  greater 
proportionately  for  low  grades,  provided  only  that  there  be 
business  enough  to  fill  up  the  trains,  and  couplings  good  enough 
to  permit  of  handling  long  trains.  On  roads  of  light  and  irregu- 
lar traffic  there  may  be  no  great  advantage  in  them;  but  many 
roads  having  large  traffic,  which  must  be  hauled  cheaply  because 
it  pays  little,  are  habitually  using  pushers  on  gradients  as  low  as 
0.5  to  0.6  per  cent.     For  example,  freight  pushers  are  used  on  the 


CHAP.  XVI,— ASSISTANT  ENGINES— POWER   OF. 


591 


Hudson  River  Railroad,  nearly  95  per  cent  of  which  is  a  dead 
level,  and  the  remainder  over  summits  a  few  feet  high  on  0.4  to 
0.5  grades. 

THE   POWER  OF  ASSISTANT   ENGINES. 

754.  By  the  use  of  assistant  engines  the  available  motive-power  is  ap- 
proximately doubled  or  trebled ;  and  it  is  evident  that  economy  in  motive- 
power  requires  that  the  rates  of  these  grades  should  be  proportioned  to 
each  other  as  nearly  as  possible,  in  order  that  neither  grade  may  be  dis- 
portionately  low,  but  that  the  true  ruling  grade  m.aybe — not  necessarily 
either  the  higher  (pusher)  grade  or  the  lower  grade,  but  that  one  which 
involves  most  difficulty  and  expense  in  reduction. 

With  certain  provisos  which  we  will  shortly  consider,  the  determina- 
tion of  a  practically  exact  balance  of  gradients  for  the  use  of  one  or  more 
assistant  engines  is  a  simple  matter.  If  the  assistant  engine  be  of  the 
same  weight  as  the  through  engine,  the  load  to  be  hauled  by  each  en- 
gine is  reduced  one  half.  If  there  be  two  pushers,  the  load  to  be  hauled 
by  each  engine  is  reduced  to  one  third  of  what  it  was.  If  the  pusher 
have,  say,  10  or  20  per  cent  more  tractive  power  than  the  through  engine, 
the  train  is  in  effect  cut  into  two  unequal  parts,  that  remaining  to  the 

i.e.,  47.6  or  45.5  per  cent 


i.o 


through  engine  bemg  T^^TTTTo'  °'  i.o  +  1.20' 
of  the  original  weight  of  the  train  behind  tender.  The  grade  on  which 
the  through  engine  can  haul  that  per  cent  of  its  load  on  a  given  through 
grade  will  therefore  be  the  corresponding  pusher  grade  for  pusher  en- 
gines of  such  weight. 

755.  By  the  aid  of  the  long  Table  170,  the  process  of  determining 
such  pusher  grades  for  any  through  grade  is  made  one  of  mere  inspec- 
tion, as  practical  convenience  requires.  For  example,  to  determine  the 
pusher  grades  corresponding  to  through  grades  of  0.5  percent,  we  have — 


Light 
American. 

Averag-e 
Consolidation. 

Net  load  behind  tender,  on  0. 5  grade 

504  tons. 

252      " 
1.24  per  cent. 

241  tons. 
1. 31  per  cent. 

229  tons. 
1.38  per  cent. 

168  tons. 
1.87  per  cent. 

II47  tons. 

573i  '' 
1.30  per  cent. 

550  tons. 
1.36  per  cent. 

522  tons. 
1.44  per  cent. 

382  tons. 
2.00  per  cent. 

Half  of  which  is 

Corresponding  pusher  grades 

■|-^  of  load,  for  pushers  10  p.  c.  heavier,  is 

Corresponding  pusher  grades 

Il"  of  load,  for  pushers  20  p.  c.  heavier,  is 

Corresponding  pusher  grades     .  .        

\  of  load,  for  2  pushers  of  equal  weight 

Corresponding  pusher  grades 

592         CHAP.  XVI.— ASSISTANT  ENGINES— POWER   OE. 

From  these  examples  it  will  be  seen  that  differences  in  type  of  en- 
gine make  no  considerable  difference  in  the  balance  of  grades,  and  we 
shall  hereafter  consider  the  average  Consolidation  type  only. 

756.  If  the  pusher  were  a  tank  engine  having  no  tender,  it  in  effect 
adds  the  weight  of  the  tender  to  the  train  hauled  by  the  pusher  ;  so  that 
to  make  the  preceding  calculation  we  should  first  have  to  subtract  the 
weight  of  tender  thus  saved  from  the  total  weight  of  train,  and  then  di- 
vide the  remainder  only  between  the  through  and  pusher  engines,  in  the 
above  proportion,  which  would  increase  the  rate  of  the  admissible 
pusher  grades  materially. 

In  this  manner  Table  182  was  computed,  which  gives  the  proper  bal- 
ance of  grades  for  an  ordinary  Consolidation,  or  practically  for  any  other 
engine,  except  tank  engines,  which  are  separately  noted. 

757.  The  requirements  of  the  passenger  service  naturally  favor  the 
adoption  of  higher  through  grades  rather  than  pusher  grades,  since  un- 
dulating gradients,  however  steep,  have  little  effect  to  impede  hauling 
any  trains  ordinarily  desired,  when  the  rise  on  a  single  grade  is  not  great- 
Owing  to  the  decrease  of  train  resistance  at  slow  speeds  (Table  166) 
and  the  simultaneous  increase  in  the  tractive  power  of  the  cylinders,  the 
limit  at  which  a  high  and  long  grade  can  certainly  be  operated  without 
a  pusher  is  still  further  increased.  The  ultimate  limit  for  the  operation 
of  a  pusher  grade  by  a  single  engine  in  passenger  service,  beyond  which 
pushers  must  be  used  for  passenger  as  well  as  freight  trains,  may  be  de- 
termined as  follows : 

The  most  that  would  be  demanded  of  an  ordinary  17  x  24  passenger 
engine,  weighing  with  tender  56  tons,  more  or  less,  such  as  is  assumed 
in  the  table  of  train  resistance  (Table  166),  is  that  it  should  haul — as  an 
average  of  a  whole  division  and  every  day  in  the  year,  and  not  for  excep- 
tional performances, — 

4  cars,  or  168  tons,  8  cars,  or  280  tons,  12  cars,  or  392  tons, 
gross  weight  of  train.  gross  weight  of  train.  gross  weight  of  train. 
At  60  miles  per  hour  maxi-  At  50  miles  per  hour  maxi-  At  35  miles  per  hour  maxi- 
mum speed  on  a  level.  mum  speed  on  a  level.  mum  speed  on  a  level. 

758.  Now  the  tractive  power  which  such  an  engine  is  capable  of  exert- 
ing in  every-day  practice  at  freight  speeds  of  15  miles  per  hour  would  be 
nearly  if  not  quite  10,000  lbs.,  there  being  from  40,000  to  44,000  lbs.  on 
the  drivers.  Therefore  the  engine  will  be  capable  of  exerting  a  maxi- 
mum tractive  force  on  these  trains,  at  freight  speeds  of  about  15  miles 
per  hour  of  10,000  lbs.  -5-  the  weight  in  tons,  or 

59.5  lbs.  per  ton,  35.7  lbs.  per  ton,  25.5  lbs.  per  ton. 


CHAP.  XVI.— ASSISTANT  ENGINES— POWER   OF. 


593 


Table  182. 
Balance  of  Grades  for  the  Use  of  Assistant  Engines. 

[Correct  within  an  unimportant  percentage  for  all  classes  of  engines  and  conditions  of 
service,  the  through  and  pusher  engines  having  the  same  weight  and  tractive  power.] 


Net  Load 

Grade  up  which  the  same  Train 

CAN  BE  Hauled 

Through-Grade 

(Tons) 

BY  THE  Aid  of— 

WORKED 

for  Average 
Consolidation. 

BY  ONE  Engine. 

One  Pusher. 

Two  Pushers, 

Three  Pushers. 

Level. 

2675 

.38 

.74 

1.08 

•05 

2370 

.47 

.87 

1.25 

.10 

2125 

.57 

1. 00 

1. 41 

•15 

1936 

.66 

I-I3 

1-57 

.20 

1758 

.75 

1.26 

1.74 

.25 

1618 

.84 

1-39 

1.89 

•30 

1496 

•94 

1.52 

2.05 

.35 

1392 

1.03 

1.64 

2.20 

.40 

1300 

1. 12 

1.76 

2.35 

■45 

1220  — 

1. 21 

1.88 

2.49 

■50 

II47 

1^30 

2.01 

2.64 

.60 

1025 

1.47 

2.24 

2.92 

.70 

925 

1.65 

2.47 

3.20 

.80 

842 

1.82 

2.69 

3-45 

.90 

771 

1.99 

2.91 

3-70 

I. GO 

711 

2.16 

3-13 

3-95 

I.  ID 

658 

2.32 

3.33 

4.20 

1.20 

612 

2.48 

3-55 

4.42 

1.30 

572 

2,64 

3-73 

4-65 

1.40 

536 

2.81 

3-93 

4.87 

1.50 

504 

2.96 

4.13 

5-07 

1.60 

475 

3-13 

4.32 

5-27 

1.80 

425 

3.43 

4.68 

5.68 

2.00 

383 

3-72 

5.03 

6,04 

2.20 

348 

4.01 

5.35 

6.40 

■     2    40 

318 

4-30 

5.67 

6.73 

2.60 

292 

4-57 

6.00 

7.05 

2.80 

269 

4.86 

6.30 

7-34 

3  00 

249 

5-10 

6.58 

7.63 

If  we  assume  \  instead  of  \  adhesion,  we  simply  reduce  the  tractive  power  of  an 
average  Consolidation  (Table  170)  from  10  tons  to  8  tons.  The  ratio  of  the  gross 
weights  of  trains  on  various  grades  remains  unchanged,  and  the  ratio  of  the  weight 
behind  tender  would  remain  so  likewise  if  the  gross  weight  of  engine  were  reduced  one 
fifth,  or  by  15  tons.  As  it  is  not,  the  column  headed  8.0  tons  tractive  power  in  Table  170 
should  be  II  tons  greater  to  give  the  net  loads,  and  we  find  the  pusher  grades  to  be — 
38 


594 


CHAP.  XVI.— ASSISTANT  ENGINES— POWER   OF. 


If  we  allow  8  lbs.  per  ton  for  tractive  friction,  and  divide  the  remainder, 
which  is  admissible  as  grade  resistance,  by  20  (par.  682),  we  have  as  the 
grades  on  which  these  passenger  trains  can  be  handled,  by  reducing 
speed  to  15  miles  per  hour, 

2.57  per  cent,  1.38  per  cent,  .875  per  cent. 

On  any  grade  up  to  these  limits,  the  trains  which  such  an  engine 
can  be  expected  to  handle  in  every-day  practice  will  be  readily  handled 
at  the  lower  speed  of  15  miles  per  hour,  if  it  is  possible  to  stand  the  loss 
of  time  thereby.  When  Mogul  or  ten-wheel  engines  are  used,  as  they 
usually  would  have  to  be  for  regular  trains  so  long  as  12  cars,  the  limits 
will  be  considerably  higher ;  so  that  we  may  say  in  a  general  way,  that 
grades  up  to  li,  or  i^,  or  even  2  per  cent,  are  not  a  serious  obstruction  to 
light  passenger  business,  except  m  loss  of  time.  If  pushers  are  used 
below  the  limits  indicated,  it  is  only  for  urgent  necessit}^  to  keep  up 
speed,  as  on  fast  through  expresses. 

759.  The  loss  of  time  involved  in  such  checking  of  passenger  speed 
is  much  less  than  is  sometimes  hastily  imagined.  Table  183  gives  its 
exact  limits,  from  which  it  will  be  seen  that  a  reduction  of  speed  from 
40  to  20  miles  per  hour,  for  example,  loses  but  i-J-  minutes  per  mile,  or  15 
minutes  on  an  incline  10  miles  long.     As  the  speed  is  higher  the  loss  of 

, Pusher  grades  for  adhesion  of > 

Through  grade  for  one  engine.  1-4.  1-5.  Difference. 

Level 0.38  0.37  o.oi 

i.o 2.16  2.08  0.08 

2.0 3.72  3.52  0.20 

30 5-IO  4.7s  0.35 

A  loiver  rolling-friction  than  8  lbs.  reduces  the  rate  of  pusher  grades  about  0.08  per 
cent  on  a  level  grade,  decreasing  to  0.04  at  a  2  per  cent  grade. 

For  assistant  engines  heavier  than  the  through  engines,  add  the  following  to  the 
above  grades  : 


Through  Grade. 

One  Assistant  Engine 
heavier  by— 

Two  Assistant  Engines 

HEAVIER   BY— 

10  p.  c. 

20  p.  c. 

30  p.  c. 

10  p.  C. 

20  p.  c. 

30  p.  c. 

Level 

•03 
.07 

.10 

.12 

.07 
.14 
.20 
.24 

.11 

.22 

•31 

.37 

.07 
.13 

.20 

.14 
.26 

•34 
.40 

.22 

1. 00 ■ 

I.  so 

•39 
•51 
.60 

2 .  00 

It  is  rarely  proper  to  assume  that  the  assistant  engines  will  be  of  greater  power  than 
the  through  engines.  Two  pushers  can  only  be  assumed  to  be  used  with  a  large  traffic 
or  very  heavy  grades,  and  three  pushers  only  with  the  very  largest  traffic. 


CHAP.  XVI,— ASSISTANT  ENGINES— POWER   OF. 


595 


time  becomes  very  much  less,  while  the  gain  of  power  becomes  very- 
much  greater — a  condition  which  goes  far  to  justify  counting  on  this  re- 
source for  all  classes  of  passenger  trains,  within  reasonable  limits. 

Table  183. 

Loss  OF  Time  in  Minutes  Per  Mile  due  to  a  Decrease  of  Speed  of 

Trains. 
The  table  gives  the  loss  of  time  per  mile  in  minutes  per  mile  in  the  column  headed  by 
the  given  higher  speed  opposite  the  given  lower  speed  to  which  the  speed  is  decreased. 


Lower  Speed. 

Higher  Speeds— Miles  Per  Hour. 

Miles      Minutes 

15 

20 

25 

30 

35 

40 

45 

50 

55 

60 

Per           Per 
Hour.       Mile. 

TiMI 

:  Lost  I 

'er  Mili 

:;   MiNU 

PES. 

lo              6.0 
15              4.0 
20              3.00 
25              2.4 

•30                        2.0 

2.0 

3-0 

I.O 

3.6 
1.6 
0.6 

4.0 
2.0 
1.0 
0.4 

4.29 
2.29 
1.29 
0.69 
0.29 

4-5 
2.5 
1-5 

0.9 

0.5 
0.2 

4.67 
2.67 
1.67 
1.07 
0.67 
0.38 
0.17 

4.83 
2.83 
1.83 
1.23 
0.83 

0-S4 
0-33 
0.16 

4.91 
2.91 
1. 91 

I-3I 
0.91 
0.62 
0.41 
0.24 
0.08 

5-0 
3-0 

1.4 

1.0 

0.71 

0.5 

0-33 

0.17 

0.09 

35               I-7I 
40               1.5 

45               1-33 
50               1.17 
55               1-09 

It  will  be  seen  that  the  amount  of  time  lost  by  considerable  reductions  of  high  speeds 
is  less  than  by  very  slight  reductions  of  speeds  below  30  miles  per  hour,  while  the  gain  in 
train  resistance  is  very  much  greater  at  high  speeds. 

The  fast  New  York  Central  Limited  Express,  which  makes  the  run  of  970  miles 
between  New  York  and  Chicago  in  24h.  5m.,  with  only  eight  regular  stops,  none  of  them 
for  meals,  loses  55  minutes  in  these  stops  alone.  Including  all  slowing  up  through  towns 
and  yards,  stops  at  crossings,  etc. ,  not  less  than  3  hours  of  the  24  are  lost  in  this  way,  or 
about  0.2  minutes  per  mile,  equivalent  to  an  average  reduction  of  5  miles  per  hour  in  speed. 
With  most  fast  trains  the  loss  would  be  more  than  double  this. 


760.  On  the  New  York,  Lake  Erie  &  Western  Railroad,  having  several  long 
maximum  grades  of  60  feet  per  mile  (r.14  per  cent),  passenger  pushers  are  used 
only  by  the  very  heavy  through  express  trains.  At  Altoona,  on  the  Pennsylva- 
nia Railroad,  at  the  foot  of  the  gS-ft.  grade  (1.61  per  cent),  pushers  are  used  for 
nearly  all  passenger  trains,  but  nearly  all  are  heavy  trains.  The  local  accom- 
modation trains,  consisting  of  4  to  6  ordinary  day  coaches  and  baggage  cars, 
use  no  pushers.  About  30  miles  per  hour  is  made  by  the  passenger  trains 
using  pushers  up  the  mountains.  Except  for  the  requirement  of  making  this 
speed,  many  of  the  passenger  trains  could  dispense  with  pushers,  although  the 


596         CHAP.  XVI.— ASSISTANT  ENGINES— POWER   OF. 

heavier  through  expresses,  consisting  of  6  to  8  cars,  each  averaging  over  25 
tons,  would  find  difficulty  in  ascending  the  mountain  without  an  assistant  en- 
gine even  at  very  slow  speed. 

On  the  Middle  Division,  having  very  easy  grades,  not  over  16  ft.  per  mile 
at  any  point,  as  many  as  12  heavy  cars,  but  not  more,  are  hauled  by  a  single 
passenger  engine,  making,  however,  even  with  this  train,  high  average  speeds. 
Similar  trains  are  hauled  over  the  New  York  Central  road  for  the  entire  dis- 
tance from  New  York  to  Buffalo,  except  that  a  pusher  is  used  for  the  grade  of 
about  1.5  per  cent  at  Albany. 

761.  Except  within  the  limits  above  noted,  passenger  trains  as  well 
as  freight  must  be  assumed  to  require  pushers.  The  more  certain  it  is 
that  high  speed  will  be  required  at  all  points,  the  more  likely  they  are 
to  be  required  ;  and  wherever  it  appears  likely  that  the  passenger  traffic 
will  be  important  and  competitive,  it  may,  for  moderately  prosperous 
road,  be  giving  no  more  than  due  weight  to  the  great  and  permanent 
value  of  easy  gradients  to  assume  that  all  trains,  both  passenger  and 
freight,  will  probably  require  helping  engines,  especially  as  the  tendency 
to  increase  the  weight  of  passenger  trains  and  cars  is  strong. 

The  assumption  made  as  to  passenger  helpers  will  make  a  consider- 
able difference  in  a  comparison  of  gradients  ;  for  if  they  be  assumed  to 
be  used,  the  advantage  of  pusher  gradients  over  moderately  favorable 
through  gradients  will  be  much  less ;  while  if  they  be  not  assumed,  the 
disadvantage  for  passenger  service  of  the  higher  rates  of  grade  can  hardly 
be  estimated  at  any  considerable  figure. 

762.  In  laying  out  pusher  grades,  the  effect  of  fluctuations  in  the 
velocity  of  trains  to  modify  the  apparent  relation  of  the  grades  to  each 
other  must  be  carefully  kept  in  mind.  The  effect  of  these  differences 
(fully  considered  in  Chap.  IX.,  par.  397  et  seq)  will  usually  be  that  the 
apparent  maximum  of  the  lower  (single  engine)  grades  will  be  higher 
than  it  really  is,  while  the  actual  maximum  of  the  higher  (pusher)  grades 
will  be  greater  than  the  profile  shows,  so  that  the  latter  will  need  to  be 
reduced  lower  than  an  apparent  balance  requires  in  order  to  give  a  true 
balance.  On  long  steep  ascents  slight  sags  in  the  grade-line  may  be  per- 
missible (par.  414  et  seq^,  but  otherwise  no  excess  of  momentum  can  be 
relied  on  to  carry  trains  over  any  increase  whatever  above  the  normal 
rate;  while  any  stop  on  the  grade,  if  the  latter  be  long,  will  increase  its 
limiting  effect  far  above  the  apparent  maximum,  unless  care  has  been 
used  to  ease  the  grades  for  all  stops  which  can  possibly  be  required. 
Even  if  this  has  been  done,  there  are  always  likely  to  be  occasional  irreg- 
ular stops,  and  the  occasional  operating  inconvenience  therefrom  will  be 
allowed  far  more  than  its  true  weight  in  cutting  down  trains. 


CHAP.  XVI.— ASSISTANT  ENGINES— POWER   OF.  ^97 

763.  On  the  other  hand,  the  lower  through  grade  will  very  commonly 
be  cut  up  into  such  short  stretches  that  momentum  will,  or  may  be  made 
to,  reduce  its  apparent  rate  very  materially,  and  even  if  not,  moderate 
improvements  in  the  future  will  often  suffice  to  accomplish  this.  More- 
over, it  is  always  comparatively  easy  to  foresee  and  guard  against  limit- 
ing effects  from  stops. 

True  economy  will  ordinarily  dictate,  therefore,  that  the  resistance 

ON   THE   PUSHER   GRADE   SHOULD    BE    AT     LEAST    TEN    PER    CENT     LESS 

THAN  AN  APPARENT  BALANCE  REQUIRES  if  attainable  at  moderate  cost, 
with  the  following  proviso  : 

If  the  rate  of  the  pusher  grade  be,  from  its  cost  or  otherwise,  the  fixed 
element  beyond  control,  as  often  happens,  then  the  rate  of  the  lower 
through  grade  should  be  reduced  at  any  reasonable  cost  (it  is  usually 
more  at  the  cost  of  care  than  money)  to  and  a  little  below  the  full  extent 
which  an  apparent  balance  requires  ;  in  accordance  with  the  sound  gen- 
eral principle,  that  the  links  in  a  chain  whose  strength  we  cannot  control 
nor  exactly  foresee  should  be  the  weakest,  and  not  those  whose  strength 
we  can  control  and  can  foresee. 

764.  Again,  the  lower  the  rolling-friction  the  greater  the  proportion- 
ate eft'ect  of  gradients  upon  the  total  train  resistance,  and  consequently 
the  lower  must  be  the  rate  of  the  higher  pusher  grade.  As  we  have  as- 
sumed (par.  623  and  Table  170)  8  lbs.  per  ton  rolling-friction,  which  is 
probably  from  2  to  4  lbs.  high  for  the  slower  working  speeds,  the  rate  of 
the  higher  grade  should  be  from  o.i  to  0.2  per  cent  less  than  theory  would 
otherwise  indicate,  where  possible,  for  this  reason  alone. 

765.  A  variation  in  the  weight  and  power  of  the  assistant  engines 
affords  a  means  of  equalizing  minor  inequalities  in  the  balance  of  gra- 
dients, should  such  be  discovered,  but  this  should  be  counted  on  with 
caution  in  original  location.  To  count  on  using  pusher  engines  lighter 
than  the  through  engines  would  ordinarily  be  very  bad  practice.  It 
would  be  preferable  to  save  money  and  length  of  pusher  grade  by  using  a 
steeper  rate  of  grade.  To  count  on  using  heavier  pushers  is  open  to  three 
objections:  (i)  The  tendency  is  always  to  use  heavier  and  heavier  through 
engines,  and  a  point  will  then  soon  be  reached  where  corresponding 
increase  in  the  weight  of  pusher  engines  would  be  objectionable  or  im- 
practicable ;  (2)  It  imposes  a  greater  tax  upon  the  rails  and  track  at  the 
very  point  where  the  alignment  makes  it  most  objectionable  ;  (3)  Such 
gain  as  is  possible  in  this  respect  is  very  apt  to  be  required  and  used  to 
make  up  for  the  inequalities  in  what  was  supposed  to  be  a  correct  balance 
of  gradients,  the  te7tdency  always  being  to  get  the  rate  of  the  pusher  grades 


598  CHAP.  XVI.— ASSISTANT  ENGINES— DUTY  OF. 

too  high  for  a  correct  balance  with  the  lower  grades.  In  actual  practice, 
at  the  present  day,  it  will  be  found  that  pusher  engines  usually  are  a 
little  heavier  than  the  through  engines,  and  yet  that  the  pusher  grades 
are  no  higher  in  rate  than  Table  i8i  would  indicate,  the  excess  being 
used,  apparently,  for  the  preceding  and  following  reasons,  and  not  to 
provide  a  true  balance  under  normal  conditions. 

766.  If  the  rate  of  adhesion  be  low,  the  admissible  rates  for  the  higher 
gradients  is  very  materially  decreased,  as  shown  in  Table  183,  for  the 
reason  that  the  percentage  of  effect  lost  in  moving  the  engine  itself  is 
very  materially  greater.  As  on  many  days  in  the  year  the  ratio  of  adhe- 
sion is  unavoidably  low,  on  those  days  the  resulting  inconvenience  will 
be  confined  to  the  pusher  grade,  but  will  be  very  apt  to  lead  to  the  per- 
manent cutting  down  of  trains  on  both  grades. 

The  consequences  of  any  unforeseen  breakdown  or  other  cause  of 
accident  or  delay  are  so  much  more  serious  on  heavy  grades  that  a  cer- 
tain excess  of  motive-power  is  naturally  sought  for  and  generally  obtained 
in  such  localities,  sometimes  at  the  expense  of  sound  economy. 

The  curvature  on  heavy  gradients  is  usually  very  much  more  severe. 
As  the  speed  is  also,  usually,  very  much  slower,  and  complete  stoppage 
from  lack  of  power  more  frequent,  it  appears  probable  (pars.  308,  335) 
that  the  curve  resistance  per  ton  is  higher,  and  hence  that  either  the  rate 
of  compensation  for  curvature  must  be  made  higher  on  high  pusher 
grades  or  a  lower  average  rate  of  grade  than  a  nominal  balance  requires 
be  adopted. 

THE   DUTY   OF   ASSISTANT   ENGINES. 

767.  Under  the  ordinary  exigencies  of  operation,  with  two  important 
exceptions,  below  noted  (par.  770  et  seq^,  pushing  or  assistant  engine 
service  must  be  rendered  by  separate  engines,  specially  detailed  for  that 
duty  and  available  for  no  other.  It  is  therefore  not  correct  to  assume 
that  the  pushing  service  will  cost  about  the  same  per  mile  run  as  for 
through  engines,  or  that  pushing  engines  will  make  the  same  annual 
mileage.  Rather,  the  safer  basis  is  to  assume  as  nearly  as  may  be  that  a 
certain  number  of  engines  must  be  maintained  for  that  service  alone,  at 
a  certain  cost  per  day  regardless  of  mileage  made,  ;plus  the  extra  cost  due 
to  running  a  certain  number  of  miles,  whether  that  number  be  50  or  100 
or  more  miles  per  day. 

768.  As  a  general  and  safe  rule,  the  mileage  of  assistant  engines  may 
be  taken  at  100  miles  per  day  if  they  will  have  a  chajice  to  run  it,  and  as 
at  least  equal  to,  if  not  considerably  in  excess  of,  the  mileage  of  ordinary 
through  engines.     As  much  as  130  miles  per  day  is  run  by  pusher  engines 


CHAP.  XVI,— ASSISTANT  ENGINES— DUTY  OF.  599 

on  various  roads,  under  favorable  circumstances,  but  experience  does  not 
justify  an  assumption  that  more  than  this  is  practicable.  If,  therefore, 
the  estimated  traffic  will  require  150  miles  per  day  of  pusher  service,  the 
only  safe  basis  is  to  assume  that  two  engines  with  two  crews  will  be  re- 
quired, making  75  miles  per  day  each.  Theoretically,  one  engine  with 
two  crews  might  do  the  work,  but  practically,  if  the  duty  were  too  much 
for  one  engine  and  crew,  convenience  would  almost  certainly  require  and 
justify  keeping  two  engines  m  working  order  with  steam  up  for  at  least 
12  hours  per  day. 

When  the  pushing  service  to  be  performed  is  over  200  miles  per  day 
the  only  safe  basis  is  to  assume  one  engine  for  each  100  miles,  or  frac- 
tion thereof  over  fifty. 

769.  From  one  to  two  months  of  every  year  is  lost  by  engines  while 
m  shop  for  repairs  (see  Table  51),  which  reduces  the  apparent  mileage  per 
engine  per  year  (and  hence  per  day)  by  10  to  16  or  more  per  cent ;  but 
this  loss  need  not  be  considered  in  computing  the  number  of  engines  re- 
quired for  pushing  service  from  the  probable  mileage  to  be  run,  or  its 
cost,  since  the  cost  of  these  repairs  is  included  in  the  cost  of  the  miles 
actually  run,  and  the  engines  actually  detailed  to  pushing  service  can  and 
will  be  always  in  working  order. 

The  exceptions  to  which  the  preceding  general  rules  do  not  apply  are 
these  ; 

770.  I.  When  traffic  is  very  light,  pusher  grades,  if  not  too  long,  may 
be  operated  by  cutting  trains  in  two,  leaving  half  the  train  at  the  bottom 
of  the  grade,  placing  half  of  it  on  a  siding  at  the  top,  returning  for  the 
other  half,  which  is  preferably  pushed  up,  and  then  proceeding,  after 
coupling  up,  with  the  entire  train  once  more. 

This  is  done  to  only  a  limited  extent  as  a  regular  practice,  although  it  is  a 
resort  in  emergencies  on  nearly  all  roads.  It  might  well  be  done  to  a  much 
greater  extent  than  it  is, if  it  were  only  to  run  a  freight  train  three  times  a  week 
instead  of  daily.  It  is  one  of  those  possibilities  of  economy  which  are  neglected 
until  necessity  compels  them,  because  they  take  some  trouble  and  some  devia- 
tion from  ordinary  routine  in  management. 

Convenience  requires  that  there  should  be  a  siding  at  least  half  a  train  long 
(preferably,  of  course,  a  full  train  long)  at  both  top  and  bottom  of  the  grade,  the 
lack  of  which  is  no  doubt  one  great  reason  why  this  expedient  is  not  oftener  re- 
sorted to. 

771.  2.  At  short  pusher  grades  near  stations,  yard  or  switching  engines 
can  often  perform  a  part  or  all  of  the  required  pushing  service  at  very 
moderate  cost — or,  what  amounts  to  the  same  thing,  the  pushing  engines 
can  be  so  utilized  for  switching  service  as  to  greatly  reduce  the  cost  and 
inconvenience  of  using  pushers. 


600  CHAP.  XVI.— ASSISTANT  ENGINES— DUTY  OF. 

The  instances  are  many  where  yard  engines  are  utilized  in  this  way,  if 
only  to  help  trains  through  yards  at  which  there  would  be  no  difficulty, 
except  for  the  fact  that  it  is  a  yard,  because,  for  obvious  topographical 
and  commercial  reasons,  it  is  very  common  to  find  large  yards  near  short 
stretches  of  objectionable  gradients.  When  the  yard  is  very  large,  so 
that  several  yard  engines  are  constantly  employed,  the  pushing  service 
cannot  be  assumed  to  be  added  without  adding  its  full  pro  rata  to  the 
number  of  engines,  but  in  all  cases  the  cost  and  inconvenience  of  the 
service  will  be  decreased,  and  so,  indirectly,  the  number  of  engines  which 
will  probably  be  required  for  the  joint  service,  to  the  extent  perhaps  of 
15  or  20  per  cent  of  the  whole  number  of  engines.  Switching  engines  of 
the  ordinary  type,  having  all  their  weight  on  drivers  are  not  well  adapted 
for  pushing  service,  on  runs  of  over  a  mile  or  two,  nor  much  used  there- 
for, since  they  are  ill  adapted  for  high  speed,  which  is  often  desirable  in 
returning  down  hill. 

772.  The  convenience  of  the  service  must  be  considered  as  well  as  the 
theoretical  requirements  in  estimating  both  the  probable  duty  and  prob- 
able cost  of  the  assistant-engine  service,  as  also  of  course  in  laying  out 
the  grades.  Unless  a  station  be  situated  immediately  at  the  foot  or  top 
of  the  grade,  the  service  must  be  assumed  to  begin  at  the  nearest  consid- 
erable station,  if  there  be  one  within  three  to  five  miles  of  either  point, 
because  that  is  where  convenience  will  require  that  it  should  begin  in 
practice. 

Unless  two  successive  pusher  grades  are  more  than  five  or  perhaps 
even  eight  miles  apart,  they  may  more  prudently  be  taken  as  one  and  the 
same  grade,  because  in  practice  that  is  the  way  in  which  they  will  be 
likely  to  be  operated.  The  tendency  is  always  to  consider  convenience 
in  such  matters,  even  at  the  expense  of  economy;  and  it  may  be  questioned 
if  there  is  even  a  theoretical  economy  in  breaking  up  a  pusher  run  into  two 
for  less  than  a  five-mile  interval,  or  even  under  special  circumstances,  with 
thin  traffic,  for  considerably  more.  The  inconveniences  of  stopping  and 
starting  and  of  maintaining  the  double  service  and  the  loss  of  time  are  too 
great.  No  stop  is  required  at  the  top  of  the  grade  for  uncoupling  the 
pusher,  but  for  coupling  on  a  stop  is  necessary,  and  a  single  stop  of  a 
heavy  train  costs  more  than  a  five-  or  even  ten-mile  run  of  a  light  engine, 
which  would  otherwise  be  standing  idle  with  steam  up. 

773.  In  considering  the  question  of  the  probable  duty  of  assistant  en- 
gines it  is  further  to  be  remembered  that  trains  do  not  come  at  equal  in- 
tervals of  time  apart,  but  some  are  likely  to  come  so  near  together  that 
two  or  more  engines  will  be  almost  indispensable  at  certain  times  of  the 


CHAP,  XVI.— ASSISTANT  ENGINES— COST  OF.  6oi 

day,  and  some  so  far  apart  that  much  time  will  be  lost  while  under  steam. 
On  the  other  hand,  good  time  can  generally  be  made  down  hill ;  and  the 
systems  of  automatic  and  other  block  signals  have  now  been  brought  so 
near  perfection  that  short  sections  at  least  can  be  so  protected  that  little 
time  need  be  lost  between  trains  for  the  sake  of  allowing  a  margin  of 
safety  in  time. 

American  railways  are  but  beginning  to  avail  themselves  of  these  in- 
terlocking and  signal  devices,  the  use  of  which  may  be  expected  to  ma- 
terially increase  hereafter.  For  sections  on  which  pushers  are  used  they 
are  particularly  well  adapted.  At  such  points  the  number  of  trains  is 
practically  doubled,  and  it  may  well  be  a  question  between  such  signals 
and  a  double  track. 

For  any  considerable  traffic  a  telegraph  station  at  top  and  bottom  of 
the  grade  is  all  but  indispensable. 

THE    COST    OF    ASSISTANT    ENGINES. 

774.  This  may  be  divided  into  three  elements : 

1.  Interest  charge  07i  the  original  cost,  special  to  the  use  of  pushers,  in- 
cluding extra  engines,  engine-houses,  if  any;  sidings;  block  signals,  if  any; 
etc. 

2.  Cost  per  day-ior  wages  and  a  certain  portion  of  the  fuel  and  repair 
charges  all  of  it  independent  of  the  mileage  run  per  day,  as  is  also  the  cost 
of  maintaining  block  signals,  if  any. 

3.  Cost  per  mile  run  for  fuel  and  repairs,  and  for  wear  and  tear  of 
road-bed,  track,  and  sidings. 

775.  When,  as  will  usually  happen,  an  approximately  fair  mileage  can 
be  obtained  from  the  assistant  engines,  say  80  to  100  miles  per  day,  it  is 
unnecessary  to  separate  these  items  from  each  other,  but  the  whole  cost 
per  mile  run,  exclusive  of  maintenance  of  way  and  interest  charges,  may 
be  assumed  not  to  vary  materially  from  that  of  ordinary  through  engines, 
unless  there  is  some  considerable  difference  in  weight. 

The  experience  of  the  Philadelphia  &  Reading  Railroad  indicates  that 
the;  intermittent  service  of  pushing  engines  does  not  add  materially  to 
expenses,  and  much  other  evidence  to  the  same  effect  might  be  given,  as 
also  for  the  fact  that  assistant  engines  will  realize  a  somewhat  higher 
yearly  service  than  through  engines,  owing  to  the  nature  of  their  service, 
which  facilitates  care  and  prompt  repairs.  At  least  the  difference  in  cost, 
if  any  exist,  must  in  general  be  trifling.  Assuming  there  were  none  at  all, 
the  DIRECT  RUNNING  EXPENSES  for  fuel,  oil,  and  water,  repairs  and  engine- 


602  CHAP,  XVI,— ASSISTANT  ENGINES— COST  OF. 

wages  would  average,  as  per  Table  80,  page  179  (see  Chap.  V.  for  further 
details),  20.8  cents  per  mile. 

776.  The  maintenance-of-way  expenses  must  also  be  estimated  at 
a  considerable  figure.  There  is  a  peculiar  temptation  in  this  case  to  fall 
into  the  error  discussed  in  par.  125,  and  assume  that,  except  in  the  one 
item  of  wear  of  rails,  there  will  be  little  additional  expense  for  mainte- 
nance of  way ;  but  partly  for  the  indirect  causes  discussed  in  par.  125 — the 
necessity  of  maintaining  a  higher  standard  as  trains  increase,  as  well  as 
of  keeping  up  to  the  same  standard — the  cost  of  maintenance  of  way  will 
certainly  be  materially  increased.  For  reasons  which  may  be  readily  de- 
duced from  pars.  717-18,  it  will  certainly  not  be  excessive,  and  probably  as 
nearly  fair  as  is  possible,  to  assume  that  the  whole  cost  per  train-mile  of 
maintenance  of  way,  excluding  maintenance  of  bridges  and  buildings,  is 
increased  about  50  per  cent  by  the  pusher,  i.e.,  is  as  much  for  the  pusher 
alone  passing  up  and  down  as  for  the  whole  train  passing  one  way. 

777.  The  total  cost  of  pusher  service  (including  the  return  light  down 
grade)  per  mile  of  incline  (on  the  basis  of  $1.00  per  train-mile  average 
cost)  will  then  be  as  follows : 

Direct  running  expenses,  fuel,  water,  oil,  repairs,  and  wages 

per  mile  of  round  trip 41 .6  cents 

Maintenance  of  way  expenses  per  mile  of  round  trip  17.5  cents 

(Table  80)  x  2 35.0      " 

Total  cost  per  mile  of  incline  per  round  trip 76.6      " 

Or  per  year  per  daily  train  per  mile  of  incline,  $0,766  x  365  =  $280.00. 

778.  The  introduction  of  steel  rails  and  the  general  cheapening  of  all  railway 
supplies  has  greatly  reduced  within  recent  years  the  cost  of  such  service,  especi- 
ally for  maintenance  of  way.  In  the  former  edition  of  this  work  this  expense 
per  mile  of  round  trip  was  estimated  at  94  cents,  of  which  54  cents  were  for  lo- 
comotive expenses  and  40  cents  for  maintenance. 

779.  This  estimate  assumes  that  the  pushing  engines  are  kept  fairly 
busy,  so  as  to  make  something  like  80  to  100  miles  per  day  average  mile- 
age. If  this  seem  impossible  or  doubtful,  it  will  require  to  be  increased 
correspondingly.  All  that  the  engine  falls  below  100  miles  per  day,  i.e., 
all  potential  mileage  not  actually  run,  may  be  assumed  to  cost  i  to  i  as 
much  per  mile  as  if  it  had  been  run,  and  is  so  much  added  to  the  cost  of 
what  is  run. 

780.  This  results  from  the  following  estimate :  Comparing  the  cost 
per  mile  run  of  an  engine  m  actual  ser\nce,  as  per  Table  80,  and  the  cost 


CHAP.  XVI.— ASSISTANT  ENGINES— COST  OF.  603 

of  an  engine  standing  still  in  the  yard  with .  steam  up  for  an  equal  period 
of  time,  we  have,  approximately,  the  following : 

Average  in  service,  Standing  in  yard. 

cts.  or  p.  c.  Per  cent.    Am't,  cts.  or  p.  c. 

Fuel, 7.6  10                   0.8 

Oil  and  water, 1.2  o 

Repairs, 5.6  10                     .6 

Wages, 6.4  100                   6.4 

Maintenance  of  way,      .    .  17.5  o 


8.3  7.8 


781.  The  chief  loss  from  standing  still  is  in  engine-wages.  Fuel  is 
not  necessarily  wasted  to  any  such  extent  as  to  make  it  an  item  of  im- 
portance. The  total  consumption  per  hour  of  an  engine  standing  in  the 
yard  to  simply  make  good  the  loss  from  radiation  has  been  determmed 
by  experiment  not  to  exceed  necessarily  24  to  35  lbs.  of  coal,  or  about  the 
quantity  burned  in  service  in  running  one  hali-mile.  This  would  indi- 
cate that  the  consumption  of  an  engine  standing  idle  in  a  yard  for  a 
whole  day  with  steam  up  would  only  be  one  or  two  per  cent  of  what  it 
would  be  m  service ;  but  an  engine  standing  idle  only  between  intermit- 
tent periods  of  service  would,  by  carrying  a  larger  fire  and  the  cooling  off 
of  the  machine,  as  well  as  by  blowing  off  through  the  safety-valve  and 
other  effects  of  careless  firing,  waste  much  more  than  this  proportion  ;  so 
that  the  allowance  made  above  (10  per  cent)  is  hardly  too  high. 

782.  The  effect  on  COST  OF  repairs  per  mile  run  of  intermittent 
work  is  likewise  slight.  There  is  no  doubt  some  bad  effect  from  the 
intermittent  and  irregular  nature  of  pusher  service,  but  the  mere  fact 
that  an  engine,  between  its  trips,  stood  idle  with  steam  up  for  an  hour, 
more  or  less,  instead  of  immediately  starting  off  on  another  trip,  would 
of  itself  add  little  to  the  cost  of  repairs  per  mile  actually  run.  Deterio- 
ration would  no  doubt  be  going  on,  but  all  the  great  causes  of  deteriora- 
tion— wear  and  tear  of  running  gear  and  machinery,  from  stopping  and 
starting,  brakes  and  running  over  the  track,  injury  to  boiler  and  boiler- 
tubes  by  cooling  off,  by  the  fierce  heat  of  the  fire  and  by  the  mechanical 
action  of  the  coal  drawn  through  the  tubes,  etc.,  etc. — are  absent.  The 
above  allowance  is  therefore  ample,  and  probably  excessive,  leading  to 
the  resulting  conclusion,  that  the  cost  of  an  engine  per  hour  standing  in 
the  yard  with  steam  up  is  little  more  than  one  fifth  as  much  as  if  in  mo- 
tion at  15  or  20  miles  per  hour. 

The  correctness  of  this  conclusion  might  be  indicated  in  another  way 


604   CH.  XVI.— ASSISTANT  ENGINES  AND  THROUGH  GRADES. 

by  comparison  with  experience  with  switch  engines,  but  more  detailed 
comparison  would  lead  us  too  far. 

783.  The  interest  charge  on  pusher  engines  is  fairly  chargeable  to  the 
cost  of  the  service  as  well  as  the  running  expenses,  for  the  same  reason 
that  the  interest  charge  in  the  extra  engines  required  to  operate  a  heavier 
grade  must  fairly  be  added  to  the  other  expenses  entailed  by  the  grade, 
as  specified  in  par.  721.  Properly  speaking,  the  first  cost  of  these  extra 
engines  is  a  part  of  the  cost  of  constructing  the  line  of  those  grades,  as 
much  as  the  bridges  or  track  thereon,  and  it  should  be  included  in  the 
estimate  of  the  cost  of  construction  unless  the  interest  charge  is  added 
to  the  operating  expenses. 

784.  To  accurately  estimate  the  cost  of  pusher  service,  then,  we  must 
determine — 

First.  The  length  of  pusher  run  in  miles  (par.  767). 

Seco7idly.  The  probable  number  of  daily  trips  per  engine,  and  hence 
the  number  of  engines  required  for  the  given  traffic. 

Thirdly.  Determine  the  annual  interest  on  their  first  cost. 

Fourthly.  Compute  the  cost  of  the  mileage  made,  according  to  pars. 
Tj'j  and  780. 

The  sum  of  the  last  two  items  will  be  the  total  cost  of  the  pusher  ser- 
vice. 

COMPARISON   OF   PUSHER-GRADE    LINES    WITH    UNIFORM    GRADIENTS. 

785.  Ordinarily,  when  pusher  grades  are  used,  they  will  not  be  per- 
fectly balanced  with  the  through  grades,  but  either  one  or  the  other, 

whichever  opposes  most  difficulties  of  con- 
struction to  obtaining  low  grades,  will  be 
the  true  limiting  gradient.  The  other 
must  then  be  assumed,  in  order  to  give  a 
fair  comparison  with  a  uniform  gradient 
line,  to  be  of  such  rate  as  to  give  a  per- 
fect balance  (Table  182),  although  the  fact 
Pj(-  that  it  is  really  lower  will  not  therefore  be  a 

wholly  valueless  advantage,  even  for  freight 
purposes.  In  Fig.  179,  for  example,  the  0.7  through  grade  and  the  1.75 
pusher  grade  are  not  perfectly  balanced.  The  pusher  grade  should  either 
be  reduced  to  1.65  or  the  through  grade  be  assumed  to  be  equivalent  to 
0.75,  unless  the  circumstances  make  it  proper  to  assume  the  use  of 
heavier  pusher  engines  than  through  engines,  which  is  rarely  the  case 
(par.  763  et  seq.). 


CH.  XVI— ASSISTANT  ENGINES  AND  THROUGH  GRADES.    605 

786.  If,  then,  we  have  two  alternate  locations,  AB  and  AA'B,  Fig. 
179,  one  of  which,  AB,  is  on  a  lower  through  grade  (say  of  1.25  per 
cent),  which  it  has  appeared  practicable  to  operate  without  assistant 
power,  and  the  other,  A'B,  is  the  lowest  through  grade  which  it  has 
been  or  will  be  practicable  to  secure  apart  from  the  incline  AA',  which 
it  is  expected  to  work  with  assistant  power,  BY  adopting  the  line 

WITH  ASSISTANT   POWER — 

First.  We  gain  what  is  equivalent  to  a  reduction  in  the  ruling  grade, 
from  the  rate  AB,  which  in  the  diagram  is  1.25  per  cent,  to  the  rate^'^, 
whatever  it  may  be.  The  amount  of  this  gain  will  depend  upon  the  skill 
and  good  fortune  with  which  the  grades  have  been  adjusted,  but  it  will 
ordinarily  be  a  very  considerable  difference. 

Second.  We  lose  the  cost  of  assistant  power  on  the  incline,  as  esti- 
mated according  to  pars.  jyj-jZ^. 

787.  The  problem  being  thus  stated,  the  values  previously  deter- 
mined give  us  a  ready  and  simple  method  of  solving  it.  Thus  if,  in  Fig. 
179,  we  have  estimated  the  probable  number  of  daily  trains  required  on 
the  pusher-grade  line  A'B,  which  is  actually  a  0.7  maximum,  but  is  virtu- 
ally made  0.75  by  the  effect  of  the  imperfect  balance  of  the  pusher 
grades,  then,  by  adopting  the  line  having  a  uniform  maximum  gradient 
of  1.25  per  cent,  we  have  in  effect  increased  the  ruling  grade  0.50  per 
cent.  Now,  assuming  the  pusher  line  to  be  100  miles  long,  with  a  pusher 
grade  of  10  miles  length  on  it,  and  the  other  line  to  be  105  miles  long, 
the  estimated  difference  in  the  operating  values  of  the  two  alignments 
would  be  as  follows,  allowing  the  rate  of  interest  on  capital  to  be  5  per 
cent. 

In  favor  of  the  pusher  line  AA'B,  PER  daily  train  : 

Difference  in  ruling  grade — a  saving  of  0.50  per  cent  increase 

above  a  0.7  per  cent  grade  :  Value  by  Table  178,  $4,300  -^ 

0.05  =:  $86,000  for  a  division  100  miles  long.    For  a  division 

105  miles  long  we  have  (par.  740)  $86,000  x  105  =      ...     $90,300 

In  favor  of  the  tmiform  gradient  AB  : 

10   miles   saved   of    assistant-engine   service,  cost  by  par.  yj'j 

$2,800,  which,  capitalized  at  5  per  cent,  = $56,000 

Net  difference  in  operating  value  due  to  difference  in  gradients 

only,  in  favor  of  line  AA'B $34,300 

Value  of  5  miles  of  distance  in  favor  of  line  AA'B  possibly  noth- 

$290  „ 

ing,  and  possibly  by  par.  196,  — —  x  5  =        $29,000 

Total  difference  in  operating  value,  per  daily  train,  in  favor  of 

low-grade  (pusher)  line $63,300 


6o6   CH.  XVI.— ASSISTANT  ENGINES  AND  THROUGH  GRADES, 

To  this  is  to  be  added  an  allowance  for  an)?-  difference  in  the  probable 
traffic,  for  any  loss  of  time  of  assistant  engines,  and  for  any  difference  in 
the  probable  capital  expenditure  for  locomotives,  which  will  naturally 
be  least  on  the  line  which  shows  the  highest  operating  value. 

788.  By  computing  various  examples  of  this  kind  it  will  be  seen  how 
very  large  an  economy  almost  invariably  results  from  using  pushers,  but 
the  condition  that  the  pushers  must  be  kept  busy  and  be  always  on  hand 
to  have  them  economical  must  be  remembered.  The  larger  the  traffic 
of  the  road  the  more  easily  can  this  be  assured,  and  consequently  the 
more  frequently  can  pushers  be  used.  They  are  sometimes  used  as 
often  as  three  or  four  times  on  a  division,  but  with  a  light  traffic  this 
would  be  inexpedient. 

All  the  preceding,  however,  applies  to  freight  business  only.  The 
use  of  pushers  in  passenger  service  is  far  less  general  (par.  757). 

789.  Whether  for  passenger  or  freight  service,  perhaps  the  most  ad- 
vantageous and  satisfactory  basis  of  comparison  of  all  for  comparing 
alternate  systems  of  gradients,  as  it  certainly  is  the  simplest,  is  to  deter- 
mine the  number  of  engine-miles  which  must  be  run  per  through  car  (or 
ton) — i.e.,  per  car  or  ton — moved  over  the  line  for  the  entire  distance 
between  termini. 

A  "  car"  has  become  in  recent  years  such  a  very  indeterminate  thing, 
owing  to  the  rapid  increase  in  weights  carried,  that  the  ton  is  the  best 
limit  to  use,  as  in  Table  170,  giving  the  capacity  of  engines  on  various 
grades. 

By  this  process  the  effect  of  differences  of  distance  as  well  as  grad- 
ients is  included  in  the  same  estimate,  and  having  assumed  a  reasonable 
price  (see  Table  143)  for  the  cost  of  the  additional  motive-power  and 
train-service  required,  the  estimate  is  very  readily  completed. 

790.  Thus  the  example  already  given  (par.  j2>7  and  Fig.  179)  may  be 
compared  as  follows : 

LinQ  AA  B  for  pushers:  105  miles;  10  miles,  1.25  per  cent  (79.2  ft. 
per  mile),  90  miles,  actually  0.7  per  cent,  but  in  effect  0.75  per  cent. 
Regular  load  for  through  engine  with  11  tons  on  drivers  (Table  170),  881 
tons. 

Line  ^^,  uniform  gradient:  100  miles,  1.25  per  cent  (52.8  ft.  per 
mile).     Engine  load  (Table  170),  592  tons. 

We  then  have  this  comparison  : 

Line  AA'B,  881  tons  x  105  miles  =  92,505  ton-miles  hauled  by  100  + 
10  miles  run  by  engine  (in  one  direction),  or  841  ton-miles  per  engine- 

8/1  T 

mile,  or  -^  =8.0  through  tons  per  engine-mile. 
105 


CH.  XVI.— ASSISTANT  ENGINES  AND  THROUGH  GRADES.    607 

Line  AB,  592   tons,  through  load,  no  pusher  service,  or  ^^—  —  5.92 

•^  100 

through  tons  per  engine-mile. 

We   have   then   — —  =  35.14  per  cent  excess  of  engine-mileage  on 

line  AB  for  the  same  through  traffic,  whatever  it  may  be  ;  and  estimating 
the  cost  of  this  extra  engine-mileage  at  about  half  the  average  cost  of  a 
train-mile,  as  in  par.  720  (which  is  not  quite  correct,  because  the  excess 
of  trazn-mile2Lge  on  line  AB  is  even  greater  than  the  excess  of  engine- 
mileage)  the  freight  operating  expenses  over  the  two  lines  will  be  to 
each  other  about  as  100  to  117.6.  Estimating  then,  however  rudely,  the 
operating  expenses  over  either  line,  we  have  a  tolerably  close  indication 
of  the  difference  in  value  between  them,  which  will  lead  to  almost  exactly 
the  same  total  as  in  par.  787. 

791.  With  reference  to  the  passenger  business  on  this  particular  line, 
if  only  a  moderate  through  traffic  is  to  be  handled,  the  difference  in  the 
gradients  will  be,  with  well-arranged  stations,  a  matter  of  little  conse- 
quence. If  only  a  little  heavy  passenger  traffic  is  to  be  handled,  under 
otherwise  favorable  conditions,  the  uniform  gradient  of  1.25  per  cent 
will  have  a  certain  advantage ;  but  if  any  really  heavy  passenger  traffic  is 
to  be  handled,  the  pusher  line  will  have  much  the  same  advantage  for 
it,  and  for  much  the  same  reasons  as  it  has  for  the  freight  traffic.  It  is 
a  much  more  indeterminate  problem,  but  the  financial  importance  of 
high  passenger  speeds  at  all  points  and  the  effect  upon  it  of  low  gradients 
and  easy  curvature  is  generally  over-estimated  (pars.  757-9). 


L 


6o8    CH.  XVII.— BALANCE  OF  GRADES  FOR  UNEQUAL  TRAFFIC. 


CHAPTER  XVII. 

THE    BALANCE    OF    GRADES   FOR    UNEQUAL    TRAFFIC. 

792.  An  engine  which  has  carried  a  full  load  in  one  direction 
must  return  at  nearly  the  same  expense,  whether  the  train  be- 
hind it  be  fully  loaded  or  not.  There  must,  of  course,  be  the 
same  number  of  cars  in  each  direction,  in  the  long-run,  or  very 
nearly  so  (there  being  some  lines  over  which  considerable  num- 
bers of  cars  run  only  in  one  direction,  returning  by  other  routes), 
and  of  course  there  is  always  precisely  the  same  amount  of 
motive-power  available.  If,  therefore,  the  movement  of  traffic 
is  permanently  heavier  in  one  direction  than  in  the  other,  or 
there  is  good  reason  to  expect  that  it  will  be,  the  grade  opposed 
to  the  lighter  returning  traffic  may  be  made  heavier  than  that  in 
the  opposite  direction  by  an  amount  sufficient  to  make  the  re- 
sistance of  trains,  and  hence  the  requisite  motive-power,  the  same 
in  both  directions.  No  advantage  whatever  results  from  reduc- 
ing the  return  grades  below  this,  beyond  the  small  amount 
which  represents  its  value  for  occasional  emergencies  when  the 
usual  balance  of  traffic  is  temporarily  disturbed,  and  the  still 
smaller  amount  which  represents  the  value  of  reducing  the  rate 
of  any  grade,  as  pointed  out  in  par.  462 ;  and  hence  great  economy 
may  sometimes  be  effected  in  construction  by  utilizing  to  the 
full  such  increase  in  grade  as  is  legitimately  made  possible  by 
the  difference  in  resistance  due  to  the  lighter  load  in  one  direc- 
tion, 

793.  The  determination  of  the  proper  balance  of  grades, 
under  any  assumed  difference  of  traffic,  is  a  simple  matter.  The 
determination  of  the  basis  of  fact  upon  which  the  adjustment 
must  rest  is  not  so  simple,  but  rather  one  of  great  uncertainty, 
except   in   some   cases   of  roads  built   for  carrying  minerals  or 


CH.  XVII.— BALANCE  OF  GRADES  FOR  UNEQUAL  TRAFFIC.    609 

other  special  traffic.  For  roads  of  a  large  and  mixed  traffic,  as 
even  our  through  East  and  West  trunk  lines,  the  problem  is  much 
complicated  by  the  fact  that  changes  of  importance,  especially 
in  the  transportation  of  minerals  or  from  the  construction  of  new 
lines,  are  liable  to  occur  at  any  time.  Thus  the  growing  an- 
thracite coal  trade  to  the  West  has  produced  and  is  producing 
great  changes  in  the  ratio  of  the  tonnage  East  and  West;  and  not 
unfrequently  on  different  parts  of  the  same  line  the  burden  of 
traffic  is  in  opposite  directions — perhaps  from  causes  entirely  be- 
yond foresigiit  when  the  road  was  first  built.  Nearly  always  the 
ratio  of  preponderance  varies  considerably  from  point  to  point. 

794.  On  the  Pennsylvania  Railroad  the  balance  of  traffic  is 
widely  different  at  different  points,  the  westward  preponderating 
greatly  at  the  western  end,  and  the  eastward  at  the  eastern  end, 
as  shown  in  Table  184,  which   is  well  worthy  of   study.     Table 


Table  184. 

Comparative  Volume  of  the  Traffic  East  and  Traffic  West  at  Various 
Points  on  the  Main  Line  of  the  Pennsylvania  Railroad,  between 
New  York  and  Pittsburg.     1885. 


Station. 

Miles  from 
New  York. 

Comparative  Volume  of 
Traffic  (Phila.  —  i.oo). 

Ratio  of  Loaded  Cars.* 
East  to  West. 

Eastward. 

Westward. 

I 

57 
91 
171 
196 
245 
327 
364 
398 
444 

0.51 
0.74 
I.OO 
1.06 
I. 17 
O.9S 

0.77 
0.72 
0.56 

0  ^o-k 

I-I5 
1. 13 
1.00 
0.92 
0.94 
0.81 
1. 10 
1.05 
0.73 

T      01 

I   to   1.47 
I   to   2.13 
I  to  3.26 
I  to  3.76 
I  to  4.09 
I  to  3.97 
I  to  2.25 

I    to    2    22 

Trenton 

Philadelphia 

Harrisburg 

Mifflin - 

Altoona 

Conemaugh 

Derrv   

T    to    2.49 

I  to  0.7S 

Pittsburg 

*  The  probability  is  that  most  of  the  loaded  cars  West  are  taore  lightly  loaded  than  those 
East,  so  that  the  actual  excess  of  east-bound  over  west-bound  was  greater  than  this  table 
indicates,  except  at  Pittsburg,  where  the  west-bound  cars  were  presumably  the  heaviest.  The 
average  disproportion  over  the  whole  road,  in  ton-miles,  may  be  deduced  from  Table  98  to  be 
I  to  3.49. 

By  referring  to  Table  98  it  will  be  seen  that  the  variation  in  the  disproportion  is  as  lawless 
in  different  years  as  the  above  table  shows  it  to  be  on  different  parts  of  the  same  line. 
39 


6lO   CH.  XVII.— BALANCE  OF  GRADES  FOR  UNEQUAL  TRAFFIC. 

98,  pages  232-3,  shows  the  revolutionary  way  in  which  this  dis- 
proportion has  varied  during  the  past  forty-five  years,  or  during 
the  entire  history  of  the  road.  Neither  the  extent  nor  the  nature 
of  these  changes  could  well  have  been  anticipated  when  the  road 
was  first  constructed;  but  from  our  present  stock  of  knowledge, 
actual  or  potential,  as  to  the  course  of  such  matters  in  the  past, 
we  may  make  a  reasonable  and  safe  approximation  at  least  to 
the  future  probabilities  in  this  respect,  by  investigating  the  facts 
as  to  neighboring  or  rival  lines.  The  proper  manner  of  doing 
this  we  will  shortly  consider.  A  large  body  of  further  statistics 
of  the  same  kind  as  to  other  roads  might  be  presented,  but  not 
enough  to  serve  any  more  useful  purpose  for  any  particular  line 
than  the  approximate  figures  given  in  this  chapter,  without  an 
inadmissible  amount  of  them. 

795.  Assuming  the  ratio  of  the  tonnage  in  each  direction  to  be 
known  or  assumed,  the  admissible  difference  of  gradients  to  correspond 
may  be  very  quickly  determined  by  the  aid  of  the  long  Table  170,  by  de- 
termining the  total  load  in  tons  behind  the  tender  which  must  be  hauled 
on  the  return  trip,  for  a  given  disproportion  of  tonnage.  The  total  load 
can  at  once  be  divided  into  paying  load  (freight)  and  dead  load  (cars),  if 
we  know  or  assume  the  average  load  and  weight  per  car.  By  1890,  with 
the  prevailing  tendency  to  increase  average  load,  it  is  probable  that  the 
total  load  hauled  in  the  direction  of  heaviest  traffic  might  fairly  be 
divided  as  follows : 


Total  weight 

per  car  or 

train. 

Live  weight 

per  car  or 

train. 

Dead  weight 

per  car  or 

train. 

General  Traffic,  . 

.     .          i.oo 

0.60 

0.40 

Mineral  Traffic,  . 

.     .         I.oo 

Q.72 

0.28 

At  present  this  is  a  little  too  favorable ;  not  as  respects  the  nominal 
loads,  but  as  respects  the  loads  actually  hauled,  although  some  of  our 
best  roads  approach  it.  For  example,  the  average  load  of  loaded  cars  on 
the  Pennsylvania  Railroad  is  now  14  tons,  and  of  East-bound  only  15I- 
tons.  The  average  weight  of  the  empty  cars  is  probably  in  the  neighbor- 
hood of  io|-tons.     See  Table  154.  p.  486. 

Then  if  the  return  tonnage  be  only  half  as  great,  the  total  weight  of 

return  trains  will  be  only  0.60  +  -—  =  80  per  cent  as  heavy  in  tons ;  and 
having  computed  this  weight  in  tons  (making  also  an  allowance  which 


CH.  XVII.— BALANCE  OF  GRADES  FOR  UNEQUAL  TRAFFIC.    6ll 

we  shall  consider  in  a  moment)  we  find  at  once  from  Table  170  the  cor- 
responding grade. 

796.  In  this  simple  manner  Table  185  below  was  computed,  which 
gives  sufficient  data  to  enable  the  proper  balance  under  almost  any- 
given  conditions  to  be  readil}^  determined  by  interpolation.  Without 
the  aid  of  Table  170,  while  each  step  in  the  process  is  simple  enough, 
there  are  a  good  many  to  be  taken,  in  each  of  which  a  mistake  is  easy, 
which  is  probably  the  reason  why  in  not  a  few  instances  of  actual  prac- 
tice errors  of  importance  have  been  made  in  it.* 

797.  The  computation  of  the  theoretical  balance  of  gradients  is  com- 
plicated by  the  following  practical  considerations,  the  effect  of  which 
should  be  included  in  the  computation  : 

1.  The  journal-friction  of  empty  cars  is  at  least  2  lbs.  per  ton  (=  o.i 
per  cent  of  grade)  higher  than  with  loaded  cars,  requiring  a  modification 
of  the  theoretical  balance  of  grade  to  that  extent  in  favor  of  the  lightest 
traffic  in  case  all  cars  return  empty,  and  proportionately  if  a  part  return 
empty.  This  has  been  done  in  computing  Table  185,  as  indicated  by  the 
two  lower  lines. 

2.  It  is  not  practically  possible  (par.  91)  to  have  all  cars  in  all  trains 
or  cars  loaded  even  in  the  direction  of  heaviest  traffic.  A  certain  pro- 
portion of  the  cars,  which  for  this  particular  purpose  may  be  estimated 
(liberally  but  not  unfairly)  at  from  5  to  even  (in  special  cases)  10  per 
cent,  will  go  empty  even  in  the  direction  of  the  heaviest  traffic.  These 
cars  serve  to  increase  by  so  much  the  proportion  of  the  dead  to  the  live 
load  of  trains,  and  by  so  much  diminish  the  admissible  difference  in  gra- 
dients, and  so  also  will  the  fact  that  even  loaded  cars  do  not  by  any 
means  average  their  full  nominal  capacity.  Both  of  these  latter  consid- 
erations, however,  affect  only  the  estimate  of  the  proportion  of  the  pay- 
ing to  the  dead  load,  which  is  the  first  thing  to  be  assumed  for  determin- 
ing the  balance  of  grades. 

798.  3.  The  disproportion  of  traffic  varies  not  only  from  year  to  year 
and  from  point  to  point,  but  from  day  to  day  and  from  week  to  week,  as 
already  noted.  That  this  must  inevitably  be  so,  more  or  less,  is  apparent : 
Traffic  cannot  be  held  until  it  is  convenient  to  move  it,  but  must  be 

*  E.g.,  a  prominent  text-book  gives  extracts  from  official  reports  of  two 
very  prominent  engineers,  each  containing  a  number  of  computations  of  this 
kind,  every  one  of  which  is  much  in  error,  and  in  quite  different  ways,  as 
pointed  out  and  corrected  in  detail  in  the  first  edition  of  this  treatise.  The 
writer  could  readily  mention  still  other  instances. 


6l2    CH.  XVII.— BALANCE  OF  GRADES  FOR  UNEQUAL  TRAFFIC^ 


Table  185. 


Proper  Adjustment  of  Ruling  Grades  for  an  Unequal  Volume  of 
Traffic  in  Opposite  Directions. 

[Correct  within  an  inconsiderable  percentage  for  all  classes  of  engines  and  conditions 
of  service.  Computed  for  an  average  Consolidation  engine  from  Table  170,  as  explained 
in  par.  795.  Rolling-friction  of  empty  cars  assumed  to  be  2  lbs.  per  ton  greater  than  that 
of  loaded  cars,] 

j  RETURN  GRADES 

I     Opposing  an  Equal  Resistance  to  the  Power  of  the  Engine  if  the 
Gross  Weight  of  Cars  and  Load  returning  is- 
(Weight  in  direction  of  heaviest  traffic  =  i.oo) 

Grade  opposed 

TO  Heaviest 

Traffic. 

Pel  Cent. 


Level 


i.o 


1.2 

1-4 
1.6 

1.8 
2.0 
2.2 

2.4 
2.6 

2.8 


3-0 


Excess  rolling- 
friction  from 
empty  cars. . 


.88 

.76 

.64 

.52    • 

.40 

.28 

Ratio  of 
Dir 

Return  Fre 
ection  of  H 

ight  only  to  that  in 
eaviest  Traffic. 

Freight 

Cars 

Returning 

Empty. 

Coal  Cars 
Returning 

0.8 

0.6 

0.4 

0.2 

Empty. 

(See  par.  802.) 

•03 

.08 

.15 

.29 

.46 

0.84 

.14 
.26 
•37 

.48 
.60 
•71 
.82 
93 
1.04 

.21 

•34 
•47 
.60 

.72 
.85 

•97 
1. 10 
1.22 

•30 
.46 
.61 

•75 

.90 

1.04 

1. 19 
1^33 
1.48 

•45 
•63 
.81 

.98 
1. 16 
1^33 

1.50 
1.66 
1.83 

.69 

.92 

1. 14 

1^35 
1.56 
1.77 

1.98 
2.17 
2^37 

1. 14 
1.44 
1.73 

2.00 
2.27 
2^54 
2.79 
3-04 
3^28 

1. 15 

1^35 

1.62 

1.99 

2.56 

3-52 

1-37 
1-59 
1. 81 

2.03 
2.24 
2.46 

2.68 
2.89 
3. II 

1.60 
1.84 
2.08 

2.33 
2.57 
2.80 

3^03 
3-26  - 
3 -50 

1.90 
2.17 
2.44 

2.71 
2.98 
3-24 

3.49 
3^74 
3^99 

2.32 
2.63 
2.94 

3^24 
3^54 
3.82 

4.10 

4-37 
4.64 

2.94 
3-31 
3-65 

3.98 
4^32 
4.65 

4.97 
5.20 
5^52 

3.96 
4.40 
4.80 

5^17 

5^55 
5^88 

6.21 

6.53 
6.83 

3-32 

3-74 

4^23 

4.91 

5.80 

7.10 

3-86 

4.38 

4.30 
4.86 

4-84 
5-44 

5^54 
6.16 

6.46 
7.10 

7.87 
8.47 

r 
.  0.4 

^0.02 

2 
0.8 

0.04 

lbs.  per  ton 
1.2       1     1.6 
grade  per  cent 
0.06          0.08 

2.0 

O.IO 

2.0 

O.IO 

A  LOWER  ASSUMED  ROLLING-FRICTION  (than  8  Ibs.  per  ton)  will  reduce  the  ad- 


CH.  XVII.— BALANCE  OF  GRADES  FOR  UNEQUAL  TRAFFIC.   613 

missible  rate  of  return  grades  by  about  0.2  per  cent  in  the  "  north-east  corner"  of  the 
table,  its  effect  decreasing  very  rapidly  from  that  point  in  each  direction. 

A  LOWER  RATIO  OF  ADHESION  (than  14)  will  also  REDUCE  the  admissible  rate  of 
return  grade,  its  effect  being  very  important  in  the  "south-east  comer"  of  the  table,  but 
decreasing  still  more  rapidly  in  each  direction  therefrom. 

The  use  of  tank  engines  will  very  materially  increase  the  admissible  rate  of 
return  grades,  having  a  directly  contrarj'  effect  to  a  lower  ratio  of  adhesion.  The  same 
is  true  in  less  degree  as  the  proportion  of  weight  on  drivers  or  ratio  of  adhesion  is  increased. 

None  of  these  changes  being  proper  ones  to  assume,  it  is  not  deemed  necessary  to  give 
exact  figures. 

moved  at  once ;  and  since  there  must  be  more  or  less  irregular  fluctua- 
tions in  the  volume  of  all  traffic,  it  may  well  happen,  and  notunfrequently 
does  happen,  that  for  the  time  being  the  burden  of  traffic  shall  be  in  the 
opposite  direction  to  the  normal  one.  Thus  on  the  leading  East  and 
West  lines  of  the  United  States,  especially  those  of  the  second  grade,  it 
is  not  uncommon  to  see  engines  running  East  light  to  handle  an  un- 
usual quantity  of  West-bound  traffic,  although  there  is  normally  a  very- 
heavy  excess  of  east-bound  traffic  on  nearly  all  of  them. 

When  this  occurs  favorable  west-bound  grades  are  a  decided 
economy,  although  ordinarily  they  may  be  unimportant. 

Nevertheless,  the  importance  of  this  cause  should  not  be  exaggerated. 
Marked  irregularities  of  this  kind  are  exceptional  and  short-lived, 
and  would  justify  but  very  small  expense  to  reduce  grades  on  their 
account  below  what  the  average  requires.  Irregularities  of  5  or  ro  per 
■cent  may  be  expected  to  exist  for  nearly  half  the  time,  and  hence  to  jus- 
tify about  half  the  expense  for  reducing  the  grades  correspondingly  that 
would  be  incurred  to  provide  for  the  average  condition  of  the  whole 
traffic.  There  is  also  a  certain  small  econorpy  in  being  able  to  send 
back  some  of  the  surplus  engines  and  train  crews  light,  as  passenger 
extras. 

4.  For  passenger  traffic  equally  balanced  grades  are  always  desirable, 
as  noted  more  fully  in  par.  807  et  seq. 

799.  It  is  noticeable  that  all  four  of  these  limiting  provisos  tend  to 
diminish  the  admissible  variation  in  opposing  rates  of  grade.  In  the 
aggregate  they  indicate  that  a  reduction  of  the  grades  against  the  light- 
est traffic  by  something  like  0.2  to  0.3  per  cent  (10  to  16  ft.  per  mile)  be- 
low what  the  assumed  average  disproportion  in  weight  of  trains  seems  to 
require,  is  worth  nearly  half  as  much  as  if  required  by  the  average  con- 
ditions themselves.  When,  in  addition  to  these  reasons  for  approximat- 
ing more  closely  to  an  even  balance  in  spite  of  a  known  disproportion  of 
traffic,  the  very  existence  of  the  assumed  disproportion  appears  doubtful. 


6l4   CH,  XVII.— BALANCE  OF  GRADES  FOR  UNEQUAL  TRAFFIC. 

still  greater  caution  should  be  used  in  assuming  that  anything  will  be 
unobjectionable,  but  an  exact  balance  of  resistances,  which  latter  is  of 
course  the  safest  assumption  to  make  when  the  future  is  for  any  reason 
very  doubtful. 

Nevertheless,  although  the  estimates  of  the  probable  future  dispro- 
portion should  always,  for  the  reasons  given,  be  exceedingly  conserva- 
tive, it  may  on  many  if  not  on  most  lines  be  determined  with  practical 
certainty  that  a  certain  minimum  disproportion  at  least  will  exist  for  the 
decade  or  so  ahead,  which  is  as  long  (par.  78  et  seg.)  as  the  engineer  is. 
financially  warranted  in  looking  ahead. 

800.  It  is  to  be  remembered  also  that  the  same  assumed  balance  of 
grades  which  permits  the  grade  in  one  direction  to  be  made  higher  re- 
quires the  grade  in  the  other  to  be  made  lower,  if  possible,  so  that  the 
assumption  of  a  certain  preponderance  of  traffic  in  one  direction  does 
not  warrant  any  relaxation  of  effort  to  obtain  low  grades,  but  merely 
gives  it  a  little  different  direction.  If  there  be  merely  a  probability  that, 
the  traffic  in  one  direction  will  be  slightly  heavier  than  in  the  other, 
with  a  possibility  that  it  may  be  either  considerably  heavier  or  evenly 
balanced,  and  the  same  expenditure  will  substitute  grades  of  o.  65  one 
way,  and  0.55  the  other,  in  place  of  0.6  grades  both  ways,  it  is  good  en- 
gineering to  do  this,  for  we  can  only  strike  an  average  between  the 
maximum  and  minimum  possibilities  and  act  in  accordance  with  the 
mean.  It  is  demonstrable  mathematically,  as  well  as  clear  to  the  reason, 
that  this  course  is  as  binding  upon  us  as  if  we  had  positive  knowledge 
that  the  mean  of  our  estimates  (if  they  really  are  such,  and  not  guesses) 
was  the  exact  truth. 

Topographical  considerations  often  make  it  impossible  to  even  at- 
tempt a  balance  of  gradients,  at  least  in  the  way  of  favoring  the  heaviest 
traffic.  It  is,  however,  nearly  always  possible  to  favor  the  expense  ac- 
count in  such  cases,  somewhat  at  least,  by  not  showing  unnecessary 
favors  to  the  lighter  traffic. 

801.  For  an  exclusively  mineral  traffic  the  expediency  of  ad- 
justing the  grades  for  the  full  theoretical  difference  can  rarely  be  ques- 
tioned, and  it  is  of  course  for  this  traffic  that  the  greatest  difference  is 
required.  At  the  present  time  the  ratio  of  load  to  weight  of  car  is  con- 
siderably over  2  to  I,  so  that  less  than  \  of  the  weight  of  a  full  train 
is  cars  and  over  f  paying  load.  Consequently,  the  return  trains  of 
empty  cars  with  less  than  ^  as  much  as  the  full  trains,  and  the  proper 
balance  of  grades  shows  a  wide  contrast  in  them,  as  will  be  seen  in 
Table  185. 


CH.  XVIL— BALANCE  OF  GRADES  FOR  UNEQUAL  TRAFFIC.   615 

802.  An  important  fact  to  remember  in  considering  an  almost  exclu- 
sively mineral  traffic  is  that  whatever  general  freight  business  there  may- 
be will  probably  be  against  the  main  traffic  almost  exclusively,  and  that 
the  consumption  of  supplies  per  inhabitant  is  large  in  mining  regions, 
and  almost  wholly  imported.  The  traffic  per  inhabitant  of  mining  re- 
gions, including  shipments  of  machinery,  etc.,  as  also  the  output  per 
miner  (about  \  10  -^  oi  the  total  inhabitants),  may  be  readily  estimated 
by  a  little  investigation.  The  figures  vary  too  greatly  to  attempt  any 
general  analysis. 

803,  For  general  freight  business  no  such  difference  as  with  mineral 
traffic  ever  exists,  but  something  closely  approaching  to  it  exists  at  times 
on  the  leading  East  and  West  trunk  lines,  on  which  the  normal  average 
is  only  from  3  to  4  tons  West  to  10  East.  It  is  probable  that  there 
will  always  continue  to  be  a  heavy  preponderance  of  East-bound  traffic 
in  the  United  States,  although  whether  it  will  continue  to  be  as  heavy 
in  the  future  as  in  the  past  is  a  far  more  doubtful  matter.  The  propor- 
tion of  export  traffic  will  become  relatively  less  as  the  population  of  this 
continent  increases,-  and  this  traffic  has  now  a  great  influence  in  causing 
the  disproportion  of  traffic  which  at  present  exists.  If  the  East  were  to 
continue  to  be  the  manufacturing  region  par  excellence  this  loss  would 
be  compensated  for,  but  that  this  will  be  the  case  seems  very  doubtful. 

804.  An  enormous  West-bound  anthracite  coal-traffic,  moreover,  has 
sprung  up  within  the  last  few  years  which  is  reducing  and  will  still  more 
largely  reduce  the  existing  disproportion.  The  rise  and  growth  of  this 
traffic  is  a  good  illustration  of  the  great  changes  which  may  come  with 
time,  but  which  are  for  the  moment  not  considered.  It  is  the  chief  cause 
for  the  very  remarkable  reversal  of  the  current  of  local  traffic  shown  in 
Table  98. 

The  only  definite  fact  seems  to  be  that  the  burden  of  traffic  will  al- 
ways be  heavily  toward  a  manufacturing  or  mining  region  and  away 
from  the  shippers  of  the  heavier  cereals.  Thus  it  is  about  three  to  one 
from  West  to  East,  and  about  two  to  one  from  the  Northern  to  the 
Southern  States. 

805,  The  latter  fact  shows  that  it  is  not  safe  to  say  broadly  that  the 
burden  of  traffic  is  from  an  agricultural  to  a  manufacturing  region  ;  for 
the  South,  which  is  chiefly  agricultural,  ships  to  the  North,  as  yet,  much 
less  in  weight  than  it  receives  ;  the  reason  being  that  its  exports  are 
largely  cotton,  and  that  the  current  of  its  commercial  business  follows  a 
kmd  of  triangular  course — from  the  South  to  New  York  or  Europe, 
thence  to  the  interior  of  the  United    States,  and  thence  to  the   South 


6l6    CH.  XVII.— BALANCE  OF  GRADES  FOR  UNEQUAL  TRAFFIC, 

again.     But  the  rapid  development  of  the  mineral  resources  of  the  South 
is  bringing  about  a  change  in  this  respect. 

806.  The  possibility  of  some  such  roundabout  process  of  exchange 
as  this,  especially  on  a  small  scale,  is  one  which  must  be  very  frequently 
remembered  if  a  reasonable  estimate  of  probabilities  is  to  be  made. 
Thus,  when  the  Mexican  system  of  railways  was  projected  it  became  at 
once  important  and  difficult  to  determine  in  which  direction  would  be 
the  largest  freight  movement.  The  central  plateau  is  a  region  of  great 
and  largely  undeveloped  grazing  and  agricultural  possibilities,  but  on 
the  other  hand  is  a  great  and  largely  undeveloped  mining  region,  hav- 
ing no  workable  coal  as  yet  known.  Bearing  in  mind  the  character  of 
the  regions  of  the  United  States  to  the  north,  the  writer  concluded  that 
the  traffic  would  not  probably  be  very  unequal,  but  that  the  tonnage 
would  be  the  heaviest  northward.  This  expectation  has  not  yet  (1885) 
been  fulfilled,  but  the  direct  contrary  is  the  case,  the  preponderance 
being  very  heavily  into  the  City  of  Mexico,  and  largely  on  account  of 
the  triangular  process  of  exchange  referred  to.  The  products  exported 
are  on  the  coast  or  seek  the  coast,  and  thence  by  very  indirect  channels 
pay  for  the  shipments  (as  yet  small)  which  go  to  Mexico  in  return  by 
rail.  Whether  or  not  this  tendency  will  continue  is  doubtful.  Proba- 
bly it  will  not,  but  the  burden  of  traffic  will  be  out  of  Mexico  when  a 
fuller  development  has  come.  In  any  case  it  illustrates  the  necessity  of 
looking  beyond  the  superficial  and  immediate  possibilities,  and  remem- 
bering that  great  changes  may  come  with  time. 

807.  For  passenger  service  grades  should  in  all  cases  be  equally 
balanced,  because  whether  passenger  cars  be  loaded  or  unloaded  makes 
but  an  inconsiderable  difference  (par.  606)  in  the  weight  of  trains,  even 
if  it  were  not  certain  that  passenger  travel  must  be,  in  the  long-run, 
equal  in  each  direction,  in  spite  of  a  temporary  preponderance  in  one 
direction,  due  to  emigration.  Therefore,  in  proportion  as  the  passen- 
ger traffic  is  a  larger  and  mineral  traffic  a  smaller  element,  and  in  pro- 
portion as  the  preponderance  of  freight  tonnage  is  doubtful,  the  expedi- 
ency of  seeking  uniform  grades  in  each  direction  increases. 

808.  It  follows  also,  that  when  an  unequal  freight  or  mineral  traffic 
exists,  combined  with  a  considerable  passenger  traffic,  there  is  always  a 
certain  advantage,  and  hence  a  certain  justifiable  expenditure,  in  reduc- 
ing the  rate  of  grade  in  either  direction,  although  the  other  be  left  un- 
changed. The  passenger  service  is  always  benefited  by  reducing  the 
higher  rate  of  grade,  whichever  it  may  be  (provided  it  is,  for  passenger 
service,  a  de-facto  limiting  grade,  as  explained  in  par.  407) ;   and  after 


CH.  XVII.— BALANCE  OF  GRADES  FOR  UNEQUAL  TRAFFIC.    6l^ 

this  has  been  done  there  is  a  certain  advantage  fo  the  freight  traffic  only 
in  reducing  the  grades  against  the  heaviest  traffic.  The  admissible  ex- 
penditure for  doing  this  is  only  that  appertaining  to  the  particular 
traffic  benefited. 

809.  For  example,  suppose  the  grades  on  any  line  to  be  i.oo  and 
1. 20  per  cent  (52.8  and  63  ft.  per  mile),  and  the  ratio  of  the  weight  of 
freight  in  each  direction  to  be  about  as  on  the  Pennsylvania  Railroads, 
viz  ;  as  i.o  to  0.3: 

Per  cent. 

Well-adjusted   grades  for  freight  service  would  be 

(Table  185) .0.6  and  1.2 

Well-adjusted  grades  for  passenger  service  would  be i.o  and  i.o 

We  can  properly  expend,  therefore,  to  reduce  the  grade  which  limits 
the  freight  traffic  (1.0  per  cent)  to  0.6  per  cent,  as  much  as  the  freight 
traffic  alone  justifies ;  and  to  reduce  the  grade  which  is  heaviest  for  pas- 
senger service  (1.2  per  cent)  to  1.0  per  cent  only  as  much  as  the  passen- 
ger service  alone  justifies,  which,  in  case  of  a  light  local  passenger  busi- 
ness, will  not  be  much  (par.  732). 

810.  Even  if  the  business  of  a  road  consists  of  three  distinct  classes 
of  traffic,  passenger,  freight,  and  mineral,  each  one  of  which  would  re- 
quire a  different  balance  of  ruling  grades,  this  difference  need  introduce 
no  confusion  in  the  estimations  of  the  value  of  reducing  grades,  for  we 
have  only  to  determine  from  Table  185  to  what  class  or  classes  of  traffic 
any  proposed  reduction  of  grade  will  be  valuable  or  worthless  to,  and 
the  justifiable  expenditure  to  reduce  it  may  be  determined  for  that 
traffic  only  by  the  methods  of  Chap.  XV.,  par.  726  et  seq. 

811.  It  may  also  be  noted  that  a  mineral  traffic  should  in  general  be 
considered  simply  as  a  part  of  the  general  freight  traffic.  It  is  only 
under  peculiar  circumstances,  as  when  the  haul  is  short  or  the  mineral 
traffic  is  very  large,  that  they  should  be  separately  considered,  and  never 
when  their  separate  conduct  would  involve  a  large  wastage  of  motive- 
power  or  of  empty  car-mileage,  in  either  direction,  since  the  two  can 
always  be  combined  together,  light  freight  trains  being  filled  up  with 
coal  cars  or  vice  versa,  as  is  now  done  on  the  trunk  lines.  It  has  even 
come  about  that  empty  grain  cars  returning  West  are  filled  up  with  coal  so 
as  to  go  loaded  in  both  directions,  and  this  tendency  may  be  expected 
to  increase  or  prevail  whenever  it  will  save  a  considerable  movement  of 
cars  in  opposite  directions,  since  it  effects  a  very  large  economy. 

812.  A  heavy  tonnage  goes  into  all  cities,  since  they  consume  much 
.and  produce  nothing  except  in  the  form  of  manufactures,  which  for  the 


6l8    CH.  XVII.— BALANCE  OF  GRADES  FOR  UNEQUAL  TRAFFIC, 

most  part  weigh  much  less  (although  they  pay  much  more)  than  the  raw- 
materials  which  are  shipped  for  producing  them. 

813.  The  exact  balance  of  grades  for  the  traffic  becomes  easy  in  the 
case  of  a  line  already  in  operation,  and  this  should  be  the  first  step  in 
studying  contemplated  improvements,  since  it  may  save  the  necessity  of 
improving  the  grades  in  one  direction,  or  at  least  some  of  them. 

814.  The  lines  of  few  existing  railways  have  been  studied  during  construc- 
tion with  this  end  in  view.  Some  of  the  earlier  lines  come  the  nearest  to  it; 
for  example,  we  may  take  three  of  the  most  sagaciously  located  lines  in  the 
United  States — the  Baltimore  &  Ohio,  the  Pennsylvania,  and  the  Erie.  The 
Bakimore  &  Ohio  mountain  grades  have  been  laid  out  to  some  extent  with  this 
end  in  view,  since  they  have  2.2  per  cent  grades  (for  16  miles)  opposed  to  West- 
bound traffic  and  only  2.0  per  cent  opposed  to  East-bound,  but  this  difference  is 
far  less  than  the  disproportion  in  traffic  would  warrant,  the  balance  for  2.0  per 
cent  with  a  disproportion  similar  to  that  of  the  Pennsylvania  road  (Table  185) 
being  about  3.2  per  cent.  This,  however,  is  the  less  important  on  such  a  line, 
because  the  heavy  grades  are  so  long  that  the  trains  and  motive-power  can  be 
adapted  quite  accurately  to  each  other,  as  they  are  in  fact,  on  each  separate 
grade.  Using  two  pushers  on  the  2.0  per  cent  grade,  and  only  one  on  the  2.2 
per  cent,  moreover,  would  about  equalize  them  for  such  a  disproportion, 
although  it  is  only  on  grades  of  some  length  that  two  pushers  can  be  advan- 
tageously used.  The  gradients  of  the  Baltimore  &  Ohio,  considered  as  a  whole, 
are  admirably  adapted  for  cheap  working,  in  spite  of  their  heavy  rates,  from 
the  fact  that  they  are  all  "bunched"  in  one  locality.  At  Piedmont  is  one  of 
the  largest  yards  in  the  world,  and  all  trains  are  made  up  anew  there. 

815.  The  Pennsylvania  road  has  i  per  cent  grades  opposed  to  East-bound 
traffic.  The  weight  of  cars  and  freight  westward  being  by  Table  184  about 
I  to  0.4  in  the  neighborhood  of  Altoona,  a  correct  balance  of  grades  would  be 
by  Table  185  about  1.6  per  cent.  Actually  it  is  1.8  per  cent,  and  the  traffic  is 
worked  with  one  pusher  eastward  and  two  pushers  westward. 

816.  The  Erie  is  at  two  or  three  of  its  leading  summits  a  good  instance  of 
well-balanced  grades,  which  is  not  the  least  of  the  striking  merits  of  the  line. 
Even  without  allowing  for  the  early  date  at  which  it  was  built,  the  consummate 
engineering  skill  with  which  it  was  carried  through  the  mountains  and  the  pri- 
meval forest,  without  the  aid  of  maps  and  without  a  single  tunnel  on  its  line  (as 
it  then  was;  one  has  since  been  built  at  Jersey  City),  with  very  low  grades,  and 
on  very  nearly  the  best  line  which  could  now  be  selected,  must  ever  excite  ad- 
miration. Nevertheless,  the  Erie  and  its  branches  afford  several  examples  of 
ill-adjusted  grades,  but  it  will  be  more  profitable,  as  well  as  more  just,  to  con- 
sider the  instances  on  its  main  line  where  they  have  been  carefully  adjusted. 

817.  The  Delaware  Division  ascends  eastward  out  of  the  Susquehanna 
Valley  on  a  60-ft.  (1.14  per   cent)  grade   for  8  miles,   thence   descends  on  a 


CH.  XVII.— BALANCE  OF  GRADES  FOR  UNEQUAL  TRAFFIC.    619 

57  ft.  (1.08)  and  49-ft.  (0.93)  grade  for  about  7  miles  to  Deposit,  and  thence 
follows  an  unbroken  descending  grade  of  10  to  15  ft.  per  mile  to  Port 
Jervis.  The  curvature  probably  increases  the  equivalent  grade  to  about  0.35 
per  cent.  Now,  in  descending  eastwardly  from  the  summit  the  low  rate  at- 
tained is  attained  only  by  following  down  the  hill-side  at  an  elevation  of  40  or 
50  ft.  above  the  bottom  of  the  valley  for  nearly  the  whole  distance,  with  much 
curvature — about  one  mile  more  of  distance  and  at  least  twice  the  cost  for  con- 
struction which  would  have  been  necessary  for  a  line  located  in  the  bottom  of 
the  valley  on  a  grade  of  1.2  or  1.3  per  cent.  It  would  have  been  most  natural, 
therefore,  under  all  the  circumstances,  to  have  chosen  the  light  line;  but  let 
us  consider  the  consequences  to  the  light  trains  returning.  As  the  grades 
are  now,  a  single  pusher  engine  will  just  suffice  to  pass  a  fully  loaded  west- 
bound train  over  the  hill,  the  balance  being  (Table  185)0.35  and  1.03.  Had 
the  grade  been  any  higher,  the  capacity  of  West-bound  engines  over  the  whole 
division  would  have  been  cut  down  in  proportion.  It  was  plainly  the  intent  of 
the  engineer,  therefore, — for  it  is  but  just  to  give  him  credit  for  the  foresight 
which  his  work  indicates, — that  East-bound  trains  should  be  taken  to  the  sum- 
mit from  Susquehanna  as  a  separate  matter,  leaving  all  the  remainder  of  the 
division,  for  trains  in  both  directions,  exceedingly  favorable.  As  a  matter  of 
fact,  trains  are  taken  up  from  Susquehanna  with  two  pushers. 

818.  On  the  Eastern  Division,  at  Port  Jervis,  a  different  adjustment  has 
been  used,  the  grades  against  East-bound  trains  being  46  ft.  and  against  West- 
bound 60  ft.,  which  is  approximately  a  correct  adjustment  for  enabling  trains 
with  pushers  to  run  over  the  hill  with  equal  loads  each  way.  The  remainder 
of  the  division  is  not  a  very  good  specimen  of  location.  Some  improvements 
in  recent  years  have  been  made  in  it,  but  it  is  questionable  if  a  radical  re- 
construction of  the  entire  division  would  not  prove  immensely  profitable.  On 
the  Buffalo  and  Western  divisions  also,  and  on  many  of  the  branches,  ruling 
grades  were  made  the  same  each  way  at  considerable  expense  without  any 
adequate  compensating  advantage. 

819.  Examples  of  badly  adjusted  grades  on  other  lines  might  be  multiplied 
almost  indefinitely,  but  it  would  be  to  little  purpose  to  do  so.  When  the 
grades  are  long,  considerable  leeway  in  rate  may  be  taken  by  assuming  that  the 
grade  will  be  separately  operated,  but  with  short  grades  of  4  to  6  or  7  miles  this 
is  not  expedient. 


620  CHAP.  XVIII.— LIMITING  CURVATURE. 


CHAPTER   XVIII. 

LIMITING   CURVATURE    AND    COMPENSATION    THEREFOR. 

820.  Under  three  different  conditions  curvature  may  come  in, 
in  advance  of  gradients,  as  a  limiting  agent  to  fix  the  weight  of 
trains: 

1.  When  curves  are  introduced  on  a  maximum  grade  without 
reducing  the  rate  of  the  latter  by  what  is  called  the  compensa- 
tion FOR  curvature,  SO  as  to  keep  the  aggregate  resistance  con- 
stant on  both  curves  and  tangents. 

2.  When  a  line  is  nearly  or  quite  level,  and  yet  runs  through 
a  region  requiring  much  curvature  which  (as  is  very  apt  to  hap- 
pen on  such  lines)  cannot  be  "compensated"  because  there  are 
no  grades,  or  no  sufficiently  high  grades  to  reduce,  in  order  to 
eliminate  their  additional  resistance. 

3.  When  on  lines  of  the  latter  (or  any  other)  class  curvature 
of  such  short  radius  is  used  as  to  limit  the  length  of  trains  more 
than  would  the  same  amount  of  curvature  with  longer  radii. 

These  causes  are  more  or  less  interrelated  with  each  other, 
but  we  will  consider  them  separately,  so  far  as  may  be,  in  the 
order  mentioned,  summarizing  our  conclusions  at  the  end  of  this 
chapter  (page  632). 

821.  We  have  seen  (par.  335)  that  curve  resistance  varies  from  less 
than  o.  5  lb.  per  ton  to  perhaps  2.0  or  even  more  lbs.  per  ton  per  degree 
of  curve,  according  to  circumstances ;  which  at  2  lbs.  per  ton  for  each 
tenth  of  grade  (par.  382)  is  equivalent  to  from  0.025  ^o  o-^o  per  cent  of 
grade  per  degree.  Assuming,  therefore,  a  "  straight"  (uncompensated) 
0.5  per  cent  grade,  Fig.  180,  with  alternate  equal  lengths  of  tangent  and 
10°  curves  succeeding  each  other,  and  assuming  that  the  curve  resistance 
is  (see  par.  834  below)  at  the  rate  of  i  lb.  per  ton,  the  effect  of  the  curve 
resistance  is  in  effect  to  double  the  grade  on  the  curves,  so  that  the 


CHAP.   XVIII.— LIMITING   CURVATURE. 


621 


curves  and  grade  together  make  the  equivalent  grade  a  succession  of  i.o 
and  0.5  per  cent  grades,  as  represented  by  the  dotted  line  of  Fig.  180. 

Such  conditions  have  precisely  the  same  deleterious  effect,  no  more 
and  no  less,  that  a  long  tangent  grade-line  would  have  if  broken  up  in 
similar  fashion. 


1^: 


y^eS*-    o^s,v»*t^ 


Fig.  180.— Effect  of  Unreduced  Curvature  to  reduce  Grades. 


822.  An  immense  portion  of  the  heavy  grade-mileage  of  the  world 
has  been  constructed  in  precisely  this  way,  the  grade  being  carried 
through  at  a  uniform  rate  over  curves  and  tangents  alike.  Until  within 
recent  years  nearly  all  American  railways  were  so  constructed,  and  when 
the  curves  were  compensated  at  all,  low  rates  of  compensation  (0.02  and 
0.03  per  cent  per  degree)  were  and  still  are  chiefly  used,  for  which  indeed 
much  can  be  said  (par.  834  below),  although  in  general  a  less  rate  than 
0.05  cannot  be  regarded  as  good  practice. 

823.  The  practice  of  reducing  grades  on  curves  appears  to  have  been 
first  introduced  on  the  Continent.  American  engineers  soon  followed. 
English  engineers  have  neglected  and  still  do  neglect  it  very  generally. 
In  no  part  of  the  world  is  it  universal,  many  prominent  roads  in  this 
country  having  neglected  it  wholly;  as,  for  instance,  the  Erie,  Boston  & 
Albany,  Baltimore  &  Ohio  (for  the  most  part).  Pennsylvania  (for  the 
most  part),  and  in  recent  years  such  lines  as  the  Cincinnati  Southern, 
Chesapeake  &  Ohio,  most  of  the  Denver  &  Rio  Grande,  and  a  host  of 
other  lines. 

824.  The  argument  by  which  a  neglect  to  reduce  grades  on  curves 
has  been  justified,  when  any  attempt  at  all  has  been  made  to  justify  it,  is 
that  the  resistance  is  averaged  by  momentum,  so  that  the  broken 
grade-line  of  Fig.  180  is  reduced  by  the  equalizing  effect  of  slight  fiuctu- 


622  CHAP.   XVIII.— LIMITING   CURVATURE, 

ations  of  velocity  to  the  continuous  0.75  grade-line  shown  below  it.  The 
general  principle  upon  which  this  argument  is  based  is  a  sound  one,  to 
the  extent  that  under  favorable  conditions  precisely  that  effect  may 
result,  either  on  actual  irregularities  of  grade,  or  on  equivalent  ones 
caused  by  unreduced  curvature.  It  is  not  true  at  all  that  any  injurious 
effect  upon  the  train,  or  any  increase  of  virtual  gradient,  necessarily  re- 
sults from  the  gradient  like  the  broken  line  in  Fig.  180  in  place  of  the 
straight  0.75  grades,  U7ider  certain  and  proper  conditions.  Why  and  how 
this  is  so,  and  under  what  conditions,  has  been  so  fully  discerned  in 
Chap.  IX.  (par.  397  et  seq.)  that  it  need  not  be  repeated,  further  than  to 
say  that  a  curve  may  be  considered  as  adding  simply  so  much  to  the 
grade,  and  the  two  cases  be  treated  alike. 

825.  But  conditions  justifying  the  assumption  that  unreduced  curva- 
ture can  thus  be  made  harmless  by  the  effect  of  momentum  cannot  exist 
on  any  actual  maximum  grade,  unless  by  some  rare  accident,  and  conse- 
quently it  is  a  rule  which  should  be  regarded  as  of  universal  application, 
and  rigidly  adhered  to,  that  unreduced  curvature  should  under  no 
circumstances  be  permitted  on  the  maximum  grade,  and  that  the  reduc- 
tion should  in  general  be  ample,  especially  near  stations  and  where  there 
is  an  excessive  resistance.     The  reasons  for  this  are  three,  as  follows  : 

I.  The  distribution  of  curvature  even  on  a  grade-line  only  a  few  miles 
long  naturally  tends  to  become  unequal.  Instead  of  being  equally  dis- 
tributed, as  assumed  for  merely  illustrative  purposes  in  Fig.  180,  it  is  far 
more  likely  to  be  concentrated  in  masses  of  perhaps  several  hundred 
degrees  of  almost  continuous  curvature,  with  long  intermediate  stretches 
of  much  better  alignment,  giving,  if  such  curvature  is  not  reduced,  an 
equivalent  profile  more  like  Fig.  185,  from  which  it  is  far  more  difficult 
to  obtain  a  straight  "  virtual  "  profile  (par.  398)  by  fluctuations  of  velocity 
than  with  a  more  even  distribution  of  curvature ;  and  when  such  excess 
of  curvature  comes  well  up  toward  the  top  of  a  long  grade  it  becomes 
under  most  circumstances  practically  impossible  to  do  so. 

826.  2.  Even  if  the  curvature  be  tolerably  evenly  distributed,  the 
speed  on  maximum  grades  is,  with  the  full  train  which  good  operating 
management  presupposes,  necessarily  slow.  With  extra  heavy  car-loads 
or  in  unfavorable  weather — wet,  frosty,  misty,  very  cold,  or  windy — it  is 
necessarily  very  slow.  At  what  point  on  the  line  the  most  unfavorable 
conditions  will  be  encountered  (for  there  are  always  slight  variations, 
from  wind  or  differences  of  track  if  nothing  more)  cannot  be  exactly 
anticipated,  but  on  the  top  of  long  grades,  especially,  it  can  be  antici- 
pated with  confidence  that  a  very  slow  speed,  not  exceeding  10  or  12 


CHAP.   XVIII.— LIMITING   CURVATURE. 


623 


miles  per  hour,  will  be  rather  the  rule  than  the  exception.  At  such 
speeds,  and  especially  at  still  lower  speeds,  there  is  every  reason  to  be- 
lieve that  the  curve  resistance  is  greater  (pars.  308,  335),  while  there  is 
no  available  momentum  to  overcome  it.  A  train  moving  at  10  miles 
per  hour  (Table  118)  has  only  3.55  ft.  of  "  velocity-head."  At  a  compen- 
sation of  0.05  per  degree  (i  lb.  per  ton)  70°  of  curvature  will  destroy  this 
head  completely,  since  at  that  rate  of  compensation  each  20°  of  central 
angle  destroys  one  foot  of  vertical  head.  In  other  words,  a  train  mov- 
ing at  10  miles  per  hour,  which  could  just  continue  that  speed  on  a 
tangent,  would  be  stalled  at  once  by  seven  stations  of  10°  curve,  or,  if  by 
good  luck  not  stalled,  its  speed  would  be  reduced  so  low  that  additional 
journal-friction  (par.  640  and  Appendix  B)  as  well  as  (probably)  addi- 
tional curve-friction  would  come  in  and  ensure  stalling  on  any  closely 
following  curve. 

827.  3.  Stopping  of  trains  on  grades  from  accident  or  otherwise  is  not 
unfrequently  necessary,  and  then  it  is  entirely  clear  that  a  stoppage  on  a 
long  unreduced  curve  is  a  disastrous  disadvantage,  especially  if  it  be  on 
a  long  succession  of  curves  so  as  to  forbid  the  expedient  of  backing  down 
off  the  curve  to  get  a  fair  start.  It  is  then  strictly  true  that  it  is  the 
grade  at  that  one  particular  point  which  is  the  limiting  gradient,  and 
that  we  cannot  strike  an  average  with  lower  tangent  grades  before  and 
behind,  and  assume  it  is  the  same  thing  as  if  we  actually  had  a  uniform 
average  resistance  at  all  points. 

828.  The  rule  that  a  grade-line  should  be  unbroken  by  unreduced 
curvature  is  still  sound,  in  spite  of  the  fact  that  there  are  certain  circum- 
stances under  which  slight  and  short  SAGS  BELOW  the  grade-line  may 
be  introduced  to  save  expense  of  construction,  especially  where  economy 
in  first  cost  is  a  great  object,  as  it  is  so  much  more  often  than  is  realized 
during  the  period  of  construction.  A  sag  below  a  grade-line  and  a  rise 
above  it — which  is  what  an  uncompensated  curve  in  effect  introduces — 
are  two  entirely  different  matters. 

Thus,  if  we  have  a  1.25  per  cent 
maximum  grade,  up  which  a  train 
can  just  make  its  way  at  a  uniform 
speed  of  10  miles  per  hour,  a  rise  of 
3.55  feet  above  the  grade-line  will,  as 
we  have  just  seen,  stall  the  train.  On 
the  other  hand,  a  sag  in  a  grade-line 
of  an  equal  amount,  as  at  C  in  the 
grade-line  AB,  Fig.  181,  not  only  does  not  endanger  a  stall,  but  actually 


Fig.  181. 


624 


CHAP.    XVIII.— LIMITING  CURVATURE. 


increases  the  velocity  of  passing  from  A  to  B.     For  by  assumption  we 
have  at 

A,  velocity  of  ten  miles  per  hour  =  (Table  ii8)  vel.  head  of  3.55  ft. 

B,  "  "  "  =  "  "  3.55  ft. 
C,  vel.  head  of  3.55  +  3.55  =  7-io  ft.  =  (Table  118)  a  velocity  of  14.14 

miles  per  hour. 

829.  Then  by  the  laws  of  accelerated  and  retarded  motion  (see  par. 
371   or  any  text-book  on  physics)  the  average  speed  between  A  and  C 

and  C  and  ^as  well,  and  hence  between  A  and  B  =  — '- ^^-^  =  12.07 

2 
miles  per  hour — a  gain  in  average  speed  of  2.07  miles  per  hour,  or  about 
3  ft.  per  second  in  passing  over  the  sag  shown  in  Fig.  181,  the  compara- 
tive times  being  about  2  m.  o  sec.  and  i  m.  40  sec. 

This  gain  of  time  is  for  the  same  reason  that  a  body  descending  from 
A  to  B,  Fig.  182,  over  the  different  paths  a,  b,  c,  d,  although  acted  on  by 

the  same  force  (gravity  acting  through 
CB),  takes  a  very  different  time  for  de- 
scending to  B,  the  cycloid  d  being  the 
"curve  of  quickest  descent."  The  re- 
sulting velocity  at  B  is  in  all  cases  the 
same,  barring  loss  by  friction,  but  the 
time  consumed  in  reaching  B  is  widely 
different. 

830.  Therefore,  while  compensation  for  curvature  should  never  be 
omitted,  it  may  still  be  admissible,  in  certain  exceptional  cases  (as  to 

temporarily  save  large 
fills  or  otherwise  reduce 
works),  to  introduce  a 
sag  below  a  grade-line, 
which  is  never  the  case 
with  a  rise  above  a  grade - 
line.  Thus  the  dotted 
profile,  bbbb,  Fig.  183,  can 
certainly  be  operated  un- 
der any  and  all  circum- 
stances (if  the  sag  be  not 
too  great,  par.  435  and 
Table  121)  as  a  virtual  grade  of  the  same  rate  as  the  average  actual 
grade  ;  but  with  the  grade-line  aaaa  this  is  not  possible,  unless  the  initial 
speed  be  very  high  or  the  points  aa  rise  but  little  above  the  average 
grade-line. 


Fig.  182. 


Fig.  183. 


CHAP.    XVIII.— LIMITING   CURVATURE. 


625 


831.  The  principle  is  the  same  as  the  one  so  familiar  to  hydraulic  engineers 
known  as  the  "hydraulic  grade-line."  If  water  is  to  be  conveyed  from  a  high 
reservoir  to  a  lower  point  of  delivery,  it  is  an  axiom  in  hydraulics  that  any  lib- 
erties whatever  can  be  taken  with  the  grade  of  the  pipes  without  affecting  the 
discharge  in  the  least,  more  than  the  same  increase  of  length  and  curvature 
would  do  in  a  pipe  laid  to  a  uniform  grade,  provided  the  pipe  at  no  point  rises 
above  a  straight  line  connecting  the  points  of  supply  and  delivery,  which  is 
known  as  the  "hydraulic  grade-line,"  as  on  the  line  bbbb.  Fig.  183.  If,  how- 
ever, the  pipe  rises  above  this  line,  by  however  little,  as  at  the  highest  a,  Fig. 
183,  the  discharge  will  immediately  be  reduced  to  correspond  with  the  new 
hydraulic  grade-line  passing  through  the  point  of  supply  and  tangent  to  the  now 
highest  point  on  the  pipe. 

In  theory  a  lo-mile  grade  of  50  ft.  per  mile  might  be  broken  up  into  (i)  5 
miles  of  level  and  (2)  5  miles  of  100  ft.  per  mile,  without  increasing  the  de-facto 
ruling  grade  above  50  ft.  per  mile;  but  we  cannot  reverse  the  orders  of  these 
gradients,  making  the  first  last  and  the  last  first,  without  a  theoretical  as  well  as 
practical  increase  of  the  gradient  to  100  ft.  per  mile.  Even  in  the  former  case, 
the  velocity  at  the  end  of  the  first  five  miles  of  level  would  have  to  be  Syf  miles 
per  hour,  assuming  an  initial  velocity  of  15  miles  per  hour.  This  is  hardly  a 
practicable  speed  for  freight  trains;  and  it  therefore  should  not  be  understood 
that  any  considerable  sags  below  a  grade-line  are  admissible.  The  only  asser- 
tion made  is  that,  assuming  such  speed  to  be  practicable,  even  250-ft.  sags 
below  a  grade-line  would  do  no  harm,  whereas  any  rise  whatever  above  it 
would  destroy  it,  theoretically  as  well  as  practically. 


832.  A  remarkable  instance  of  the  advantage  thus  to  be  gained  at 
times  occurred  in  the  writer's  practice,  and  is  shown  in  Fig.  184.     Near 
40 


626  CHAP.   XVIII.— LIMITING   CURVATURE. 


the  middle  of  a  long  grade-line  which  it  was  very  desirable  to  keep  down 
to  the  lowest  limits,  occurred  a  saddle  between  two  hills,  where  support- 
ing ground  was  wholly  lost.  Consequently,  although  there  was  no  ma- 
terial difference  in  the  profile  at  any  other  point,  both  being  side-hill,  at 
this  point  any  lift  of  the  grade-line  meant  so  much  addition  to  the  fill. 
To  bring  the  grade-line  down  to  within  a  few  feet  of  the  surface  meant 
an  increase  of  the  pusher  grade  from  1.15  to  1.25,  equivalent  to  an  increase 
of  ruling  grade  on  a  long  division  from  0.4  to  0.5.  To  obtain  the  lower 
grade  required  a  very  long  fill,  containing  some  190,000  cubic  yards  when 
fully  made  (estimated  to  cost  20  cts.  per  yard);  but  by  introducing  a  sag  in 
the  grade-line  of  some  25  feet  (shown  by  dotted  lines  on  Fig.  184),  as- 
sumed as  about  the  extreme  depth  of  sag  which  it  would  be  proper  to  at- 
tempt to  operate  as  a  continuous  virtual  profile,  even  temporarily,*  the 
fill  could  b^ reduced  to  some  30,000  cubic  yards,  leaving  the  track  to  be 
gradually  raised  up  to  the  straight  grade-line  when  and  if  necessity 
should  appear  and  convenience  serve.  To  make  the  fill  in  the  beginning 
was  not  justified  by  the  financial  status  of  the  company,  nor  by  the  time 
at  it?  disposal,  nor  could  material  be  obtained  at  reasonable  cost  except 
by  train. 

833.  There  were  then  three  possibilities,  besides  that  of  making  the 
fill  complete  : 

1.  That  the  grade  would  continue  to  be  operated  indefinitely  as  a  vir- 
tual straight  grade  by  the  aid  of  momentum,  tolerating  the  necessary 
velocity  of  30^-  miles  per  hour  in  the  bottom  of  the  sag. 

2.  That  the  fill  would  be  raised  somewhat  from  time  to  time,  so  as  to 
reduce  the  necessary  fluctuation  of  velocity  to  less  objectionable  limits. 

3.  That  the  traffic  of  the  line  would  prove  so  thin  (it  was  very  doubt- 
ful) that  the  trains  would  for  the  most  part  be  light  and  the  necessity  for 
either  expedient  not  be  great. 

In  this  way  it  was  possible  to  have  one's  cake  and  eat  it  too;  to  econ- 
omize as  much  as  was  otherwise  possible  against  the  contingency  of 
future  poverty,  and  to  lose  nothing  (but  rather  gain  the  interest  on  the 
cost  of  the  fill)  in  case  the  future  should  prove  prosperous  ;  for  at  the 
worst  the  1.15  line  could  certainly  be  operated  as  a  virtual  1.25. 

So  pronounced  an  instance  of  the  legitimate  use  of  sags  in  grade-lines 
will  rarely  occur,  but  the  same  principle  may  be  availed  of  often  on  a 

*  Velocity-head  due  to  speed  of  15  miles  per  hour  (Table  118) 7.99  ft. 

Add  for  depth  of  sag  below  virtual  profile 25.00  " 

Velocity-head  in  bottom  of  sag  (giving  speed  of  30^  miles  per  hour),   32.99  ft. 


CHAP.    XVIII.— LIMITING   CURVATURE.  627 

smaller  scale,  if  only  to  introduce  a  little  extra  compensation  in  a  long 
curve  on  a  high  fill,  returning  to  the  original  grade-line  by  a  slightly 
steeper  grade  beyond. 

834.  It  will  naturally  follow  from  what  has  preceded  that  the  proper 

RATE    OF    COMPENSATION    IS    NOT   A    FIXED   QUANTITY,   but    may  under 

varying  circumstances  vary  within  somewhat  wide  limits.  The  more 
usual  rates  are  from  0.03  to  0.05  per  cent  per  degree  of  curvature,  corre- 
sponding to  0.6  to  i.o  lbs.  per  ton  per  degree.  If  the  precise  amount  of 
curve  resistance  were  known,  and  if  it  were  always  the  same,  of  course 
but  one  rate  of  compensation  would  be  proper,  but  as  its  precise  rate  is 
not  known,  and  as  there  is  strong  reason  to  believe  (Appendix  A)  that 
in  starting  a  train  it  may  possibly  amount  to  as  much  as  2.0  lbs.  per  ton, 
•a  compensation  sufficient  to  equalize  curve  resistance  in  ordinary  circum- 
stances cannot  be  assumed  to  be  certainly  sufficient  at  points  where 
speed  may  be  expected  to  be  very  slow,  as  toward  the  top  of  long  grades 
and  occasionally  at  other  points. 

835.  Under  these  circumstances,  prudence  would  indicate  that  wher- 
ever there  is  NO  physical  limit  to  the  possible  reduction  of  grade  on 
curves,  it  should  be  made  ample,  so  that  the  curves  should  certain-ly  offer 
no  greater  resistance  than  the  adjacent  tangents.  At  stations  this  rule 
would  require  a  grade  reduction  of  o.  i  per  cent  per  degree. 

On  the  other  hand,  when  we  are  merely  trying  to  equalize  the  tangent 
and  curve  resistance  on  a  long  ascent ;  and  whatever  is  taken  off  the 
curves  must  be  added  on  to  the  tangents  and  vice  versa,  no  such  practice 
7S  proper.  A  chain  is  only  equal  to  the  strength  of  its  weakest  link,  and 
it  avails  little  to  know  which  is  the  weakest  link  if  we  cannot  strengthen 
it.  If  we  come  as  near  to  an  exact  equality  as  we  can,  in  compensating 
for  curvature,  it  is  of  no  importance  whether  our  compensation  is  a  little 
too  great  or  a  little  too  small.  In  the  one  case  trains  will  stall  on  the 
tangents  and  in  the  other  on  the  curves— that  is  all.  Our  object  is  simply 
to  guard  against  a  certainty  of  stalling  on  either.  Nothing  more  than 
this  is  important. 

836.  Hence  it  may  well  be  that  on  a  long  and  crooked  ascent,  where 
the  curvature  greatly  exceeds  the  tangents,  yet  where  there  are  one  or 
two  considerable  tangents,  prudence  will  require  the  assumption  of  a  very 
low  rate  of  compensation  ;  for  otherwise  a  very  slight  loss  of  elevation 
on  each  curve,  multiplied  by  many  curves,  will  prevent  our  attaining  the 
desired  summit  at  all  without  a  considerable  increase  of  the  normal  tan- 
gent grade.  If  we  have  guessed  aright  as  to  the  real  curve  resistance, 
this  may  do  no  harm,  but  on  the  other  hand,  if  we  have  guessed  wrongly. 


628  CHAP.    XVIII.— LIMITING   CURVATURE. 

and  exaggerated  the  probable  curve  resistance,  we  shall  have  unneces- 
sarily increased  our  tangent  grade.  Hence,  by  assuring  a  low  rate  of 
curve  resistance  in  such  a  case,  we  can  hardly  in  any  case  lose  anything 
appreciable,  and  may  save  a  needless  loss  of  grade.  A  compensation 
rate  of  0.03  per  degree  of  curvature  may  then  be  proper,  below  which  the 
rate  of  compensation  should  never  fall. 

837.  For  the  same  reasons,  it  may  well  happen  that  at  different  points 
on  the  same  line  different  rates  of  compensation  may  be  proper.  Where 
the  loss  of  elevation  by  a  high  rate  of  compensation  is  a  very  serious  mat- 
ter, because  of  a  great  amount  of  curvature,  it  may  be  taken  at  a  mini- 
mum. At  other  points,  where  there  is  less  cu.vature  to  be  compensated 
and  a  higher  compensation  can  be  had  at  little  or  no  cost,  it  should  there 
be  used.  The  effect  will  be  to  make  most  of  the  maximum  grade  scat- 
tered over  the  division  a  little  easier  to  handle  trains  on  than  the  longest 
or  worst  grade.  This  may  well  result  in  handling  a  car  or  two  more  than 
would  be  deemed  possible  were  the  resistance  as  great  at  two  or  three 
points  as  it  is  at  one. 

It  has  been  elsewhere  said  (see  Table  124)  that  it  is  always  worthwhile 
to  keep  a  little  below  the  maximum  where  possible,  at  moderate  cost. 
This  is  only  another  application  of  the  same  principle,  but,  owing  to  the 
uncertainty  which  hangs  about  the  question  of  curve  resistance,  it  is  a 
wiser  way  of  attaining  the  same  end  than  to  reduce  the  nominal  tangent 
grade,  especially  in  the  vicinity  of  stations. 

838.  To  illustrate  the  importance  of  eo-metimes  varying  the  rate  of 
compensation  to  suit  circumstances,  assume  a  1.5  percent  average  grade. 
Fig.  185,  nearly  ten  miles  long  (500  stations — taking  a  "  mile"  at  5000  ft. 
for  convenience  of  computation),  subdivided  as  follows  in  respect  to 
amount  of  curvature  : 

^  ,  j  150  stations  with  about  80°  per  mile  =  continuous  1°  curve 

^^'    •*•    \  (with  f  of  the  line  tangent). 

(  100  stations  with  about  300°  per  mile  =  "  6''       " 

Middle.  .  .  ]  100        "  "         "       400°    "       "     =  "  8°       " 

(  (with  i  of  the  line  tangent). 

^  3  150  stations  with  about  50"  per  mile  =  "  ii°     " 

i^ocver.  .  .  ^  ^^.^j^  ^  ^^  ^^^  j.^^  tangent). 

Assume  also  a  stoppmg-place  near  B,  at  the  foot  of  the  grade,  so  that 
no  assistance  from  velocity  can  be  counted  on  : 

This  is  in  no  respect  an  unreasonably  or  improbably  irregular  distri- 
bution of  curvature  on  such  a  line,  nor  an  unusually  large  amount  of 
curvature  for  a  cheap  line  in  rough  country.  In  all  there  will  be  150°-!- 
600° +  800° +  22 5° =177 5°  of  curvature  on  the  ascent. 


CHAP.  XVIII— LIMITING  CURVATURE. 


629 


At  various  rates  of  compensation  for  curvature  the  grades  required 
on  tangents  for  various  rates  of  compensation  would  be  as  follows,  as 


the  student  will  do  well  to  determine  for  himself  by  a  brief  compu- 
tation :  * 

At  0.03^  per  degree,  1.50  +  -1065  =  1.6065  P^i"  cent. 
"0.05      "        "        i.5o  +  .i775  =  1.6775    "       " 
"   o.io      "        "        1.50 +  -355    =  1-855      "      " 

839.  If  the  topography  were  such  that  we  had  just  500  stations  in 
which  to  rise  750  feet,  this  would  mean,  if  we  adopted  a  compensation 
of  o.io  per  degree  instead  of  0.03,  that  our  tangent  grade  (which  would 
then  certainly  be  the  governing  one,  because  we  have  adopted  a  compen- 
sation which  will  CERTAINLY  bring  the  resistance  on  curves  below  that 
on  tangents)  will  be  greater  by  0.25  per  cent,  or  5  lbs.  per  ton,  than  with 
the  lower  rate  of  compensation.  In  other  words,  in  order  to  secure  the 
wholly,  or  almost  wholly,  worthless  end  that  trains,  when  and  if  they 
stall,  shall  stall  always  on  tangents  and  never  on  curves,  we  have  greatly 
increased  the  chances  of  their  stalling  on  tangents,  on  the  top  or  bottom 
sections  of  the  grades  at  least,  where  the  tangents  are  the  longest; — 
a  plain  act  of  folly. 

840.  But  this  is  but  one  side  of  the  question.  The  total  rise  in  feet 
and  the  elevation  of  intermediate  points  would,  under  the  various  as- 

*  Knowing  approximately  the  total  degrees  of  central  angle  on  any  grade, 
we  have  only  to  multiply  the  total  by  the  assumed  rate  of  compensation  to  find 
how  much  total  elevation  will  be  lost  by  the  compensation.  The  elevation, 
divided  by  the  length  of  the  grade,  will  give  the  rate  by  which  the  tangent 
maximum  must  be  increased  to  introduce  the  compensation, 


630 


CHAP,   XVIII.— LIMITING  CURVATURE. 


sumed  rates  of  compensation,  have  to  be  as  shown  in  Table  186;  and  it. 
will  be  seen  that  the  middle  point  c  of  the  entire  grade  comes  at  about 
the  same  elevation  with  either  rate  of  compensation,  but  that  there  is  a 
material  difference  in  the  height  of  the  grade-line  at  the  beginning  and 
end  of  the  middle  sections  C  and  D,  or  at  the  "  quarter  points"  of  the 
grade.  While  the  through  uncompensated  grade-line  falls  as  shown  by 
the  dotted  line,  the  effect  of  introducing  the  curve  compensation,  by- 
whatever  rate,  is  to  give  a  profile  like  the  solid  line,  the  point  C  being 
from  \i\  to  38  feet  higher  than  before,  and  the  point  D  from  9  to  31  feet 
lower,  according  to  the  rate  of  compensation. 


Table  186. 

Illustrating  the  Effect  of  Different  Rates  of  Curve  Compensation 
TO  Modify  the  Elevation  of  Intermediate  Points  on  Long  Grade- 
Lines. 

[Based  on  the  data  of  par.  838  and  Fig.  185.] 


(Foot  of 
Grade.) 


D  

E  (summit). 


1-5 
Straight. 
No  compensa- 
tion. 


Rise. 

225 
150 
150 
225 


Eleva- 
tion, 
o. 

225. 

375- 

525- 

750. 


I . 6065 
Tangent  Grade. 
.03  compensation. 


Rise. 

236.48 
142.65 
136.65 
234.22 


Eleva- 
tion. 
0.00 

236.48 

379- t3 

515.78 

750- 


1-6775 
Tangent  Grade. 
.05  compensation. 


Rise. 

244.12 
137-75 
127.75 
240.38 


Eleva- 
tion. 
0.00 

244.12 
381.87 
509 . 62 
750- 


1-855 
Tangent  Grade. 
.  10  compensation. 


Rise. 

263.25 
125.50 
105.50 
255-75 


Eleva- 
tion. 
0.00 

263.25. 
388.7s 
494.24 
750. 


Difference  in  Resulting  Elevations  at  Variotis  Points  on  the  Grade,  from  the 
Straight  Tangent  Grade. 


B  (foot  of  grade) 

C 

c 

D 

E  (summit) 


Constant 

11.48  ft.  higher 

413"         " 
9.22  "    lower. 
Constant 


38.25  ft.  higher. 
13-75"        " 
30.76  "    lower. 


Topographical  conditions  will  sometimes  permit,  but  will  more 
usually  forbid  assummg  that  we  have  such  leeway  in  the  necessary  posi- 
tion of  the  grade,  thus  depriving  us  in  a  measure  of  the  privilege  of  free 
choice. 

841.  Now  suppose,  on  such  a  grade,  that  the  middle  200  stations  or 
about  4  miles,  on  which  most  of  the  curvature  is  bunched,  was  so  situ- 


CHAP.   XVIII.— LIMITING   CURVATURE.  63 1 

ated  as  to  make  it  essential  to  rise  only  some  230  feet,  unless  consider- 
able extra  expense  were  to  be  incurred,  while  at  the  same  time  the 
character  of  the  line  elsewhere  was  not  such  as  to  admit  of  a  lower 
maximum  tangent  grade.  Under  these  circumstances,  which  may  fre- 
quently occur,  it  would  be  a  great  error  not  to  reduce  grade  on  curves  by 
the  full  amount  which  the  topographical  conditions  made  possible  with- 
out loss  up  to  even  o.  10  per  cent  per  degree  of  curve,  in  the  existing 
state  of  our  knowledge,  even  if  at  other  points  we  used  less,  in  that 
case,  if  we  have  overestimated  the  probable  or  possible  resistance  on 
curves,  it  is  not  likely  to  do  harm,  because  the  large  amount  of  curva- 
ture and  small  amount  of  tangents  will  enable  any  excess  of  resistance 
in  the  latter  to  be  equalized  by  momentum,  whereas  if  we  have  under- 
estimated the  curve  resistance  a  similar  effect  is  not  possible,  or  at  least 
not  as  fully  possible,  on  account  of  the  greater  length  of  curves. 

On  the  upper  and  lower  sections,  where  tangents  prevail  and  curves 
are  the  exception,  the  opposite  principle  prevails.  If  the  curve  compen- 
sation be  too  little  it  will  be  equalized  easily  enough  by  momentum  on 
short  and  infrequent  curves,  so  that  the  result  will  be  the  same  in  effect 
as  if  the  balance  were  exact. 

842.  Under  the  circumstances  of  the  example  just  considered,  as- 
suming the  middle  part  of  the  grade  to  be  fixed  as  just  assumed,  the 
proper  course  to  pursue  with  the  lower  part  of  the  grade  would  be  to 
ease  its  rate  a  little,  if  circumstances  permitted  doing  so  at  little  or  no 
expense ;  otherwise,  to  reduce  its  virtual  rate  by  the  simple  expedient 
of  removing  the  stopping  point  at  the  foot  of  the  grade  some  distance 
from' it,  so  as  to  ensure  gaining  something  by  momentum.  A  speed  of 
25  miles  per  hour  at  the  foot  of  the  grade  reduced  to  10  miles  per  hour 
at  Cwill  (Table  118)  ensure  a  gain  from  surrendered  energy  of  22.20  — 
3.55  =  18.65  vertical  feet  (see  Fig.  185),  which  will  reduce  the  grade  on 

the  first  150  stations  by  — —  =  0.124  per  cent,  and  so  secure  an  equality 

with  the  virtual  grade  of  the  next  section  above,  even  with  the  lowest 
possible  rate  of  curve  resistance.  The  curve  compensation  on  this  lower 
section  should  in  any  case  be  small,  whatever  it  may  be  on  the  middle 
section  just  above. 

843.  On  the  upper  section  DE,  assuming  the  lower  and  middle  sec- 
tion to  have  been  fixed  as  above,  an  effort  will  naturally  be  made  to 
lengthen  the  line  a  little  at  the  upper  end  at  the  expense  of  a  moderate 
amount  of  distance  and  curvature,  so  as  to  give  a  gradient  DF  instead 
of  DE,  Fig.  185  ;  but  if  this  be  not  possible,  the  disadvantage  will  not  be 
very  serious.     Our  case  will  be  this  :    By  virtue  of  an  excess  in  rate  of 


632  CHAP.   XVIII,— LIMITING  CURVATURE. 

curve  compensation  we  have  the  broken  virtual  gradient  ACDE  in- 
stead of  the  straight  grade  BE,  which  is  of  course  preferable.  The  dis- 
advantage at  the  lower  end,  which  would  naturally  be  the  most  serious 
(par.  828),  since  it  carries  our  virtual  gradient  above  the  grade-line  BE, 
which  we  desire,  we  have  neutralized  by  momentum.*  The  disadvan- 
tage at  the  upper  end,  since  it  merely  carries  our  profile  a  little  below 
the  grade-line,  will  in  great  measure,  if  not  entirely,  neutralize  itself  by 
momentum. 

In  this  way  we  have  done  the  best  which  can  be  done  to  avail  ourselves 
of  every  chance  in  our  favor,  whereas  by  assuming  any  hard-and-fast  rule 
whatever,  and  then  following  it  blindly  (as  we  might  be  justified  in  doing 
if  we  knew  it  was  correct),  we  are  certain  to  lose  something,  and  may  lose 
a  good  deal. 

844.  Our  practical  conclusions  as  to  rate  of  curve  compensa- 
tion, therefore,  may  be  summarized  as  follows: 

1.  With  short  grades  or  under  favoring  topographical  condi- 
tions compensate  as  liberally  as  possible  up  to  a  maximum  at 
special  points  of  o.io  per  cent  per  degree. 

2.  Where  speed  may  sometimes  be  very  low,  and  hence  in- 
variably on  or  very  near  to  known  stopping-places,  this  maxi- 
mum rate  appears,  with  our  present  knowledge,  none  too  much. 
In  general,  however,  0.05  per  cent  per  degree  (=  i  lb.  per  ton) 
is  an  ample  equivalent  for  curve  resistance,  and  fo7'  fast  trains 
alone  probably  0.02  to  0.03  per  cent  (=  0.4  to  0.6  lb.  per, ton) 
is  sufficient  to  balance  the  resistance. 

3.  On  sections  where  curves  largely  predominate  over  tan- 
gents it  is  particularh^  desirable  to  have  ample  compensation,  and 
if  excessive  it  will  do  least  harm.      On  the  contrary, 

4.  On  sections  v^^here  the  amount  of  curvature  is  small  it  is  less 
important  to  have  full  compensation,  and  if  excessive  it  will  do 
most  harm. 

5.  When  the  rate  of  compensation  can  only  be  increased  at  the 
CERTAIN  cost  of  a  Corresponding  increase  in  the  rate  of  tangent 
grades  (making  very  sure  that  it  is  certain,  and  not  an  over-hasty 

*  The  word  "  momentum"  here  and  elsewhere  is  used  in  a  somewhat  un- 
scientific way,  to  correspond  with  the  popular  use  of  the  word.  The  scientist 
will  not  be  confused  thereby,  while  the  average  reader  is  assisted. 


CHAP.    XVIII.— LIMITING   CURVATURE.  633 

conclusion  from  inexperience  or  lack  of  care),  no  larger  rate  than 
we  feel  practically  certain  will  be  required  to  balance  the  curve 
resistance  (0.03  to  0.04)  should  be  chosen. 

Otherwise,  we  are  committing  the  folly  of  making  a  certain 
addition  to  the  grade  in  one  place,  to  avoid  one  in  another  place 
which  is  merely  problematical. 

6.  On  any  minor  gradients  where  the  curvature  is  not  suffi- 
cient to  bring  the  virtual  profile  up  to  the  maximum  it  is  not 
important  to  compensate  for  curvature  at  all,  although  it  is  gen- 
erally as  well  to  do  so,  especially  at  points  where  to  do  so  will 
slightly  reduce  the  cost  of  construction,  as  is  very  apt  to  be  the 
case  on  long  curves. 

When  not  compensated,  the  curvature  merely  has  an  equiva- 
lent effect  to  a  slight  undulation  of  gradient  (Class  A  of  rise  and 
fall,  par.  438)  which  produces  no  shock  to  the  train  and  so  is 
not  a  measurable  disadvantage. 

7.  It  is  not  in  the  least  essential  or  important  to  precisely 
adapt  the  compensation  to  the  exact  length  of  each  curve.  The 
reduced  rate  may  as  well  as  not  begin  and  end  at  the  nearest  even 
station,  and  may  be  made  a  little  less  on  one  curve  and  a  little 
more  on  one  immediately  above  if  a  horizontal  slice  of  a  foot  or 
more  may  thereby  be  taken  off  a  high  fill  on  the  tangent  connect- 
ing them,  but  never  so  as  to  cause  the  grade  to  rise  above  the  uniform 
grade-line. 

8.  Curves  immediately  below  a  known  stopping-place  for  all 
trains  need  not  and  should  not  be  compensated  at  all. 

9.  The  rate  of  compensation  should  be  uniform  per  degree 
for  all  degrees  of  curvature,  or  in  no  case  made  greater  for  the 
sharper  curves.  It  may  even  be  made  less  for  curves  of  over  10° 
[par.  335  (9)].  If  the  rate  be  reduced  one  half  for  the  excess 
over  10°,  making  the  compensation  for  a  16°  curve  thirteen  times 
that  for  a  1°  curve,  it  will  certainly  lead  to  no  bad  results,  although 
a  rather  rough  rule. 

This  is  directly  contrary  to  the  usual  practice,  which  is  to  increase  the  rate 
of  compensation  with  the  sharpness  of  the  curve,  if  anything;  but  this  oractice 
rests  upon  the  assumption  which  we  have  seen  to  be  the  direct  contrary  of  the 
truth  (par.  321  et  al.),  that  the  curve  resistance  increases  with  the  degree  of  the 


634  CHAP.   XVIII.— LIMITING   CURVATURE. 

curve.  The  results  of  experience  on  the  New  York  elevated  lines  and 
numerous  others  with  very  sharp  curves,  both  of  standard  and  narrow  gauge,  is 
enough  to  disprove  this,  confirmed  as  it  is  very  directly  by  the  indications  of 
theory. 

lo.  Since  we  have  seen  in  Chap.  VIII.  (par.  330-335)  that 
there  is  no  reason  to  believe  that  curve  resistance  increases  per 
ton  with  the  length  of  the  train,  or  even  (appreciably)  with  the 
type  of  engine  (par.  285  et  seq.)  there  is  no  reason  for  varying  the 
compensation  because  of  the  grades  or  length  of  train,  except  for 
this — that  it  is  usually  easier  to  spare  the  elevation  for  a  liberal 
rate  of  compensation  with  low  grades  than  with  high  ones.  It 
is  therefore  proper  to  do  so. 


CHAP.   XIX.— THE  LIMIT  OF  MAXIMUM  CURVATURE.   635 


CHAPTER   XIX. 

THE    LIMIT    OF    MAXIMUM    CURVATURE. 

845.  Although  badly  adjusted  grades  have  a  more  serious 
effect  on  operating  expenses,  there  is  no  detail  connected  with 
location  which  has  so  great  an  effect  on  the  cost  of  construction 
as  that  which  we  are  about  to  consider — nor  any  in  which  the  ten- 
dency is  so  notable  to  go  to  one  extreme  or  the  other,  without 
any  very  definite  or  defensible  reasons.  It  is  evident  that,  while 
circumstances  will  often  justify  and  require  the  use  of  very  sharp 
curvature  or  of  very  easy  curvature,  they  will  in  no  case  either 
justify  or  require  that  conclusions  should  be  jumped  at  in  some 
such  manner  as  that  sketched  in  par.  245. 

846.  Moreover,  it  may  be  again  repeated,  and  cannot  be  too 
fully  recognized  and  clearly  borne  in  mind,  that  both  the  amount 
and  radius  of  curvature,  like  the  amount  and  rate  of  grades,  is 
even  more  dependent  upon  study,  care,  and  skill  than  on  topog- 
raphy. There  exists,  too,  a  most  dangerous  tendency  to  use 
more  and  sharper  curvature  than  is  at  all  necessary  in  country 
of  some  difficulty,  and  less  and  easier  curvature  than  is  at  all 
expedient  in  country  of  no  difficulty,  or  in  country  whose  only 
difficulty  comes  from  trying  to  hold  close  to  an  air-line  (Chap. 
XX.).  Errors  of  this  kind,  resulting  merely  from  lack  of  care 
or  skill,  are  especially  apt  to  lead  to  the  use  of  absurdly  sharp 
curvature  if  one  has  imbibed  the  notion  that  easy  radii  are  unim- 
portant. 

847.  Recognizing  these  dangers,  we  proceed  to  analyze,  as 
nearly  as  may  be,  the  causes  which  fix  the  advisable  limit  of 
maximum  curvature  and  the  cost  of  exceeding  it.  We  have 
seen  (par.  343)  that  these  causes  may  all  be  separated  under  the 
two  following  heads,  sharply  defined  from  each  other: 


636  CHAP.  XIX,— THE  LIMIT  OF  MAXIMUM  CURVATURE. 


First.  The  inherently  greater  costliness,  not  of  curvature 
measured  by  degrees.^  but  of  sharp  curvature  instead  of  easy 
curvature  y<?r  approxii7iately  the  sa??ie  number  of  degrees.  In  other 
words,  the  greater  wear  and  tear  of  track  and  rolling-stock,  con- 
sumption of  fuel,  danger  of  accident,  loss  by  decreased  speed, 
etc.,  which  results  from  using  100  feet  of  10°  curvature  instead 
of  1000  feet  of  1°  curvature  for  deflecting  the  line  through  a  cen- 
tral angle  of  10°,  or  from  using  900  feet  of  10°,  and  550  feet  of 
tangent  at  each  end,  for  deflecting  through  an  angle  of  90°,  as  in 


Fig.  186. 


• 
1 

! 

\ 
1 
1 
1 
.-I 

Fig.  187. 


[There  is  a  certain  loss  of  distance,  aa,  in  using  the  sharper  instead  of  easier  curve,  which  is 
not  referred  to  in  the  text.     See  par.  859.] 


Fig.  187,  instead  of  using  1800  feet  of  5°  curve  and  only  50  feet 
of  tangent,  as  in  Fig.  186. 

Secondly.  The  limiting  effect  of  sharp  curvature  on  the 
weight  and  length  of  trains,  provided  it  be  sharp  enough  to  have 
such  effect.     Some  is,  and  some  is  not. 

848.  In  other  words,  we  are  here  met,  upon  the  threshold  of 
the  subject,  with  a  distinction  precisely  analogous  to  that  which 
we  have  already  found  (par.  361)  to  exist  in  the  case  of  gradients. 
All  grades,  without  distinction  and  wherever  situated,  entail  a 
certain  additional  expense  per  train  passing  over  them;  and  in 
addition  to  this  the  highest  rate  of  grade  entails  a  certain  and 
much  greater  expense  which  does  not  appear  at  all  in  the  ex- 
penses per  train-mile  (except  as  it  may  tend  to  decrease  them  by 
shortening  trains),  but  solely  in  an  increase  in  the  number  of 
trains.  In  like  manner,  all  curves,  without  distinction,  entail  a 
certain  additional  expense  per  train  passing  over  them  for  every 


CHAP.  XIX.— THE  LIMIT   OF  MAXIMUM   CURVATURE.  637 

degree  of  the  curve,  and  this  cost,  it  may  be, — or  may  not  be, — 
increases  rapidly  with  the  sharpness  of  the  curve;  but  in  addi- 
tion to  this,  the  sharpest  curve  (or  curves)  on  the  line,  if  it  be 
sharp  enough^  will  have  the  further  effect  of  limiting  the  weight 
and  length  of  trains.  In  fact,  if  made  sharp  enough,  it  will  so 
severely  limit  the  weight  of  trains  as  to  make  it  impossible  to 
run  any  trains  at  all. 

At  a  certain  definite  radius,  therefore,  the  expense  and  loss 
arising  from  short  radii  take  a  sudden  jump.  The  inherent 
cost  per  train-mile  per  degree  of  sharp  instead  of  easy  curvature 
continues  on  as  before,  and,  in  addition  thereto,  there  is  the 
large  additional  expense  caused  by  the  limiting  effect  of  any 
shorter  radius  upon  the  weight  of  trains. 

849.  It  is  plain  that  the  point  at  which  this  sudden  jump  will 
or  may  occur  is  intimately  connected  with  and  depends  upon 
the  rate  of  the  maximum  grade,  because  the  higher  the  grade 
the  greater  the  resistance  on  a  tangent,  and  hence  the  sharper 
the  curve  which  may  be  used  (i.e.,  which  it  is  possible  to  use)  on 
levels  or  minor  gradients  without  any  limiting  effect  on  trains. 
Hence  the  shorter  the  trains  which  can  be  hauled  independent 
of  the  sharpest  curve,  the  shorter  the  radius  which  may  be  freely 
used  on  levels  or  minor  gradients  without  affecting  the  number 
of  trains  required  for  a  given  business. 

850.  Now,  just  as  in  the  case  of  gradients,  this  distinction 
between  these  diverse  sources  of  expense  is  one  which  must  be 
carefully  kept  in  mind  if  any  correct  and  intelligent  decision  as 
to  the  limit  of  maximum  curvature  is  to  be  reached. 

In  the  first  place,  it  needs  no  great  effort  of  mind  to  perceive 
that  the  first  item  mentioned  above,  the  inherent  costliness  of 
sharp  curvature, — that  portion  which  is  visible  in  increased  wear 
and  tear  and  expenses  per  train-mile, — affords  no  ground  for  the 
fixing  of  any  arbitrary  and  inflexible  standard  or  limit,  nor 
should  it  be  considered  or  allowed  to  have  any  weight  what- 
ever in  ascertaining  at  what  radius  to  fix  that  limit.  For,  mak- 
ing for  a  moment  the  exaggerated  estimate  that  the  cost  of 
curvature  per  degree  increases  as  the  square  of   the  degree  of 


638   CHAP.  XIX.— THE  LIMIT  OF  MAXIMUM   CURVATURE. 

the  curve,  it  may  easily  be,  and  often  is  the  case  at  certain 
points,  that  the  cost  of  construction  will  vary  as  the  cube  of  the 
radius,  and  hence  a  sudden  sharp  ravine  or  rocky  spur  might 
justify  and  require  a  12°  or  15°  curve  for  this  account  alone, 
although  3°  or  4°  curves  were  the  maximum  on  all  the  rest  of 
the  line.  But  what  we  then  require  to  determine  is:  Will  any 
such  curve  have  the  further  effect  of  limiting  the  weight  of  trains 
over  the  whole  line,  or  injuriously  restricting  speed  ?  For  in 
that  case,  plainly,  a  large  additional  expenditure  will  be  justifi- 
able to  increase  its  radius. 

851.  This  latter  expenditure  does  not  vary  with  the  number 
of  curves,  as  does  the  wear  and  tear,  but  is  a  certain  fixed 
amount,  which  can  alone  be  used  to  take  out  such  curves,  how- 
ever many  or  few  they  may  be,  and  must  be  distributed  to  one 
curve  or  to  fifty,  according  to  their  number.  This  fact  alone  is 
sufficient  to  show  the  essential  dissimilarity  between  it  and  the 
sum  which  represents  the  direct  or  inherent  disadvantage  of 
using  short  instead  of  long  radii.  As  the  latter  is  always  so 
much  per  sharp  curve,  or  per  degree  of  sharp  curvature,  it  always 
has  its  effect — much  or  little,  as  the  case  may  be — on  the  justifi- 
able expense  to  increase  the  radius  of  each  particular  curve,  for 
it  is  to  be  added  in  each  case  to  the  proportion  for  that  curve  of 
the  estimated  value  of  avoiding  any  limiting  effect  from  its 
radius;  but  it  does  not  form  an  element  in  fixing  the  point  at 
which  limiting  effect  begins,  and  hence  should  be  allowed  no 
weight  whatever  in  ascertaining  that  limit. 

All  this  seems  clear  enough  when  the  attention  is  specially 
directed  to  it,  but,  as  with  many  other  problems  which  advance 
from  simple  premises,  it  requires  a  constant  effort  of  the  mind 
to  keep  it  always  in  view.  Hence,  although  it  has  no  real  or 
necessary  connection  with  our  present  subject,  we  may  first 
briefly  consider 

THE    INHERENT    COSTLINESS    OF    SHARP    CURVATURE. 

852.  For  the  consideration  of  this  question  all  actual  or  possible  lim- 
iting effect  from  curvature  on  the  length  or  speed  or  easy  riding  of  trams, 
or  the  use  of  any  desired  type  of  locomotive,  must  be  disregarded.    Such 


CHAP.    XIX. —  THE    COST   OF  SHARP    CURVATURE.       639 

injurious  effect  as  the  sharpest  curves  may  have  on  these  details,  if  an}^ 
is  another  matter.  The  question  is  simply — as  between  the  two  methods 
shown  in  Figs.  186,  187 — of  turning  an  angle  of  90°  within  a  distance 
of  1900  feet  of  track  :  Which  adds  the  most  to  the  operating  expenses 
per  train  due  to  that  1900  feet — the  method  of  Fig.  186,  showing  1800 
feet  of  5°  curve  and  50  feet  of  tangent  at  each  end,  or  that  of  Fig.  187, 
with  900  feet  of  10°  curve  and  500  feet  of  tangent  at  each  enr'  ? 

853.  Rigorously  excluding  all  thought  of  possible  limiting  effect 
from  the  mind,  it  is  very  difficult  to  see  reasons  why  the  inherent  cost  of 
curvature,  per  train-mile  per  degree,  should  be  in  the  least  increased  by 
using  short  instead  of  long  radii,  i.e.,  by  using  100  ft.  of  10°  curve  instead 
of  1000  ft.  of  1°  curve,  to  cover  the  same  central  angle.  The  wear  and 
cost  of  rails  appear  from  superficial  investigations  (the  writer's  among 
others:  see  par.  317)  to  indicate  that  rail  wear  increases  faster  than— or 
even  (as  the  writer  once  suggested)  as  the  square  of — the  degree  of 
curvature ;  but  this  is  a  purely  deceptive  appearance,  due  to  the  fact  that 
the  rate  of  wear  increases  as  the  rails  become  worn  to  "  fit  the  flange" 
{par.  338),  and  thus  expose  a  greater  area  to  rubbing  friction.  It  is  plain 
that  at  any  given  date  in  a  large  lot  of  rails  laid  at  the  same  time  those 
on  the  sharper  curves  will  have  fulfilled  a  greater  proportion  of  their  total 
life,  and  hence  will  have  begun  earlier  to  wear  more  rapidly.  From  a 
more  correct  comparison  of  all  the  data  it  appears  rather  as  if  both  curve 
resistance  and  rail  wear  (and  hence  fuel  consumption)  increased  more 
slowly  instead  of  faster  than  the  degree  of  the  curve  (par.  311).  If  so, 
the  total  RAIL  WEAR  caused  by  10°  of  central  angle  will  be  less,  rather 
than  more,  on  a  10°  curve  than  on  a  1°  curve.  While  this  cannot  as  yet 
be  positively  asserted,  it  may  be  regarded  as  certain  that  the  balance  is 
at  least  even. 

854.  It  may  with  far  more  certainty  be  claimed  that  the  cost  of  main- 
tenance OF  ROAD-BED  AND  TRACK  is  Considerably  decreased,  per  de- 
gree of  central  angle,  by  the  use  of  short  radii,  because  a  good  portion  of 
it  is  nearly  constant  per  100  feet  of  curve,  regardless  of  radius,  such  as 
the  extra  cost  of  lining,  maintaining  uniform  and  proper  elevation,  and 
the  shorter  life  of  ties,  in  order  that  they  may  be  capable  of  sustaining 
the  lateral  reaction  of  the  rails,  which  latter  is  theoretically  (although 
probably  not  quite  practically)  the  same  on  all  curves  (par.  311). 

It  would  be  a  most  liberal  estimate  to  assume  that  the  additional  cost 
per  station  for  maintaining  road-bed  and  track  due  to  curvature  increases 
as  the  square  root  of  the  degree  of  curvature,  making  it  3.16  times  as 
much  per  100  ft.  of  line  on  a   10°  curve  as  on  a   1°  curve,  or  making 


640        CHAP.  XIX.— THE    COST  OF  SHARP    CURVATURE. 


the  additional  cost  due  to  A°  of  central  angle  compare  as  10  on  a  1° 
curve  to  3.16  on  a  10°  curve.  This  entire  item  is  a  small  one,  but  so  far 
us  it  goes  it  is  distinctly  favorable  to  the  use  of  sharp  instead  of  easy 
curvature. 

855.  Figs.  186,  187  are  literal  copies  of  diagrams  which  the  writer 


Fig.  187. 

submitted  to  two  or  three  of  the  most  thoughtful  practical  road-masters 
of  his  acquaintance  for  an  opinion  as  to  probable  comparative  main- 
tenance expenses.     The  reply  of  one  of  them  was  as  follows  : 

"  Assuming  a  tie  to  last  8  years  on  tangent  it  will  last  about  6  years  on  a  10° 
curve,  so  as  to  keep  gauge  safe,  and  we  will  say  7  years  on  the  5°  curve.  Then — 
For  10°  line — Cost  of  ties  for  eight  years  on  looo-ft.  tangent, 

500  ties  at  50  cts., $250  00 

450  ties  on  goo  ft.  of  10°  curve  at  50  cts.  =  $225  for  6  years, 

=  for  8  years, 30  000— $550  00 

For  5°  line — Cost  of  ties  for  8  years  on  loo-ft.   tangent,   50 

ties  at  50  cts., 25  00 

900  ties  for  1800  ft.  of  5°  curve,  at  50  cts.  =  $450  for  7  years 

=  for  8  years, 514  3°— 1539  30 

"  Therefore  there  is  a  saving  of  $10.70  at  the  end  of  8  years  in  favor  of  the 
5°  line,  and  we  may  conclude  that  the  maintenance  of  line  and  surface  will  bear 
the  same  proportion  as  ties. 

"According  to  this  figuring  there  is  a  saving  of  about  2  per  cent  in  main- 
tenance in  taking  the  5°  line.  This  is  small,  and  in  looking  at  the  two  lines  in 
all  their  bearings  I  believe  the  10°  line  is  the  preferable  one  for  maintenance,  as 
on  it  we  get  more  tangent  than  curve,  while  the  5°  for  the  same  distance  is 
nearly  all  curve  and  very  little  tangent." 

The  fallacy  in  the  first  part  of  this  estimate,  which  was  perceived  but 
not  located,  lies  in  assuming  that  a  5°  curve  will  only  dimmish  the  life 
of  a  tie  half  as  much  as  a  10°  curve;  which  is  hardly  so,  the  flange  pres- 
sure being  the  sarne  on  both.     Moreover,  the  extra  work  of  Iming  and 


CHAP.  XIX.— DISTANCE   AND    SHARP   CURVATURE.      64 1 

surfacing  is,  still  more  nearly,  so  much  per  lineal  foot  of  curve,  regardless 
of  the  radius. 

856.  The  wear  and  tear  of  wheels  and  running  gear  of  rolling- 
stock  will  naturally  follow  the  same  general  law  as  the  rail  wear,  so  that 
it  may  be  considered  to  vary  directly  as  the  degree  of  curvature,  remain- 
ing constant  per  degree  of  central  angle. 

857.  Moreover,  the  total  cost  of  repairs  of  rolling-stock  and  track,  for 
those  items  which  are  at  all  liable  to  be  affected  by  the  wear  and  tear 
and  loss  of  power  on  curves,  is  very  small,  as  thus  : 

Per  cent  of 
total  expenses. 
Engines,  19  per  cent  only  of  the  total  cost  of  repairs  appears  to 
vary  with  curvature  and  grades(Table  85);  19  per  cent  of  5.6 

per  cent  (Table  80), =        1.07 

Cars  (Table  86),  23  per  cent  appears  to  vary  as  above;  23  per  cent 

of  lo.o  per  cent  (Table  80), =        2.30 

Rails,  say  50  per  cent  of  2.0  per  cent, =        i.oo 

Fuel,  say  10  per  cent  of  7.6  per  cent, =        0.76 

A  total  per  cent  of  only 5.13 

Thus  only  about  5  per  cent  of  the  total  operating  expenses  is  likely  to 
be  affected  at  all  by  curvature,  and  a  good  part  of  that  only  slightly,  and 
a  good  part  of  what  remains  by  sharp  and  easy  curvature  of  equal 
amount  nearly  equally. 

858.  It  is  also  to  be  remembered  that  sharp  curves  lengthen  short 
TANGENTS,  as  is  clearly  brought  out  by  Figs.  186,  187 — an  advantage 
which  facilitates  what  would  otherwise  be  impossible,  the  use  of  easy 
transition  curves  (see  Index),  and  hence  may  be  made  to  greatly  decrease 
the  unavoidable  shock  in  entering  and  leaving  curves. 

859.  The  effect  of  a  change  of  radius  on  the  total  length  of  the 
LINE,  although  apparently  pertinent,  has  no  real  bearing  on  this  ques- 
tion. The  use  of  sharp  curvature  always  increases  the  length  of  the  line 
between  the  same  tangents  by  the  amount  aa.  Fig.  187,  and  has  besides 
a  marked  further  tendency  both  to  increase  the  length  of  the  line  and  to 
increase  the  degrees  of  central  angle,  because  of  the  differences  of  loca- 
tion which  naturally  result.  But  the  disadvantage  of  this  extra  length 
and  curvature  is  a  matter  for  separate  estimation,  because  it  is  not  an 
essential  and  unavoidable  feature  of  a  mere  change  of  radius,  and  hence 
does  not  directly,  although  it  commonly  will  indirectly,  affect  the  deci- 
sion in  favor  of  using  easy  curvature.  In  fact,  although  it  rarely  occurs 
in  practice,  it  is  not  in  the  nature  of  things  impossible,  that  the  use  of  a 

41 


642      CHAP.  XIX.— DISTANCE  AND   SHARP   CURVATURE. 


shorter  radius  should  result  in  a  decrease  of  both  distance  and  degrees 
of  central  angle.  On  a  small  scale  it  very  frequently  does  so,  in  the  man- 
ner outlined  in  Fisr.  188. 


Fig.  188. 


860.  On  the  other  hand,  it  may  well  happen  that  the  adoption  of  a 
location  adapted  to  short  radii  would  double  the  amount  of  curvature, 
and  that  the  estimated  cost  of  this  would  be  more  than  the  estimated 
saving  on  construction.  In  that  case  the  short  radii  would  not  be  used, 
but  they  would  be  abandoned,  not  because  of  the  sharpness  of  the  curv- 
ature, but  because  there  was  so  much  of  it. 


Fig.  189. 

861.  The  loss  or  gain  in  distance  by  connecting  any  two  given  tangents  with 
one  curve  instead  of  another,  Fig.  189,  may  be  very  simply  determined  as 
follows: 

To  DETERMINE  THE  DIFFERENCE  IN  LENGTH  OF  LINE  via  ANY  TWO 
CURVES    OF   DIFFERENT   RADII,  CONNECTING   THE   SAME   TANGENT: 

Let  /  =  length  of  longer  curve,  of  D" ,  with  tangents  T\ 
"    /'=       "       "shorter     "        "  Z>'°,      "  "         T', 


CHAP.  XIX.— DISTANCE  AND   SHARP   CURVATURE.      643 

IDT 
Then  geometrically  —  =  -—  =  —    if  we  assume,  as  for  all  practical   pur- 
poses we  may, — if  curves  of  over  8°  or  10°  are  run  in  with  50-foot  chords, — that 
the  degree  of  curvature  is  directly  as  the  radius. 

Then/' =^/ and  T'  =~T,  t-T'  =  {i-^T. 

Letting  L  =  the  length  via  any  one  of  the  sharper  curves  shown  in  Fig.  189, 
from  tangent-point  to  tangent-point  of  any  curve  of  longer  radius  (from  T  to 
T )  we  have 


D' 

But  the  value  of  2  7"  —  /  for  a  D°  curve  is  to  its  value  for  a  1°  curve  as  — -. 

Consequently,  tabulating  (2  7"—  Z)  for  a  r°  curve,  we  have  as  fAe  difference  in 
the  length  of  the  line  via  any  two  curves  of  D  and  D'  degrees,  connecting  t-he  same 
tangents  : 

I        D'-D 


=  tabular  number  X  -7:^  X 
=  tabular  number  X 


D  D' 

D'-D 
D'D 


,    ,  ,  difference     ^    , 

—  tabular  number  X  -^^—, of  the  two  degrees  of  curvature, 

product     -^  &  J 

862.  Table  187  gives  such  a  tabulation  for  angles  differing  by  1°  up  to  130°. 
The  "  tabular  number"  is  simply  the  difference  between  the  length  of  a  1° 
curve  of  any  given  central  angle  and  the  lengths  of  its  tangents.  It  is  there- 
fore given  for  any  angle  whatever  by  the  formula 

T—  tan  ^/X  5730  X  2  —  ioo7; 

in  which  7*=  tabular  number  for  Table  187, 

/  =  intersection  angle  in  degrees. 

The  problem  is  rarely  one  of  practical  importance,  since  two  curves  of  con- 
siderable difference  in  radius  rarely  connect  the  same  tangents,  but  is  some- 
times convenient  for  determining  the  effect  of  minute  changes.  For  the  two 
curves  shown  in  Figs.  186,  187,  we  have — 

Tab.  no.  for  90°  (Table  187)  =  2459.3  X  to  ( — r; — I  =  246  feet  loss  of  distance 

^10  X  5 ' 
by  the  10°  curve. 


644   CHAP,  XIX,— THE  LIMIT  OF  MAXIMUM  CURVATURE. 

Table  187. 

Difference    in    Length    of    Line  vid    any    Two   Curves   of   Different 

Radii,  connecting  the  same  Tangents. 
[To  determine  the  required  difference,  multiply  the  tabular  number  below,  corresponding 

difference 


to  the  given  central  angle  by  the 


product 


of  the  two  degrees  of  curvature.] 


0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

o° 

0.00 

0.00 

0.02 

0.08 

0.16 

0.32 

0.56 

0.88 

1.32 

1.86 

10° 

2.56 

3-40 

4.42 

5.62 

7.02 

8.64 

10.50 

12.60 

14.98 

17.62-: 

20° 

20.6 

23-8 

27.4 

31-4 

35-8 

40.4 

45.6 

51.2 

57-2 

63.6 

30° 

70.6 

78.0 

86.0 

94.2 

103.4 

II3-2 

123.4 

134.2 

145.8 

158.0 

40° 

170.8 

184.4 

198.8 

214.0 

229.8 

246.6 

264.2 

282.6 

302.0 

322.4 

50° 

343-6 

365-8 

389-0 

413-4 

438-8 

465-4 

493-0 

521.8 

552.0 

583-4 

60° 

616.0 

650.0 

685.4 

722.2 

760.6 

800.4 

841.8 

884.8 

929.4 

975.8 

70° 

1023.8 

1073.8 

1125.6 

"79-4 

1235.2 

1293.0 

1353-0 

1415-2 

1479.6 

1546.4 

80° 

1615-4 

1687.2 

1761.4 

1838.4 

1918.0 

2006.0 

2086.0 

2174.4 

2266.2 

2361.0 

90° 

2459.4 

2561.0 

2666.4 

2775.6 

2888.6 

3005.6 

3126.8 

3252.4 

3382.4 

3517-2 

100° 

3656-4 

3801.2 

3951 -o 

4106.4 

4267.2 

4434.0 

4607.0 

4786.4 

4972.4 

5165.4 

110° 

5365-6 

5573-4 

5789.2 

6013.2 

6245.8 

6487.6 

6738.8 

6999-8 

7271.4 

7554-0 

120° 

7848.0 

This  table  is  not  correct  to  the  nearest  tenth,  but  only  to  the  nearest  even  two-tenths. 
As  a  certain  small  fraction  only  of  the  tabular  number  is  to  be  taken,  the  error  was  not 
deemed  of  enough  moment  to  require  recomputation.  The  table  gives  merely  the  differ- 
ence between  the  length  of  the  two  tangents  to  a  i°  curve  and  the  length  of  its  arc,  for 
any  given  central  angle. 


863.  Precisely  this  same  method  of  analysis  will  enable  us  to  determine  at 
once  the  difference  between  the  radius,  long  chord,  middle  ordinate,  tangent, 
or  any  other  function  of  any  two  similar  curves  if  we  know  the  value  of  the 
same  function  for  a  similar  1°  curve.  Thus  the  difference  between  the  radii  of 
a  5°  and  io°  curve  is 


10  —  5 
573oX——-=  573-0  feet; 
10  }\  5 


and  between  a  7°  and  8°, 


5730  X 


8_^_7  _^  5730 
8  X  7~    "56 


=  102.3  feet. 


864.  From  all  the  considerations  which  have  been  suggested 
together  we  may  perhaps  assume  that  the  inherent  cost  of  curv- 
ature per  train-mile  is  independent  of  the  radius,  or  at  l^st  does 
not  increase  appreciably  with  the  sharpness  of  the  curve,  and  this 


CHAP.   XIX.— LIMITING  EFFECT  OF  CURVATURE.       645 

view  simplifies  a  decision  as  to  the  limit  of  radius.  But  whether 
this  view  be  entirely  correct  or  not  is  a  matter  of  perfect  indiffer- 
ence for  deciding  the  problem  immediately  before  us,  as  it  is 
hoped  has  been  made  perfectly  clear. 

Dismissing,  therefore,  from  our  minds  this  confusing  and  irrel- 
evant question,  we  will  now  confine  our  attention  exclusively  to 
the  LIMITING  EFFECT  of  curvature  as  the  only  cause  which  justi- 
fies the  fixing  of  any  arbitrary  limit  whatever  to  the  sharpness 
of  curves. 

THE    LIMITING    EFFECT    OF    CURVATURE. 

865.  Curvature  may  have  a  limiting  effect  in  three  ways  : 

1.  It  may  forbid  the  use  of  certain  types  or  weights  of  en- 
gines, or  so  impede  it  as  to  make  it  practically  inexpedient.  The 
extent  to  which  this  cause  does  or  may  operate  has  been  already 
•considered  (par.  285  ef  seq.)  and  found  to  be  small. 

2.  It  may  impede  the  running  of  trains  at  high  speeds  by  the 
necessity  of  frequently  checking  speed  or  maintaining  a  low  rate 
of  speed  for  considerable  distances  when  the  intervals  between 
the  sharper  curves  are  small. 

3.  It  may  compel  the  hauling  of  shorter  trains  by  its  addition 
to  curve  resistance. 

The  second  cause  has  been  already  considered  from  the  me- 
chanical side  (in  par.  268  et  seq.)  and  found  to  appreciably  affect 
passenger  trains  alone. 

866.  As  a  business  question,  the  effect  which  we  there  saw 
sharp  curves  to  have  on  the  safe  speed  shows  their  use  to  be  on 
many  roads  of  heavy  passenger  traffic  a  consideration  of  extreme 
importance,  justifying  and  requiring  an  extremely  low  limit  of 
curvature.  Nevertheless,  under  average  conditions,  the  same 
facts  show  it  to  be  one  of  minor  importance. 

867.  It  depends  chiefly  on  a  road  of  any  given  character  on  the 
amount  and  disposition  of  the  sharp  curvature.  Thus  on  the  ele- 
vated railways  of  New  York,  with,  perhaps,  the  heaviest  passen- 
ger traffic  in  the  world,  a  few  excessively  sharp  curves  are  used, 
such  as  those  shown  in  Figs.  189,  190,  191.     These  are  not  found 


646       CHAP.   XIX.— LIMITING  EFFECT  OF  CURVATURE. 


t 

1 


Fig.  189. — Reversed  Curves  of  90  Feet  Minimum  Radius  for  Turning  Right  Angles  on 
Manhattan  RailwIay,  Sixth  Ave.  Line. 


There  are  four  right-angled  turns  on  the  Sixth  Avenue  line  similar  in  substance  to 
Fig.  189.  In  order  to  be  able  to  turn  within  the  street  limits  short  reversed  curves  were 
introduced,  making  the  total  of  the  central  angles  134°  34',  or  44*  34'  over  the  necessary- 
right  angle.  The  dotted  curve  of  200  feet  radius  (or  about  29°  instead  of  63°),  shows 
with  how  little  encroachment  on  private  property  the  radius  could  be  more  than  doubled. 
In  Fig.  190  the  dotted  alignment  would  save  212°  30'  —  144°  =  68°  30',  besides  nearly 
doubling  the  radius.  About  800  trains  per  day  pass  around  these  curves.  The  shortest 
interval  or  "  headway"  between  trains  is  only  ^  minute  on  the  Third  Avenue  line  and  ij^ 
minutes  on  the  Sixth  Avenue  Hne,  during  the  busiest  hours.  Counting  both  curves  to- 
gether, more  than  one  third  as  many  passengers  pass  over  them  per  year  as  ther3  are  who 
enter  all  the  trains  of  all  the  125,000  miles  of  railway  in  the  United  States.  The  gross 
earnings  per  mile  mount  up  to  $230,000,  and  the  operating  expenses  to  $125,000. 

The  property  on  the  corners  which  is  cut  by  the  dotted  curves  is  in  no  case  particularly 
valuable,  and  $20,000  or  $30,000  would  have  been  the  greatest  net  loss  which  would  be 
likely  to  result  from  substituting  any  one  of  the  dotted  cun^es  for  the  constructed  curve. 
No  accidents  of  any  kind  have  happened  on  any  of  these  sharp  curves  since  the  roads  were 
opened  in  1878. 

The  curves  are  of  standard  gauge,  and  the  cars  are  about  48  feet  long.  Their  draw- 
bars go  from  truck  to  truck,  and  not  between  the  car-bodies. 


CHAP.    XIX.— LIMITING  EFFECT  OF  CURVATURE.       647 


Fig.  190. — Reversed  Curves  of  119  Feet  Radius  on  Manhattan  Eletated  Railway, 

Third  Ave.  Line. 


Line  oF  UniFonn  Speed. 


Fig.  191. — Illustrating  the  Effect  of  Longer  Radius  on  Comparative  Speed. 


648       CHAP.   XIX.— LIMITING  EFFECT  OF  CURVATURE. 

to  be  a  measurable  disadvantage  as  respects  limiting  speed  (for 
if  they  were,  a  few  thousand  dollars  would  take  them  out),  be- 
cause, although  every  moment  of  lost  time  is  of  great  import- 
ance, the  speed  between  the  frequent  stops  is  slow  (not  over  30 
miles  per  hour)  and  the  motive-power  between  stations  (because 
of  the  frequency  of  stops)  abundant.  Therefore  the  speed  is 
checked  to  a  safe  limit  almost  instantaneously  on  approaching 
the  curve,  and  resumed  again  on  passing  it  almost  as  quickly,  and 
the  total  loss  per  curve  does  not  exceed  20  to  30  seconds  for  each 

curve;  only  a  small  of  part  which  (     ,—  or    39.    3    per    cent,    on 

curve  and  |- or  50  per  cent  in  approaching  and  leaving  the  curve, 
as  a  brief  analysis,  which  the  student  should  make,  will  show) 
could  be  saved  by  doubling  the  radius  of  curvature.  Fig.  192 
and  Table  107,  page  273,  will  indicate  the  method  of  determin- 
ing this. 

868.  If,  however,  there  were  many  of  these  curves,  the  loss  of 
time  would  not  only  increase  pari  passu,  but,  by  frittering  away 
the  time  and  nervous  energy  of  the  engineman,  obstructing  his 
view  ahead,  and  similar  indirect  causes,  cause  a  still  further  de- 
crease in  the  practicable  speed,  and  likewise  decrease  the  admis- 
sible frequency  of  trains,  thus  causing  an  unwarranted  loss,  if 
any  ordinary  expenditure  would  avoid  it.  As  the  line  now 
stands,  an  avoidance  of  all  curves  on  the  line  would  have  a  con- 
siderable money  value,  but  to  simply  double  the  radius  would  be 
worth  little  or  nothing — as  is  sufficiently  evidenced  by  Figs.  189- 
190.  The  management  is  not  unintelligent  nor  unduly  parsi- 
monious, but  it  is  not  thought  of,  simply  because  it  would  not 
pay. 

869.  So  on  the  various  railway  lines  connecting  Boston,  New 
York,  Philadelphia,  Baltimore,  and  Washington.  The  value  of 
avoiding  any  considerable  amount  of  curvature,  and  especially 
curvature  sharper  than  3"  or  4°,  is  to  be  measured  only  by  a  vast 
sum,  under  the  growing  business  advantage  of  very  fast  trains. 
Its  existence  in  large  amounts  would  make  quick  time  impossi- 
ble ;  but  the  same  is  not  at  all  true  of  a  small  amount  of  curva- 
ture at  some  one  point,  even  of  very  short  radius,  for  reducing 


CHAP.   XIX — LIMITING  EFFECT  OF  CURVATURE.       649 

speed  for  one  ftiile  only  from  60  to  30  miles  per  hour  means  only 
the  loss  of  \\  to  2  minutes  time  (Table  183).  The  justifiable  ex- 
penditure to  avoid  it  would  certainly  be  far  less  than  one  tenth 
of  what  would  be  justifiable  on  the  same  line  to  avoid  ten  times 
as  much  curvature  and  delay,  both  because  (i)  more  than  ten 
times  as  much  time  would  be  lost  thereby,  and  because  (2),  even 
if  not,  the  loss  would  be  more  than  ten  times  as  injurious.  Two 
minutes  more  time  between  New  York  and  Philadelphia  might 
not  place  a  competing  line  under  measurable  disadvantage. 
Twenty  minutes  would  not  simply  decrease,  but  destroy  its 
chance  for  competition  on  equal  terms. 

870.  When  we  come  to  long  trips,  of  500  to  1000  miles,  we 
have  already  (par.  240)  seen  that  any  probable  loss  of  time  which 
is  remediable  by  any  expenditure  within  bounds  for  easing  curv- 
ature is  not  likely  to  have  any  effect  whatever,  measurable  in  dol- 
lars and  cents,  upon  competitive  equality.  The  most  trifling 
differences  in  neatness  of  stations  and  equipment,  courtesy  of  em- 
ployees, character  of  "  lunch  counters,"  etc.,  would  be  far  more 
important  for  that  purpose,  as  well  as  far  more  cheaply  obtained. 

871.  The  true  principle  in  regard  to  this  matter  would  there- 
fore seem  to  be :  To  estimate  the  total  loss  of  time  which  is 
likely  to  result,  on  a  given  line,  from  the  location  naturally  re- 
sulting from  one  radius  of  curvature  instead  of  another,  and  the 
probable  money  value  of  so  much  competitive  business  as  is 
likely  to  be  lost  on  account  of  this  loss  of  time.  While  this  is  an 
exceedingly  delicate  and  difficult  matter  to  estimate  even  approx- 
imately, and  an  impossible  one  to  determine  with  exactness,  yet 
(par.  21)  "what  we  can  do  is  to  fix  a  maximum  and  minimum 
limit,  somewhere  within  which  lies  the  truth  and  anywhere  out- 
side of  which  lies  a  certainty  of  error.  Due  judgment  and  cau- 
tion require  that  we  should  do  so." 

872.  As  a  general  rule,  the  limiting  line  between  the  traffic  to 
which  every  minute  is  and  is  not  important  lies  at  the  point  where 
it  ceases  to  be  possible  to  make  a  round  trip  in  a  day,  with  some 
time  to  spare  at  destination.  For  distances  under  100  or  150 
miles  this   is  possible,  as  for  instance  between   New  York  and 


650       CHAP.    XIX.— LIMITING  EFFECT  OF  CURVATURE. 

Philadelphia,  and  time  is  valued  greatly.  For  longer  distances, 
as  from  New  York  to  Boston,  this  is  not  possible,  and  fast  trains 
are  not  run,  nor  are  they  likely  to  be  until  over  50  miles  per  hour 
can  be  made,  when  there  will  be  demand  for  several  daily.  Be- 
tween New  York  and  Chicago,  until  it  finally  appeared  possible 
to  shorten  up  the  time  to  24  hours,  quicker  time  than  36  hours 
was  not  important,  and  was  not  made.  To  St.  Louis,  which  is 
only  200  to  250  miles  further  from  New  York  than  Chicago,  or 
some  20  per  cent,  the  time  is  still  eight  or  ten  hours  longer,  for 
the  same  reason. 

The  effect  of  sharp  curvature  on  safety  and  the  comfort  of  travellers  is  con- 
sidered in  Chap.  VIII.,  pars.  247  and  279. 

873.  We  will  now  analyze  the  extent  to  which  the  third  and  chief 
cause  for  limiting  effect  from  curvature  operates — that  it  may  compel 
the  hauling  of  shorter  trains  by  its  addition  to  the  train  resistance : 

We  have  on  tlie  tangent  maximum  grade,  whatever  it  may  be,  two 
resistances  to  overcome : 

1.  The  ordinary  roinng-friction. 

2.  The  resistance  of  gravity — a  known  and  constant  quantity. 

In  the  case  of  curvature  on  a  level  we  have  also  two  resistances : 

1.  Tlie  ordinary  rolling-friction,  as  before. 

2.  All  additional  resistance  which  may  or  can  arise  from  the  curve. 

In  either  case,  it  is  evident  that  the  resistance  from  the  rolling-fric- 
tion proper,  being  the  same  in  any  case,  whatever  its  amount  may  be, 
may  be  entirely  neglected.  In  any  case,  also,  it  is  obvious  that  the  grade 
on  any  curve  may  be  reduced  to  a  level,  if  desired,  so  as  to  eliminate  all 
grade  resistance. 

874.  The  normal  rolling-friction  being  eliminated,  what  we  require, 
in  order  to  determine  the  proper  limit  of  maximum  curvature  so  far  as 
length  of  tram  is  C07icer7ied,  i.e.,  the  point  at  which  a  limiting  effect 
begins,  or  should  begin  on  a  properly  laid  out  line,  is  simply  the  curve  on 
which,  in  all  cases  and  under  the  most  unfavorable  circumstances,  the  same 
engine  can  haul  the  same  train  on  a  level  as  it  can  haul  on  a  ta7igent  up 
the  maximum  grade. 

It  is  not  sufficient  to  determine  merely  the  curve  on  which  there  will 
probably  be  no  greater  resistance  on  a  level  than  on  the  tangent  maxi- 
mum grade,  nor  the  curve  on  which,  under  average  or  favorable  condi- 
tions, there  will  be  no  limiting  effect.  When  there  is  even  a  possibility 
that  under  any  circumstances  whatever,  exceptional  or  unexceptional. 


CHAP.    XIX.— LIMITING  EFFECT  OF  CURVATURE.       65 1 

the  resistances  on  a  level  maximum  curve  may  exceed  the  known  and 
invariable  effect  of  gravity  on  the  actual  tangent  maximum  grade,  that 
curve  is  in  a  sense  a  limiting  curve,  because  there  is  a  certain  disadvan- 
tage in  even  the  possibility  that  curvature  may  at  times  limit  the  trains 
in  advance  of  gradients,  and  hence  a  certain  money  value  in  avoiding  it. 

875.  Viewed  from  this  standpoint,  with  our  existing  experimental 
knowledge  of  curve  resistance,  all  that  can  safely  be  assumed  is  that  an 
allowance  of  2  lbs.  per  ton  per  degree  of  curvature  is  none  too  great  to 
cover  the  highest  possible  curve  resistance  at  very  low  speeds,  with  well- 
worn  rails  and  long  trains  of  empty  cars,  especially  on  easy  curves.  So 
high  a  curve  resistance  is,  we  may  be  very  certain,  rarely  reached  in 
practice,  but  that  it  is  sometimes  reached  is  at  least  possible. 

On  the  other  hand,  the  very  lowest  limit  for  the  resistance  on  ordi- 
nary railway  curvature,  under  the  most  favorable  circumstances,  at  high 
speeds  and  with  new  rails,  is  probably  about  (somewhat  less  than)  \  lb. 
per  degree  of  curvature,  falling  on  the  very  sharpest  curves,  such  as  on 
the  elevated  railways  of  New  York,  to  something  less  than  -|-  lb.  per  ton 
per  degree ;  but  the  latter  curves  are  out  of  the  range  of  ordinary  expe- 
rience. 

876.  The  assumed  2  lbs.  per  ton  of  train  resistance  is  equivalent  to 
0.1  per  cent  of  grade,  and  0.5  lb.  to  0.025  P^^  cent  of  grade.  Multiplying 
the  former,  therefore,  by  the  degree  of  any  curve,  gives  a  rate  of  maxi- 
mum grade  which  will  certainly  oppose  more  resistance  to  all  trains 
under  all  circumstances  than  the  given  curve  will  on  a  level,  while  mul- 
tiplying the  latter  by  the  degree  of  curve,  in  the  same  way,  will  give  a 
rate  of  maximum  grade  which  will  certainly  NOT  oppose  more  resistance 
to  any  train  under  any  circumstances  than  will  the  curve,  and  hence  the 
latter  will  be,  in  the  fullest  sense,  a  "  limiting"  curve. 

In  between  these  limits  sometimes  the  curve  and  sometimes  the 
grade  may  offer  the  maximum  resistance 

877.  From  the  above  simple  data  we  may  construct  the  following 
Table  188,  showing  the  proper  limits  of  practice  in  respect  to  maximum 
curvature  : 

Table  188  assumes  that  the  most  which  can  possibly  be  done  to  eUm- 
inate  curve  resistance  is  to  reduce  the  grade  to  a  level,  which  is  the  case 
with  an  evenly  balanced  traffic  and  with  long  stretches  of  level  or  undu- 
lating gradients  having  a  great  deal  of  curvature.  It  is  evident,  how- 
ever, that  under  the  three  following  conditions,  at  least,  this  is  not  the 
case,  and  hence  that  the  table  will  not  then  apply: 


65: 


CHAP.   XIX.— LIMITING  EFFECT  OF  CURVATURE, 


Table  188. 

Maximum  and  Minimum  Limits  for  the  Degrees  of  Limiting  Curvature 
ON  Various  Grades. 
[Being  the  degrees  of  the  curves  which  certainly  will  and  certainly  will  not  cause  a 
greater  resistance  on  a  level  than  a  given  tangent  rate  of  maximum  grade.     Subject  to  the 
limitations  of  pars.  878  et  seq.'\ 


Tangent  M 

\xiMUM  Grade. 

Degree  of  Maximum  Curve  on  a  Level 

which  will 

which  certainly 
will  have  a  limiting 

Feet 
Per  Mile. 

certainly  have  no 

Per  Cent. 

limiting  effect 

effect  on  all 

on  any  train  under 

trains  under  all 

any  circumstances. 

circumstances. 

O.I 

5.28 

1° 

4° 

0.2 

10.56 

2° 

8" 

0.3 

15.84 

3° 

12° 

0.4 

21.12 

4° 

16° 

0.5 

26.40 

5° 

20° 

0.6 

31. 68 

6° 

24° 

0.7 

36.96 

7° 

0.8 

42.24 

8° 

0.9 

47-52 

9° 

I.O 

52.80 

10° 

etc. 

etc. 

etc. 

Fig. 192. 


878.  I.  On  a  long  maximum  grade,  of  any  considerable  rate,  we  can, 
if  necessary,  not  only  reduce  it  to  a  level,  but  break  the  grade  to  a  de- 
scent, as  at  BB',  Fig.  192,  and  in  this 
way  completely  eliminate  the  limiting 
effect  of  the  curve  resistance  of  any 
curve,  however  sharp ;  for  we  have  to 
consider  trains  in  one  direction  only. 
To  descending  trains  the  break  of  grade  can  (ordinarily)  do  no  harm. 
On  such  a  grade,  therefore,  there  is  no  reason  why  any  curve  whatever 
should  not  be  used,  so  far  as  the  limiting  effect  of  its  resistance  is  con- 
cerned, and  the  other  two  causes  alone  (par.  865)  justify  fixing  a  limit  of 
radius. 

2.  When  the  grade  is  level  or  slightly  undulating  for  a  considerable 
distance,  and  the  percentage  of  curvature  is  not  too  great,  some  little 
assistance  at  least  from  momentum  may  be  relied  on,  to  eliminate  a  por- 
tion of  the  resistance  of  very  sharp  curves. 

3.  When  the  burden  of  traffic  is  heavily  in  one  direction,  as  in  min- 
eral traffic,  even  with  nearly  level  grades  and  with  no  assistance  from 
momentum,  quite  sharp  curves  can  be  used  wherever  the  necessary  com- 


CHAP.    XIX.— LIMITING  EFFECT  OF  CURVATURE.      653 

pensation  to  equalize  the  curve  resistance  for  trains  moving  in  one  direc- 
tio7i  can  be  made,  because  the  loaded  trains  return  light  with  a  surplus 
of  motive-power. 

879.  Summarizing  our  conclusions  as  to  limit  of  maximum 
curvature,  we  have  found: 

1.  That  there  is  rarely  (although    there    is    sometimes)    real, 
difficulty  in  using  engines  of  any  desired  power,  of  types  approxi- 
mate for  efficient  service,  on  any  probable  alignment,  and   (par. 
285)  that  on  curves  below  10°  or  12°  there  is  no  difficulty  what- 
ever. 

2.  That  those  railways  are  the  exception  (although  they  do 
exist)  on  which  any  probable  loss  of  time  from  the  necessity  of 
slowing  up  at  sharp  curves  will  be  a  matter  of  much  financial 
importance,  and  that  the  gain  in  this  respect  by  any  modifica- 
tion of  curvature  ordinarily  possible  is  much  less  than  is  sup- 
posed. 

3.  That  all  danger  of  limiting  effect  upon  the  weight  of  trains 
from  sharp  curvature,  within  the  limits  specified  in  Table  188, 
can  ordinarily  be  avoided,  and  that  these  limits  afford  sufficient 
range  for  using  those  curves  which  best  fit  the  ground  under  all 
ordinary  topographical  conditions. 

4.  That  the  difference  in  danger  of  accident  which  is  liable 
to  result  from  any  modifications  of  curvature  ordinarily  possible 
is  too  small  for  estimation,  as  an  element  justifying  additional 
expenditure. 

5.  That  the  effect  of  any  difference  of  radius  on  the  expenses 
due  to  wear  and  tear  and  consumption  of  fuel  per  train-mile,  the 
degrees  of  central  angle  remaining  the  same,  is  probably  either 
nil  or  in  favor  of  sharp  radii;  but  that  whether  this  be  so  or  not 
(par.  252)  is  a  question  which  should  be  allowed  no  weight  what- 
ever in  fixing  on  a  limit  of  radius. 

6.  That  the  effect  of  shorter  radii,  if  they  have  any,  to 
lengthen  the  line  or  increase  the  degrees  of  central  angle,  or 
both,  through  the  different  location  which  naturally  results,  is 
likewise  a  matter  which  does  not  directly  affect  the  question, 
although  it  often  may  indirectlv. 

880.  We  may  likewise  close,  as  we  began,  with  another  very 
important  conclusion: 


654       CHAP.    XIX.— LIMITING  EFFECT   OF   CURVATURE, 

7.  That  the  natural  tendency  of  inexperienced  engineers  is  to  go  to 
extreines  in  the  matter  of  czcj'vatnre,  either  spending  too  much  money  to 
obtain  easy  curvature^  or.,  when  convinced  that  that  is  i?npolitic,  going  to 
the  other  extreme.,  introducing  recklessly  more  and  sharper  curvature 
than  there  is  any  real  necessity  for  j  in  both  cases  alike  failing  to  perceive 
and  utilize  to  the  utmost  the  topographical  possibilities. 

881.  It  may  at  first  sight  appear  to  follow  from  the  aggregate 
of  this  summary  that  there  is  little  reason  to  fix  any  minimum 
limit  whatever  to  the  radius  of  curvature  except  the  physical 
limit  of  the  capacity  of  the  locomotive,  and  this  is  so  far  correct 
that  it  is  entirely  indefensible  to  start  out  upon  surveys  with 
a  limit  determined  in  advance,  or  to  adhere  to  a  limit  at  every 
point  because  at  all  but  one  or  two  points  there  is  little  difficulty 
in  so  doing.  If  at  such  exceptional  points  a  large  expenditure 
is  necessary  to  adhere  to  it,  the  expenditure  should  not  be  made 
without  a  correspondingly  good  reason.  In  such  a  case  we  are 
justified  in  making  a  moderate  additional  expenditure  for  the 
mere  sake  of  a  uniformity  which  may  prove  advantageous  for 
operating  certain  engines  or  for  certain  high  speeds;  but  it 
should  in  general  be  a  very  moderate  one. 

882.  In  view  of  the  ever-present  danger  of  overloading  the 
capital  account  of  new  enterprises,  the  better  course  in  such 
cases  is  to  build  a  light  bold  line  for  a  short  distance,  laid  out 
with  the  idea  that  it  may  be  subsequently  improved  if  desired, 
and  if  means  exist  for  doing  it,  in  the  manner  elsewhere  dis- 
cussed (par.  283  et  al.). 

Nevertheless,  it  is  not  true  that  the  conclusions  summarized 
above  do  not  warrant,  under  all  ordinary  circumstances,  the 
maintenance  of  a  reasonable  and  moderate  limit  of  curvature  ; 
considerably  more  favorable,  if  their  spirit  be  closely  adhered 
to,  than  has  been  adopted  without  adequate  necessity  on  many 
lines.  For,  although  each  of  the  conclusions  specified,  taken 
separately,  does  not  warrant  the  fixing  of  arbitrary  limits  to  be 
adhered  to  at  large  expense,  yet  they  do  in  the  aggregate  indi- 
cate, as  common-sense  also  indicates,  that  reasonably  easy  curva- 
ture is  a  matter  of  much  absolute  although  possibly  of  small  rela- 
tive importance. 


CHAP.    XIX.— LIMITING  EFFECT  OF   CURVATURE.      655 

883.  The  true  conclusions  to  be  drawn  may  perhaps  be  better 
put  in  this  way  : 

8.  That  A  STANDARD  HARMONIZING  WITH  THE  NATURAL  TOPO- 
GRAPHICAL CHARACTERISTICS    AND    READILY    ADAPTABLE    TO    THEM 

is  the  only  right  and  proper  one,  until  the  topography  becomes 
so  rugged  that  the  physical  limit  of  the  capacity  of  the  locomo- 
tive, of  the  class  and  at  the  speeds  practically  required,  begins  to 
be  approached.  This  is  true  both  in  letter  and  in  spirit,  and 
should  be  rigidly  adhered  to.  When  so  adhered  to  it  will  rarely 
cause  embarrassment,  for  there  is  usually  a  certain  natural  limit 
of  radius  which  can  be  obtained  without  much  difficulty  or 
expense,  and  except  in  extremely  rugged  mountainous  regions 
this  limit  will  rarely  be  a  high  one.  This  implies  that  the 
limit  should  be  varied  from  point  to  point  along  the  line,  as 
the  general  character  of  the  topography  varies,  and  the  sharp 
curvature,  so  far  as  possible,  bunched. 

884.  In  proportion  as  the  natural  limit  of  radius  is  favorable 
the  justifiable  expenditure  to  obtain  a  still  more  favorable  limit 
decreases  rapidly,  and  it  can  never  be  amiss  to  bear  in  mind  that 
there  is  no  case  on  record  where  a  railway  has  been  brought  to 
bankruptcy  by  the  expenses  resulting  from  sharp  curvature,  nor 
is  there  any  likelihood  that  there  ever  will  be  such  a  case,  while 
the  instances  are  many  where  companies  have  been  bankrupted 
by  their  expenditures  to  obtain  easy  curvature.  Hence,  since 
the  money  of  even  the  richest  corporations  is  limited,  and  in  the 
case  of  new  roads  almost  always  more  limited  in  proportion  to 
its  needs  than  its  over-sanguine  projectors  have  any  idea  of,  true 
wisdom  requires  that  the  available  capital  should  first  be  devoted 
to  the  really  important  ends — getting  close  to  and  well  into  the 
large  towns,  getting  suitable  terminal  facilities,  getting  low 
grades,  building  what  is  built  well,  protecting  the  public  and  the 
railway  company  at  once  from  danger  and  loss  by  proper  inter- 
locking apparatus  at  grade  crossings,  or  by  under-  and  over-cross- 
ings, rather  than  by  expenditures  for  some  fanciful  standard  of 
curvature,  which  probably  makes  the  largest  addition  to  the  cost 
of  construction  of   any  detail  and    (for   any   change  within  the 


656      CHAP,    XIX.— LIMITING  EFFECT   OF   CURVATURE. 

power  of  the  engineer  at  any  cost  whatever)  the  smallest  addition 
to  either  the  safety  or  economy  of  operation. 

885.  The  argument  in  favor  of  adapting  curvature  to  the  nat- 
ural topography  of  the  country  is  greatly  strengthened  by  the 
fact  that  sharp  curves  frequently,  if  not  universally,  render  pos- 
sible LOWER  RULING    GRADIENTS  IN  DIFFICULT  COUNTRY  and  often 

permit  the  use  of  otherwise  favorable  routes  which,  without  this 
concession  to  natural  conditions,  would  be  wholly  impracticable. 
The  writer  could  readily  mention  a  number  of  important  in- 
stances of  the  kind  from  his  own  experience. 

886.  But  because  other  ends  are  more  important,  this  is  not 
therefore  unimportant.  Becauseit  is  unjustifiable  to  expend  any 
large  proportion  of  the  available  capital  for  this  end,  it  does  not, 
follow  that  a  very  large  proportion  of  the  time  given  to  surveys 
should  not  be  devoted  to  it.  Almost  invariably  it  should  be,  and 
the  engineer  who  finds  himself  in  rough  country  devoting  little 
thought  and  tim.e  to  saving  every  degree  of  curvature  possible 
may  be  tolerably  sure  that  he  has  fallen  into  that  most  danger- 
ous fault — blindness  to  its  undoubted  and  great  disadvantages. 

887.  It  is  so  important  that  the  proper  course  in  respect  to  fixing  ar- 
bitrary limits  of  curvature  should  be  so  plain  as  to  be  fully  understood, 
that  we  may  profitably  add  a  word  as  to  the  specific  manner  in  which 
these  conclusions  are  frequently  violated,  and  the  error  in  doing  so. 

Many  thousands  of  miles  on  this  and  other  continents  have  been  built 
on  standards  of  grades  and  curvature  closely  approximating  to  this  : 

1.  No  grade  shall  under  any  circumstances  exceed  60  ft.  per  mile. 

2.  No  curve  shall  under  any  circumstances  exceed  6°.     But, 

3.  These  limits  may  be  freely  used  in  combination  with  each  other; 
i.e.,  6°  curves  may  be  inserted  in  unreduced  60-ft.  grades. 

This  precise  standard  has  been  perhaps  more  used  in  this  country  than 
any  other  one  combination.  It  was  used  on  the  Erie,  the  Cincinnati 
Southern,  the  Chesapeake  &  Ohio,  the  Blue  Ridge  of  South  Carolina,  and 
a  long  list  of  other  roads  of  less  engineering  pretensions  ;  having  been 
copied  from  one  to  another,  apparently,  without  much  regard  to  topo- 
graphical requirements — perhaps  because  the  round  figures  and  the  al- 
literation of  the  6's  had  a  certain  charm.  Far  less  defensible  combina- 
tions have  been  the  rule  throughout  the  vast  expanse  of  the  Mississippi 
Valley  from  the  causes  alluded  to  on  page  6 — such  as  2°  or  3°  or  4°  limits 


CHAP.    XIX.— LIMITING  EFFECT  OF  CURVATURE.      657 

of  curvature  with  40  to  80  ft.  grades  (0.8  to  1.5  per  cent);  but  it  should  be 
added  that  in  general  the  topography  favors  long  radii,  and  the  chief  error 
has  been,  not  the  radius  of  curvature,  but  the  reckless  sacrifices  of  gradi- 
ents to  save  degrees  of  central  angle. 

888.  We  have  already  determined  (par.  825)  that  the  use  of  unreduced 
curvature  on  a  maximum  grade  is  never  defensible.  Except  that  it  has 
been  done  in  such  repeated  instances  and  on  so  large  a  scale,  it  would  seem 
incredible  that  any  one  could  spend  large  sums  of  money  to  keep  curva- 
ture down  to  6°,  and  grades  down  to  60  ft.  per  mile,  and  yet  pile  one  upon 
the  other  freely,  giving  in  effect  a  75-ft.  grade.  We  may  more  clearly  see 
the  folly  of  it  by  an  example  from  hmnl  Ic  life.  Suppose  some  plain  coun- 
try farmer  should  find  that  his  team  could  just  draw  him  up  a  steep  hill 
through  mud  a  foot  deep,  and  should  forthwith  draw  two  conclusions — 
that  it  could  not  draw  him  up  any  steeper  hill  without  any  mud,  nor 
through  any  deeper  mud  without  any  hill :  should  we  not  think  the  man 
less  intelligent  than  the  beasts  he  drove  }  Yet  this  is  precisely  what  has 
been  done,  and  to  some  extent  is  still  done,  on  thousands  of  miles  the 
world  over,  by  engineers  of  standing. 

889.  Passing  this  error  as  no  longer  likely  to  be  committed,  let  us 
consider  the  propriety  and  efifect  of  the  joint  standard  of  60  ft.  per  mile 
and  REDUCED  6°  curves  maxima  : 

A  60  ft.  per  mile  grade  is  1.14  per  cent.  If  we  may  use  6°  curves  on 
such  grades  by  reducing  them  to  0.96  or  0.84  per  cent  (0.03  to  0.05  per 
cent  per  degree  compenstion),  which  is  the  largest  compensation  used  by 
those  who  adopt  such  standards,  why  should  we  not  feel  free  to  use  some 
sharper  curves  with  more  compensation,  or  on  a  dead  level,  if  we  can 
thereby  save  some  money  to  put  where  it  will  do  more  good  } 
890,  The  answer  can  only  be  one  of  four  reasons  : 

1.  A  7°  or  8"  or  10°  curve  of  equal  angular  length  will  be  so  much 
more  costly  in  wear  and  tear,  that  on  no  single  curve  can  the  saving  m 
cost  for  construction  pay  for  the  loss  therefrom.     Or, 

2.  A  few  such  curves,  even  if  fully  compensated,  will  in  some  unex- 
plained way  so  limit  trains  that  the  same  engine  cannot  do  the  same 
work.     Or, 

3.  They  will  cause  such  loss  of  time  from  slowing  up  (and  certainly 
require  slowing  up)  that  a  loss  of  speed  involving  greater  loss  of  traffic 
than  the  value  of  any  possible  saving  will  result.     Or, 

4.  They  are  so  exceedingly  unsafe  to  operate,  compared  with  a  6°, 
that  in  no  case  can  the  additional  danger  therefrom  be  repaid  by  an  ade- 
quate economy  m  construction. 

42 


658      CHAP.    XIX.— LIMITING  EFFECT  OF  CURVATURE. 

891.  There  is  no  escape  from  accepting  one  or  more  horns  of  this 
double  dilemma  if  such  a  standard  is  to  be  justified  at  all ;  and  probably 
no  man  would  have  the  hardihood  to  attempt  to  maintain  anyone  of  them 
for  explicit  reasons  given.  It  is  not  thus  that  such  utter  and  evident 
blunders  as  this — which  simply  to  state  their  nature  clearly  is  to  con- 
demn— have  come  about ;  but  rather  by  the  vague  process  of  jumping  at 
conclusions  outlined  in  par.  245 — that  "the Railway  is  to  be  first- 
class  ;"  that  "  nothing  over  6°  curvature  is  generally  considered  first- 
class  ;"  ergo,  etc.  etc.  The  fact  that  most  of  the  great  trunk  lines  have 
8°  to  10°  curves  (Table  116),  and  that  the  lines  which  have  set  up  such 
purely  arbitrary  standards  have  been  to  a  very  large  extent  lines  of 
a  secondary  class,  increases  the  obviousness  of  the  error  committed. 


CHAP.  XX.— CHOICE    OF   GRADIENTS.  659 


CHAPTER   XX. 

THE    CHOICE    OF    GRADIENTS,    AND    DEVICES    FOR    REDUCING    THEM. 

892.  We  have  seen  clearly  enough  in  preceding  chapters  that 
the  gradients  are  the  one  thing  among  the  purely  engineering 
details  on  which  the  engineer  should  concentrate  his  attention, 
subordinating  them  only  to  the  end  of  reaching  the  sources  of 
traffic,  if  even  to  that. 

We  have  seen  also,  in  Chap.  XVII.,  that  the  use  of  assistant 
engines  for  short  distances  with  low  ruling  grades  elsewhere,  is 
generally  preferable  to  a  uniform  through  grade,  both  topo- 
graphically and  financially;  for  the  reason  that,  do  the  best  we 
can,  a  uniform  grade  must  usually  approximate  pretty  closely  to 
the  rate  of  the  pusher  grade  if  it  passes  over  the  same  summit, 
and  by  adopting  it  we  throw  away  the  advantage  of  the  low  grades 
on  all  the  rest  of  the  line,  which  may  be  had,  as  it  were,  for  nothing. 

893.  Having  recognized  these  abstract  truths,  however,  the 
next  thing  is  to  apply  them,  and  here  we  pass  beyond  the  point 
where  specific  instructions  can  be  easily  given,  since  the  circum- 
stances will  vary  on  every  line.  A  great  part  of  the  danger  of 
error  has  been  overcome  when  the  comparative  importance  of 
the  various  details  has  been  realized,  but  even  with  that  advan- 
tage the  inexperienced  engineer  is  almost  certain  to  conclude 
that  a  certain  grade  is  the  lowest  attainable,  when  with  longer 
practice,  or  more  skill,  or  harder  work,  or  less  self-confidence, 
he  would  readily  obtain  grades  a  third  or  a  half  lower  at  the 
same  cost,  and  not  unfrequently  at  less  cost. 

894.  There  is,  however,  one  general  rule,  which  directly  re- 
sults from  what  has  preceded,  and  which  comes  so  near  to  being 
an  infallible  guide  for  the  correct  projection  of  lines  in  the  field 
that,  as  a  rule,  the  engineer  should  follow  it  strictly,  deviating 
from  it  only  for  very  good  reason,  viz.: 


66o  CHAP.  XX.— HOW   TO  PROJECT  LOW  GRADES. 

Follow  that  route  which  affords  the  easiest  possible  grades  for 
THE  LONGEST  POSSIBLE  DISTANCES,  usliig  to  that  eiid  such  amoiiiits  of 
distance^  curvature.^  a?id  rise  and  fall  as  may  be  necessary,  and  then  pass 

OVER  THE  INTERVENING  DISTANCES  ON    SUCH    GRADES  AS  ARE    THEN 
FOUND  NECESSARY. 

This  law  is  to  be  applied  with  intelligence  and  not  pushed 
too  far,  but  so  far  as  there  can  be  said  to  be  any  universal  and 
fundamental  law  for  location,  this  is  such  a  law. 

895.  When  the  higher  grades  are  in  danger  of  exceeding  2  per 
cent  or  2^  per  cent,  it  is  to  be  accepted  only  with  great  cau- 
tion, and  anything  beyond  3  per  cent  will  be  probably  bad  prac- 
tice, except  in  very  mountainous  country.  As  a  line  falls  below 
100  miles  in  length  the  economy  of  using  pushers  decreases,  and 
the  practical  advantage  of  a  uniform  gradient  increases. 

Accepting  this  general  rule  as  an  axiom,  our  problem  then 
divides  itself  into  two  parts: 

1.  How  to  obtain  the  lowest  possible  low  grades. 

2.  What  to  do  as  to  the  rates  of  the  high  grades. 

HOW    TO    PROJECT    LOW    GRADES. 

896.  Considering  only  a  naturally  low-grade  country  with  no  long- 
continued  ascents  to  encounter,  but  only  a  more  or  less  rolling  topog- 
raphy, three  fourths  of  almost  every  line,  or  of  the  part  thereof  lying  in 
such  low  country,  will  naturally  admit  of  an  extremely  low  gradient,  if 
some  considerable  lateral  deviations  to  throw  the  line  into  a  generally 
favorable  country  are  considered  admissible,  as  they  ought  to  be,  so  that 
such  alternates  between  any  two  points  as  those  sketched  to  a  rude  scale 

in  Fig.  193  are  considered 
as  prima  facie  equally  eli- 
gible. To  obtain  the  same 
grades  on  the  remaining 
fourth  will  often  involve 
some  disagreeable  sacrifices,  especially  when,  as  so  often  in  the  Western 
States,  we  can  take  an  air-line  by  accepting  i  per  cent  or  ij  per  cent 
grades,  if  we  are  foolish  enough  to  do  so. 

These  disagreeable  sacrifices,  however,  ought  ordinarily  to  be  met, 
even  to  the  extent  of  doubling  the  distance  on  one  quarter  of  the  line  if 
we  can  tliereby  reduce  the  grades  to  half  as  high  a  rate.     We  shall  then 


CHAP.  XX.— HOW   TO   PROJECT  LOW  GRADES. 


66i 


simply  have  a  line  112^  miles  long  with  0.5  per  cent  grades,  as  against  a 
line  100  miles  long  with  i.o  per  cent  grades.  The  former  is  immensely- 
preferable  from  every  point  of  view.  But  usually  a  smaller  sacrifice  will 
make  a  greater  gain. 

897.  Let  us  consider,  for  example,  the  case  of  a  long,  low  ridge  or 

swell  in  a  generally  flat  country,  which  cannot  be  run  around  at  all,  by 

any  device,  since  it  continues  indefinitely.     Assume 

Q  \  this  swell  to  be  three  miles  across  and  50  feet  high 

\         by  the  grade-line,  after  making  as   large  cuts  and 

\^         fills  as  seem  expedient  at  A,  B,  C,  and  D,  Fig. 

\  194.     A  tangent  over  this  ridge  will  give  the 

\  profile  shown  in  Fig.  195,  with  two  miles  of  i 

\  per  cent  grade  and  a  mile  of  level  interven- 

\  ing.     The  exaggerated  vertical  scale  makes 


Fig.  195. 
Plan  and  Profile  of  a  Break  in  a  Long  Tangent  to  pass  over  a  Long,  Low  Ridge  in 

Flat  Country. 

the  rise  seem  considerable,  but  on  the  ground  it  will  be  hardly  percep- 
tible to  the  eye  as  an  objectionable  feature  to  the  railway  line. 

This  is  especially  likely  to  be  the  case  because  the  ground  approach- 
ing such  a  rise  will  not  ordinarily  be  on  a  dead  level,  but  is  more  likely 


662  CHAP.  XX.— HOW   TO   PROJECT  LOW  GRADES. 

to  have  about  half  as  steep  a  rise,  perhaps  for  a  long  distance  back,  giv- 
ing a  long  0,5  grade  approaching  the  ridge.  This  we  will  assume  to  be 
the  case,  as  also  that  except  for  this  swell,  and  a  few  others  like  it,  the 
0.5  grade  might  be  the  maximum  of  the  whole  line.  Such  conditions 
have  existed  on  thousands  of  miles. 

898.  Now  to  the  eye  of  a  country  farmer,  and  to  the  eye  of  many  an 
engineer,  perhaps,  who  may  inspect  the  line  during  construction,  as  it 
runs  over  the  surface  of  an  apparently  flat  cornfield,  this  whole  region 
will  seem  practically  a  dead  level.  In  the  first  place,  the  long  0.5  ap- 
proach will  invariably  be  taken  by  the  eye  to  be  a  level,  or  perhaps  even 
(by  well-known  optical  illusion)  a  slight  descent.  This  at  least  takes, 
off  a  full  half  of  the  apparent  vertical  angle,  and  hence  of  the  apparent 
height  of  the  ridge;  and,  more  probably,  there  will  seem  to  be  a  slight, 
dip  of  the  ground  toward  the  ridge  and  merely  a  corresponding  rise  be- 
yond it.  In  the  second  place,  even  if  the  approach  were  a  dead  level,  a 
rise  of  only  i  per  cent  in  a  natural  surface  seems  to  the  eye  a  very  small 
thing,  especially  before  the  track  is  laid,  so  that  it  would  seem  ridiculous 
to  turn  four  right  angles  "  for  nothing"  and  lose  two  or  three  miles  of 
distance,  at  the  cost  of  four  such  ugly  curves  through  the  cornfields  as 
are  shown  in  Fig.  194. 

899.  Nevertheless,  under  all  the  given  circumstances,  THAT  IS  pre- 
cisely THE  THING  TO  DO.  The  very  fact  of  the  long  0.5  approach,, 
which  diminishes  the  visible  necessity,  makes  it  the  more  essential  to  do 
so,  because  it  forbids  us  to  resort  to  the  assistance  of  momentum  to  sur- 
mount the  ridge,  which  otherwise,  by  approaching  the  foot  of  it  at  30 
miles  per  hour  and  reaching  the  top  at  10,  would  take  off  (Table  118) 
31.95  —  3.55  =  28.40  vertical  feet,  and  give  us,  out  of  our  i  per  cent 
grade,  a  virtual  profile  of  0.5  per  cent,  with  something  to  spare. 

900.  On  arriving  at  the  point  A,  therefore,  even  if  it  be  with  a  30- 
mile  tangent  which  might  be  continued  for  30  miles  more  by  running 
straight  over  the  ridge,  a  sharp  turn  to  the  right  of  something  over  60° 
should  be  made  in  the  flat  cornfield,  on  about  a  3'  curve,  for  the  sole 
purpose  of  lengthening  out  the  one-mile  ascent  into  two  miles,  so  as  to 
give  half  the  grade.  To  start  the  curve  A  farther  back,  as  shown  by  the 
dotted  line  A' ,  so  as  to  diminish  the  central  angle,  would  do  no  good, 
but  rather  destroy  the  very  purpose  of  the  curve,  which  is  to  gam  dis- 
tance between  A  and  B  and  not  to  reach  B' . 

When  the  line  reaches  B' ,  another  curve  of  60°  +  ,  in  another  corn- 
field, brings  it  back  again  parallel  with  itself,  but  nearly  two  miles  off. 
In  a  mile  more,  a  third  curve  of  60°  -f-  enables  it  to  descend  the  ridge  on 
the  0.5  maximum  by  losing  another  mile  of  distance,  and  at  D  another 


CHAP.  XX.— HOW   TO   PROJECT  LOW  GRADES.  663 

curve  of  60°+  brings  it  back  to  its  proper  position ;  giving  in  all  2  miles 
interpolated  distance  in  a  distance  of  3  miles,  250°  of  curvature  where 
before  there  was  none,  and — what  would  sometimes  be  the  hardest  blow 
of  all — utterly  ruining  the  60-mile  tangent  which  had  been  run  in  ex- 
actly straight  by  foresights  only ;  and  all  for  the  sake  of  obtaining  a  line 
so  ugly  that  numerous  fingers  of  scorn  may  well  be  pointed  at  it. 

901.  And,  no  doubt,  the  same  end  might  ordinarily  be  accomplished 
in  such  a  case,  in  some  more  pleasing  and  economical  fashion  ;  as  by 
striking  the  ridge  obliquely  with  the  line,  or  in  such  manner  that  the 
dotted  line  C'B" ,  Fig.  194,  might  be  used  for  the  descent,  so  as  to  utilize 
most  of  the  otherwise  waste  distance.  Or,  by  going  further  back  and 
swinging  the  line  at  this  point  10  or  20  miles  to  the  north  or  south,  better 
ground  may  be  obtained  with  less  aggregate  loss  of  distance  (Fig.  193) 
than  on  this  three  miles  alone.  The  instance  has  purposely  been  made 
somewhat  extreme  in  this  respect  to  enforce  the  principle.  But  in  an- 
other sense  it  is  not  extreme.  If  none  of  these  things  can  be  done  to  ad- 
vantage, IF  there  is  nothing  to  be  gained  by  deviating  from  an  air-line  be- 
tween two  points  100  miles  apart,  and  if  this  air-line  will  admit  of  o.  5  grades 
each  way,  except  for  one  or  two  or  three  or  five  or  six  such  ridges  as  that 
described,  then,  as  between  the  air-line  ^Z>,  which  will  give  a  surface-line 
hundred-mile  tangent  on  i  per  cent  grades  and  Six  breaks  like  AB'C'B, 
Fig.  194,  which  will  introduce  1500°  of  curvature  and  lose  12  miles  of 
distance,  and  break  the  hundred-mile  tangent  into  five-and-twenty  pieces, 
but  give  0.5  percent  grades — the  ugly  and  crooked  line  is  be3^ond  all 
possibility  of  question  in  every  instance  the  line  to  take,  as  of  very  much 
greater  operating  value,  unless  the  line  be  an  exception  to  most  Ameri- 
can roads,  by  having  a  preponderance  of  passenger  traffic,  which  is  both 
large  and  competitive.  Almost  every  general  principle  connected  with 
laying  out  railways  admits  of  more  or  less  doubt,  and  requires  exceptions. 
This  particular  example  admits  of  no  doubt  and  requires  no  exceptions. 

902.  For,  computing  the  values  of  the  losses  and  gains,  we  have — 

Yearly  saving  by  avoiding  an  increase  of  0.5  per 

cent  in  a  0.5  grade,  by  Table  178,  per  daily 

train,  $4,300  X5= $21,500  00 

Per  contra  : 
Cost  of  1 500°  of  curvature  by  Table  1 1 5,  per  daily 

train,  $0,433  x  1500= $649  50 

Cost  of  12  miles  of  distance,  by  Table  89,  per  daily 

train,  $290  x  12= 3,480  00 —     4,129  50 

Difference,  being  excess  of  value  of  the  low  grade- 
line,  with  SIX  such  breaks  of  tangent  as  is 
shown  in  Figs.  194,  195,  ^^r  ^«//k /r^zz«, $17,37050 


664 


CHAP.  XX.— HOW   TO  PROJECT  LOW  GRADES. 


This  is  equivalent  to  the  addition  of  a  capital  sum  of  nearly  $350,000  (at 
5  per  cent)  to  the  value  of  the  property,  or  $3500  per  mile,  per  daily  train. 
For  ten  daily  trains  each  way  the  line  will  pay  interest  on  $35,000  per 
mile  larger  valuation. 

This  assumes  that  all  trains  are  affected  by  the  difference  in  gradients, 
as  by  the  difference  in  other  details.  No  passenger  train,  however,  would 
under  any  circumstances  be  much  benefited  by  the  reduction  of  grade, 
so  that  if  one  quarter  or  one  half  the  trains  are  passenger  trains  the 
estimate  should  be  corrected  correspondingly.  On  the  other  hand,  no 
credit  side  whatever  has  been  assumed  for  the  loss  of  distance,  whereas 
there  must  always  be  some  (par.  227  et  seq?)  and  often  enough  to  wipe  out 
the  debit  side  altogether.  How  the  account  will  then  stand  is  worthy  of 
careful  study. 

903.  This  example  makes  it  clear  that  the  assumption  may  be  still 


Figs.  196,  197.— Plan  and  Profile  of  a  Break  in  a  Long  Tangent  to  obtain  0.4  per  cent 

INSTEAD    OF    I.O    PER   CENT   GrADES. 


more  extreme,  as  by  assuming  that  the  attainable  through  grade,  except 
at  a  few  such  points  as  this,  is  0.4  per  cent.  We  then  have  the  condi- 
tions of  Figs.  196-7,  if  we  are  to  obtain  0.4  per  cent  in  the  same  way; 


CHAP.  XX.— HOW   TO   PROJECT  LOW  GRADES.  665 

the  lateral  deviation  from  the  airline  being  2.39  miles  and  the  loss  of 
distance  at  each  such  point  3  miles,  in  an  air-line  of  3  miles.  Even  in 
that  case  three  or  four  or  even  five  such  points  might  be  stood  before  it 
was  concluded  to  give  up  the  low  grade,  but  at  six  the  loss  of  distance — 
18  miles — would  be  too  great,  threatening  to  discourage  traffic,  and  the 
indication  would  be  very  strong  that  a  ditferent  general  route  should  be 
chosen. 

904.  The  general  principle  which  should  govern  the  laying  out  of 
low  grade-lines  or  sections  of  lines  cannot  be  made  much  clearer  than  by 
these  examples.  The  difficulties  of  obtaining  a  low  grade  are  ordinarily 
confined  to  a  few  points  on  the  section.  Adopt,  then,  the  rate  which  can 
be  obtained  without  much  difficulty  on  three  fourths  or  four  fifths  of  the 
low  grade-Hne  or  section,  and  concentrate  attention  on  the  remainder 
with  the  determination  that  the  low  grade  must  be  preserved 
THERE  ALSO,  if  in  any  way  possible.  A  way  will  generally  appear  after 
careful  study,  and  a  very  much  neater  one  than  that  sketched  in  Figs. 
194-197. 

905.  Much  of  the  lamentably  prevalent  bad  practice  in  such  details  as  we 
have  been  considering  comes  from  the  fact  that  the  line  is  studied  in  detail  only, 
or  bit  by  bit,  and  not  as  a  whole,  as 
it  should  be.  If  we  allow  ourselves 
to  think  only  of  the  three-mile  stretch 
AD,  Figs.  194,  196,  198,  and  think 
of  the  consequence  of  throwing  the 
line  out  to  C B'  to  pass  from  A  to 
D,  the  mind  revolts  from  it  at  once. 
The  rectangle  CC'B'B,   Fig.  198,  ob- 

f)  C  13  A 

trades    itself    upon    the  mind   while  ^         „ 

^  Fig.  198. 

the  project  is  inchoate,  and  thus  the 

mind  is  more  repelled  by  it  than  when  the  complete  line  is  laid  down,  as  may 
be  seen  at  once  by  comparing  Figs.  198  and  194,  which  are  really  "  similar"  to 
each  other,  although  they  do  not  look  it.  If  the  mind  were  able  to  take  in  in 
due  proportion  the  vastly  greater  distances  on  each  side  which  are  not  injuri- 
ously affected  at  all,  while  they  are  made  passable  for  twice  as  heavy  trains  there- 
by, the  objections  to  the  deviadon  would  at  once  begin  to  fade  away.  But  this  the 
mind  cannot  do  without  some  assistance,  which  is  one  of  the  many  reasons  why 
SMALL  SCALE  maps  and  small  scale  profiles  should  be  kept  up  during  the  prog- 
ress of  surveys  with  even  greater  care  than  those  on  working  scales. 


C'            L 

/ 

/ 

\ 

666  CHAP.  XX.— PROJECTING  PUSHER   GRADES. 


HOW    TO    PROJECT    PUSHER    GRADES. 

906.  Suppose  that  instead  of  there  being  five  or  six  such  low- 
ridges   as   tliat   shown  in  Figs.  194  or  196,  scattered  irregularly 

over   the    division,   there    is 
only  one,  but    six   times   as 
.^    high,  as  sketched  in  Fig.  199. 
P^^-  ^99-  Fig.  196  may  still  serve  as  a 

map  of  such  a  point.  As  between  the  air-line  and  the  bowed 
line,  IF  EACH  IS  to  be  operated  in  THE  SAME  WAY,  the  case  is  not 
affected  in  the  slightest  by  the  greater  height  of  the  ridge  and 
length  of  the  lines  AB'  and  CD.  The  bowed  line  is  much  the 
best.  The  bunching  of  the  obstacles  at  one  point  does  make 
this  difference,  however,  that  there  is  now  a  rational  choice  in 
favor  of  assistant  engines.  For  any  considerable  traffic  the  short 
line  with  pusher  grades  will  be  very  probably  the  better.  The 
volume  of  traffic  makes  a  difference  in  two  ways :  First,  the  as- 
sistant power  can  be  more  exactly  adapted  to  requirements  ; 
second,  a  heavy  traffic  is  almost  sure  to  be  largely  competi- 
tive, thereby  diminishing  the  credit  side  to  the  value  of  dis- 
tance. 

Pusher  grades  may  be  divided  into  two  classes,  each  of  which 
requires  different  treatment  and  will  be  considered  separately  : 

1.  Those  surmounting  low  elevations  by  the  easier  gradients, 

2.  Those  making  long  ascents  (say  over  700  or  800  feet)  on 
rates  which  must  be  conspicuously  more  severe  than  the  through 
grades  on  either  side,  as  where  i^-  per  cent  grades  or  over  are 
required. 

PUSHER  GRADES  ON  EASY  GRADIENTS. 

907.  When  it  is  seen  that  the  use  of  pushers  is  unavoidable  if  a  low 
through  grade  is  to  be  obtained,  the  first  question  which  arises  is  :  Which 
is  to  be  the  li^niting-  gradient, — the  low  through  grade  operated  by  one 
engine,  or  the  pusher  grade  operated  by  two  engines.^  Ordinarily  it 
will  be  the  pusher  grade,  for  two  reasons : 

I.  The  lower  pusher  grades  must  be  reduced  in  rate  nearly  twice  as 


CHAP.  XX.— PROJECTING  LOW  PUSHER   GRADES.       66^ 

fast  as  the  through  grades  to  keep  the  balance  equal,  as  is  evident  from 
the  following  figures,  taken  frorh  Table  182  : 

Through  Grade ...  .       Level  o.i  0.2  0.3  0.4  0.5  0,6 

Pusher  Grade 0.3S  0.57         0.76         0.95         1.12         1.29         1.47 

Differences 0.19  0.19         0.19         0.17         0.17         0.18 

For  a  uniform  difference  in  through  grade  of  o.io. 

It  will  usually  be  very  much  easier  to  reduce  the  through  grades, 
complicated  by  no  high  elevations,  from  0.6  to  0.4,  than  to  reduce  the 
corresponding  pusher  grade  from  1.47  to  1.12,  especially  as  the  through 
grade,  from  the  nature  of  the  case,  will  be  mostly  in  short  undulations  ; 
and  hence, 

2.  The  infiuence  of  momentum  (par.  397  ef  seq.,  and  see  also  close 
of  this  chapter)  will  frequently  assist  greatly  in  reducing  the  virtual 
through  gradients  below  the  nominal  maximum,  or  can  be  made  to ; 
whereas  long  pusher  grades  must  be  taken  at  their  actual  rate. 

908.  Assuming,  therefore,  the  pusher  grade  to  be  the  one  that  fixes 
the  virtual  gradient  of  the  whole  line  or  division,  all  that  has  been  said 
above  about  reducing  through  grades  applies  to  it  in  an  intensified  de- 
gree. The  saving  of  distance  or  curvature  should  be  wholly  subordi- 
nate to  the  end  of  reducing  the  rate  of  grade  to  the  lowest  limits,  taking 
care,  however,  not  to  introduce  development  which  adds  so  much  to  cur- 
vature that  the  compensation  destroys  nearly  all  the  gain.  A  resource  in 
extreme  instances  may  be  to  introduce  a  temporary  sag  in  a  grade-line, 
as  described  in  par.  832.  Sharp  curvature,  if  absolutely  unavoidable, 
should  be  used  here,  if  nowhere  else. 

In  this  way  reductions  of  grade  which  are  far  beyond  the  apparent 
possibilities  may  often  be  secured.  If  the  engineer  who  has  at  last 
secured  what  he  thinlcs  the  best  the  country  admits  of,  will  then  throw 
aside  all  his  preconceived  impressions,  and  start  in  afresh  with  the  idea 
that  he  is  all  wrong,  and  might  reduce  his  grade  o.i  per  cent  or  more  as 
well  as  not,  if  he  went  about  it  right,  the  chances  are  many  to  one  that 
he  will  not  be  disappointed,  and  reductions  rising  to  even  0.3  to  0.5  per 
cent  may  sometimes  be  obtained  without  a  dollar  of  extra  cost,  by  ab- 
surdly simple  means,  as  in  the  instance  described  below,  and  illustrated 
in  Fig.  200,  which  was  the  key-note  for  a  reduction  of  a  2  per  cent  grade 
some  15  miles  long  to  a  1.5  per  cent  grade,  with  a  cheaper  line. 

909.  In  the  case  illustrated  in  Fig.  200  a  located  line  aaa  had  first  been 
run,  on  a  2  per  cent  grade,  through  a  most  attractive  saddle  A  over  which  the 
main  highway  already  ran,  requiring  a  short  tunnel  of  about  1000  ft.     The  sum- 


66S 


CHAP.  XX.— PROJECTING  HIGH  PUSHER    GRADES. 


mit  of  the  grade  was  but  a  short  distance  back,  and  A  was  approached  by  a  much 
lighter  grade;  but  accepting  ^  as  a  finality,  it  was  utterly  impossible  to  find  sup- 
porting ground  for  the  grade  at  a  saddle  about  4  miles  below  A  with  a  less 
grade  than  2  per  cent.  The  grade  was  in  all  some  20  miles  long,  in  two  suc- 
cessive sections  of  g  and  6  miles,  respectively,  with  some  little  broken  grade  in- 
termixed. 


Fig.  200. 


Examination  indicated  (i)  that  except  over  this  stretch  at  the  head  of  the 
grade  there  would  be  no  serious  difficulty  in  reducing  the  whole  grade  to  1.5  per 
cent,  and  (2)  that  the  only  chance  for  reducing  it  above  was  by  gaining  develop- 
ments around  the  hill  DG.  The  very  capable  and  experienced  engineer  who 
had  made  the  first  location  was  therefore  instructed  that  the  hill  must  be  turned 
if  possible.  He  ran  the  line  bbb,  accordingly,  to  the  point  Z,  turned  a  maximum 
curve  K,  and  reported  it  absolutely  impossible  to  turn  the  hill,  without  two  very 
high  viaducts  over  the  deep  gorge  H  and  a  tunnel  at  K. 

This  looked  plausible  on  the  ground,  if  it  does  not  on  the  map.  Standing 
at  L  there  was  an  abysmal  gorge  below,  a  precipitous  knife-edge,  G,  of  soft 
rock  above,  and  the  smoother  side  of  the  hill,  M,  wholly  invisible  and  almost 


CHAP.  XX.— PROJECTING  HIGH  PUSHER   GRADES.       669 

inaccessible,  but  known  to  be  very  steep.  Really,  however,  there  was  no  diffi- 
culty. Running  an  approximate  line  EM  from  below,  and  connecting  across 
the  top  of  the  hill,  it  was  found  that  the  entire  line  could  be  fitted  closely  to  a 
steep  side-hill  except  for  one  deep  rock  cut  at  G  so  very  narrow  in  proportion 
to  its  height  that  a  single  heavy  blast  would  remove  it  all  at  once.  This  threw 
the  line  nearly  100  ft.  lower  at  E,  saved  the  tunnel  A,  and  gave  much  better 
ground  below  as  well,  while  enabling  the  1.5  grade  to  be  easily  obtained. 

It  is  especially  important  to  exhaust  all  such  possibilities  on  low  and  short 
pusher  grades  (down  to  the  limit  which  balances  the  lowest  attainable  through 
grade),  because  the  use  of  two  pushers,  or  still  less  the  breaking  up  of  trains,  is 
rarely  expedient,  as  it  often  is  on  the  longer  and  higher  pusher  grades,  which 
we  will  next  consider. 

LONG    PUSHER    GRADES    ON    HEAVY    GRADIENTS. 

910.  This  second  class  of  pusher  grades  should  ordinarily  be 
studied  by  themselves,  quite  apart  from  the  remainder  of  the 
line.  Their  cost,  both  for  construction  and  for  operation,  will 
be  a  leading  factor  in  the  finances  of  the  line,  and  hence  should 
be  a  controlling  factor.  They  are  sufficiently  prominent  features 
in  the  operation  of  the  line  to  enable  the  motive-power  to  be  well 
adapted  to  the  requirements  of  the  gradients,  whatever  they  may 
be. 

911.  These  causes  favor  the  adoption  of  low  rates  of  grade  for 
such  a  line: 

I.  As  the  gradients  rise  above  2  per  cent  the  loss  of  net  haul- 
ing capacity  becomes  more  serious,  owing  to  the  weight  of  the 
engine  and  tender,  and  (for  freight  trains)  caboose,  becoming  a 
larger  and  larger  factor,  as  shown  in  Table  189,  p.  688.  From 
Table  170  we  see  that  on  grades  differing  by  i  per  cent  the  net 
hauling  capacity  is — 


Grade 
per  cent. 

Net  tons  load 

for  St'nd. 

American  engine. 

Per  cent 

(2  per  cent 

grade  =:  100). 

Grade 
per  cent. 

Net  tons  load 

for  St'nd, 

American  engine. 

Per  cent 
(2  per  cent 
grade  =  100) 

I.O 
2.0 

371 
192 
118 

193.2 
1 00.0 
61.46 

4.0 

6.0 

78 

S3 
36 

40.62 
27.60 
18.75 

2.  The  lower  grade  (if  obtained  by  development)  not  only  re- 
duces the  cost  of  operation,  but  increases  the  revenue  somewhat, 
by  giving  a  larger  mileage.     On  some  costly  lines  of  thin  non- 


6/0      CHAP.  XX.— PROJECTING  HIGH  PUSHER   GRADES. 

competitive  traffic  this  may  justly  be  regarded  as  an  additional 
advantage  from  a  low  grade.  On  other  lines  it  might  be  an  al- 
most unmixed  disadvantage. 

3.  As  grades  rise  above  2  per  cent  or  2-J  per  cent,  such  great 
caution  has  to  be  used  to  keep  trains  under  full  control,  both  in 
going  UD  and  down,  as  to  add  considerably  to  the  theoretical 
disadvantage,  both  in  loss  of  time  and  danger  of  accident. 

4.  A  lower  grade  will  often  be  found  to  lie  on  such  ground  as 
to  decrease  rather  than  increase  the  total  cost  per  mile  to  sub- 
grade  (as  we  have  just  seen  in  par.  909),  so  that  the  difference  in 
cost  of  a  low-grade  or  high-grade  line  will  be  at  the  most  not 
great. 

5.  A  large  portion  of  a  continuous  descent  will  often  not  ad- 
mit of  using  a  higher  grade  than  a  certain  rate.  It  then  becomes 
a  regrettable  sacrifice  to  use  a  higher  grade  elsewhere  on  the 
same  descent,  although  if  the  grade  be  long,  traffic  small,  and 
difference  of  cost  great,  it  should  be  done. 

912.  The  Jalapa  line  between  Vera  Cruz  and  Mexico,  described  in 
Appendix  C  and  its  accompanying  plates,  is  a  good  example  of  the  effect 
of  every  one  of  these  causes  favoring  low  grades.  On  the  first  30  kilo^ 
metres  (20  miles)  of  the  descent  from  the  summit,  although  a  slightly 
steeper  than  2  per  cent  grade  might  have  assisted  somewhat,  a  4  per  cent 
grade  would  have  thrown  the  line  so  low  as  to  bring  it  on  much  worse 
ground. 

913.  The  descent  from  Tepic  (see  par.  917),  on  which  the  spiral  oc- 
curs, shown  in  Figs.  207,  208,  is  a  good  illustration  of  the  fifth  cause 
above.  From  the  summit  down  to  the  foot  of  the  spiral  more  than  the 
adopted  rate  of  2.6  per  cent  could  not  possibly  be  used,  except  by  throw- 
ing away  elevation  with  level  stretches,  since  that  grade  brought  the  line 
down  to  the  very  bed  of  the  stream  under  the  viaduct.  The  same  grade, 
in  the  main,  fitted  the  bed  of  the  stream  very  well,  although  for  5  or  6 
miles  it  was  necessary  to  hold  up  above  the  bed  somewhat  at  some  expense. 
As,  therefore,  there  were  only  some  5  or  6  miles  out  of  the  30  miles 
of  2.6  grade  (broken  by  some  short  unavoidable  levels  below)  in  which 
the  descent  of  3000  feet  to  sea-level  was  made,  it  would  have  been  an  un- 
warrantable sacrifice  to  break  the  grade  on  the  short  stretch,  where 
(only  by  raising  it  to  about  4  per  cent)  some  appreciable  economy  might 
be  realized,  even  for  the  thin  traffic  expected. 


CHAP.  XX.— PROJECTING  HIGH  PUSHER   GRADES.       67 1 

914.  The  following  causes  favor  the  selection  of  high  rates 
of  grades  for  such  sections  of  line: 

1.  It  usually  very  much  reduces  the  cost  of  construction 
which  is  probably  high  at  best — a  consideration  of  great  impor- 
tance (par.  29). 

2.  If  the  rate  of  a  higher  grade  can  be  maintained  unbroken, 
so  that  its  length  is  decreased  in  proportion  as  its  rate  is  increased^  the 
total  motive-power  is  not  increased  (Table  181  and  par.  747) 
even  if  the  total  length  of  the  line  between  termini  is  not  de- 
creased by  the  higher  grade,  i.e.,  if  the  respective  profiles  be- 
tween the  two  termini  are  as  in  Fig.  201.  If  the  lower  grade 
is  only  to  be  obtained  by  interpolated  distance,  so  that  the  foot 
of  both  the  low  grade  and  high  grade  falls  at  nearly  the  same 
point,  the  advantage  in  motive-power  needed  is  still  more  in 
favor  of  the  high-grade  line. 

3.  The  loss  by  multiplication  of  trains  and  train-wages, 
Avhich  is  otherwise  so  very  serious 
on  high  grades,  is  obviated  in  part 
by  using  two  or  three  engines  per 
train,  which  it  is  not  practicable 
to    do  with  heavy  through    trains  ^'^'  ^°^' 

over  a  whole  division.  This  advantage  is  to  be  assumed  with 
caution,  however,  as  within  the  extreme  limits  of  choice  which 
the  engineer  has  ordinarily  before  him  (say  not  over  i  per  cent 
in  most  cases)  the  same  number  of  engines  per  train  can  be  used 
on  either  the  highest  or  the  lowest  rate. 

915.  4.  The  case  is  much  stronger  in  favor  of  high  grades 
when  the  low  grade  is  only  to  be  obtained  by  hanging  on  a 
rough  side-hill  as  against  lying  in  the  bed  of  a  stream,  or  with 
other  great  contrasts  in  facilities  of  construction,  as  in  the 
St.  Gothard  Railway,  where  a  low  grade  was  obtained  only  by 
the  desperate  expedient  shown  in  Figs.  202  to  206: — turning 
spiral  tunnels  into  the  solid  rock  and  thus  introducing  so  much 

■pure  development  between  the  same  termini,  so  that  a  higher 
grade  would  have  shortened  the  pusher  runs  almost  exactly /r^ 
rata.,  and  left  the  same  amount  of  motive-power  required  for  the 
passage  between  termini  in  either  case.  On  the  Italian  side  of 
the  mountain,  indeed,  these  spirals  appear  to  have  been  an  en- 


^^2       CHAP.  XX.— PROJECTING  HIGH  PUSHER   GRADES. 


tirely  superfluous    luxury  (see    note   to   Figs.   202-206  on   page 
following  them),  not  even  serving  to  reduce  the  grades. 

Apart  from  the  cost  of  these  spirals,  had  the  grade  been  higher 
it  would  have  lain  for  a  considerably  larger  portion  of  its  length 
nearer  to  the  bottom  of  the  valley,  and  hence  on  better  ground. 

The  St.  Gothard  line,  therefore,  furnishes  a  good  example, 
although  certainly  not  an  extreme  example,  of  unjustifiable 
adoption  of  low  grades.  It  is  mag- 
nificent, but  in  this  detail  of  its  loca- 
tion it  is  not  engineering,  because  it 
does  not  accomplish  the  desired  end 
in  the  most  economical  way. 


dotttfl  Lines  hidlurtTunnetJ. 


Figs,  202-3. — Profile  of  St.  Gothard  Railway,  Swiss  Side 


CHAP.   XX.— PUSHER   GRADES. 


673 


o  = 


6/4  CH.  XX.— REDUCING  RATE  AND  COST  OF  HIGH  GRADES. 

Figs.  202  and  204  are  profiles  of  the  bed  of  the  valleys  approaching  the  St. 
Gothard  tunnel,  with  the  scale  shown  in  miles.  On  the  Italian  side  of  the 
mountain  the  bed  of  the  stream  was  broken  by  cataracts,  and  it  will  be  seen  by 
the  dotted  grade-lines  plunging  below  the  river-bed  that  by  simply  developing 
the  spiral  tunnels  into  straight  ones,  adding  nothing  to  their  length,  the  same 
grade  up  the  mountain  would  have  been  obtained  with  a  material  saving  of  dis- 
tance and  curvature,  and  hence,  of  course,  of  cost.  Such  a  straight  tunnel 
would  start  in  at  the  lower  portal  of  the  fifth  rising  curve,  near  K,  Fig.  205,  and 
take  a  straight  course  through  the  words  "  Fig.  205"  to  a  point  beyond  the  limits 
of  Fig.  205,  where  it  would  again  emerge  into  the  valley,  requiring  a  tunnel  of 
a  trifle  over  3  miles  long,  or  about  what  there  is  now  of  tunnel  on  the  same 
stretch,  saving  all  the  other  work  and  distance.  The  same  is  true  in  substance 
of  the  two  lower  raising  curves,  or  of  the  upper  one  at  least. 

The  fact  that  this  throws  the  grade-line  below  the  bed  of  the  stream  looks 
bad  on  the  profile,  but  should  not  be  allowed  to  deceive.  The  tunnels  plunge 
into  the  bowels  of  vast  overhanging  mountains  of  solid  rock,  and  can  be  kept 
as  far  away  from  the  stream  as  desired,  if  there  were  need  to  consider  it  at  all. 
The  only  visible  gain  from  the  spirals,  therefore,  was  to  have  the  same  engi- 
neering curiosities  on  one  side  of  the  mountain  as  on  the  other. 

On  the  Swiss  side  of  the  mountain.  Fig.  202,  the  spiral  developments  shown 
in  Fig.  203  were  essential  for  the  purpose  sought,  to  reduce  the  grade  to  137  ft. 
per  mile.  To  have  followed  the  natural  grade  of  the  valley  would  have  required 
from  197.5  to  237.5  ft.  per  mile  grades,  according  to  how  closely  the  bed  of  the 
valley  was  followed.  By  the  aid  of  the  long  Table  170  we  may  see  how  much 
real  economy  in  motive-power  was  effected  by  these  developments  in  taking  the 
traffic  from  Silenen  to  the  St.  Gothard  tunnel.  Neglecting  the  actual  distance, 
which  it  would  be  unfair  to  consider,  we  may  say  that  the  length  of  the  moun- 
tain grade  in  miles  should  be  about  inversely  as  the  rate  of  grade.  Then  we 
have,  for  a  standard  Consolidation: 


Grade. 
Ft.  Per  Mile. 

Comparative 
Length. 

Comp.  Net 
Tons. 

Load  of  Eng. 
Per  Cent. 

Comp.  Eng.  Miles 
Per  Through  Ton. 

137 

IGO.G 

319 

100. 0 

100 

i97i 
219 

237i 

69.3 
62.5 

57-7 

210 

184 
165 

65-9 

57.7 
51-7 

105 
108 
mi 

In  other  words,  comparing  the  constructed  grade  with  the  197.5-ft.  grade 

only,  in  a  vallev  distance  of  10  miles,  4.4  miles  ( 1  of  tmtnel developfnentwSiS, 

V69-3/ 
introduced  with  the  effect  of  saving  only  5  per  cent  of  the  engine-miles  necessary 

to  move  a  car  through,  and  perhaps  2^  percent  of  the  cost  of  movement.  Such 
errors  result  from  lack  of  study  of  the  economic  side  of  railway  location.  There 
could  be  no  better  illustration  of  the  broad  distinction  between  reducing  the 
rates  of  through  grades  and  of  pusher  grades  stated  in  par.  747. 


CH.  XX.— REDUCING  RATE  AND  COST  OF  HIGH  GRADES.  675 


EXPEDIENTS    FOR  REDUCING  THE   RATE  AND   COST   OF   HIGH   GRADES. 

916.  The  following  are  among  the  chief  resources  for  obtaining  the 
best  results  on  long  ascents.     They  should  always  be  borne  in  mind  : 

I.  Hunt  for  some  place  on  any  part  of  the  ascent  where,  for  half  its 
total  length  or  more,  a  fairly  good  and  cheap  line  may  lie,  in  spite  of  sur- 
rounding difficulties.  Find  what  rate  of  grade  will  fit  this  sec- 
tion AND  work  each  WAY  FROM  IT,  instead  of  going  always  to  the 
summit  and  working  down — which  is  a  good  rule  for  small  descents,  but 
will  often  lead  one  far  astray  on  long  ones.  In  other  words,  find  out 
what  are  or  ought  to  be  the  governing  points,  which  may  or  may  not 
be  the  summit,  and  work  from  them.  In  running  a  first  rough  prelimi- 
nary it  is  ordinarily  best  to  start  from  the  summit,  but  on  a  second  line 
it  is  rather  the  rule  than  the  exception  that  it  should  not  be  done. 

917.  Fig.  207  shows  a  remarkable  example  of  the  advantages  of  this  method, 
from  the  location  of  the  lower  end  of  the  Pacific  Branch  of  the  Mexican  Central 
Railway,  on  the  descent  from  the  city  of  Tepic  to  the  coast  flats.  Several 
efforts  were  made  by  various  engineers  to  obtain  a  practical  line,  which  are 
distinguished  as  first,  second,  and  third  lines  in  Fig.  207,  but  without  any 
very  satisfactory  result,  until,  aided  by  the  knowledge  gained  in  the  previous 
surveys,  the  idea  of  the  spiral  line  was  conceived  and  pushed  to  a  successful 
completion,  with  a  reduction  of  considerably  over  half  in  the  estimated  quanti- 
ties of  the  line.     The  conditions,  briefly  stated,  were  these: 

The  town  of  Tepic  is  at  an  elevation  of  915  metres,  or  3035  feet,  above  the 
sea,  and  distant  only  some  17^  miles  east  therefrom,  half  of  which  is  a  dead 
fiat  rising  but  a  few  feet  above  the  sea,  so  that  the  entire  rise  would  have  had 
to  be  made  on  a  direct  route,  within  an  air-line  distance  of  some  nine  miles. 
Descending  from  Tepic  (see  Fig.  207),  the  line  first  follows  the  valley  of  the 
Tepic  River  until  it  diverges  therefrom  (as  it  flows  in  an  entirely  wrong  direc- 
tion and  becomes  impracticably  rough)  and  strikes  across  into  the  valley  of  the 
smaller  Ingenio  River  at  the  Rincon  Pass,  marked  "controlling  summit "  on 
Fig.  207,  at  an  elevation  of  2508  feet  (795  metres)  above  the  sea. 

Up  to  this  point  the  descent  was  on  less  than  a  2  per  cent  grade  and  offered 
no  difficulty,  although  requiring  some  heavy  work  and  affording  views  of  great 
sublimity  and  beauty  over  the  rugged  and  abrupt  descent  to  the  coast  flats. 

In  descending  from  this  controlling  pass  into  the  valley  of  the  Ingenio 
River  (which  is  the  long  stream  in  Fig.  207  which  the  line  follows  below  the 
spiral),  the  usual  difficulty  was  encountered,  that  the  first  descent  was  ex- 
ceedingly sharp.  In  an  air-line  distance  of  two  miles,  from  the  controlling 
summit  to  the  lower  left-hand  corner  of  the  spiral  in  Fig.  208,  there  was  a  de- 
scent  of  some  490  feet.  Moreover,  the  valley  of  the  Ingenio,  while  entirely 
practicable  for  a  line  in  or  very  near  to  the  bed  of  the  stream,  had,  for  many 


^7^  CH.  XX.— REDUCING  RATE  AND  COST  OF  HIGH  GRADES. 

miles  below  the  spiral  (to  near  B,  Fig.  207),  abrupt  and  rugged  banks  several 
hundred  feet  high,  of  the  same  impracticable  character  as  those  shown  imme- 
diately below  the  spiral  bridge,  Fig.  208,  although  below  B  the  valley  became 
more  tractable. 

918.  Under  these  circumstances,  since  it  was  impossible  to  descend  into 
the  bottom  of  the  valley  on  any  practicable  grade,  and  since,  unless  this  were 
done,  the  line  must  be,  for  a  long  distance  below  the  spiral  afterward  adopted, 
entirely  above  the  immediate  slopes  of  the  valley  ;  to  avoid  the  most  excessive 
work,  a  comparatively  light  trial  grade,  2  per  cent,  was  not  unwisely  adopted 


First  Line. 
.Second   Line. 
-Third   Line 
-Final  Location, 


KILOMETERS 
234 


Fig.  207.— Routes  of  Various  Surveys  for  the  Grade  cIescending  to  the  Coast  n 

[Black  figures  give  elevation  in  i 


for  running  the  three  first  lines  shown  by  dotted  lines  on  the  map.  These 
lines,  otherwise  differing  from  each  other  greatly,  agreed  in  swinging  around 
the  area  covered  by  the  spiral  and  close  to  the  latter,  although  off  the  area  cov- 
ered by  the  map  of  the  spiral  in  Fig.  208.  To  trace  them  on  Fig.  208,  start 
from  near  the  scale  and  title  and  pass  thence  to  the  right,  then  down,  and  then, 
at  the  bottom  of  the  map,  to  the  left,  to  a  point  between  A  and  B  on  the  small 
scale  map,  Fig.  207.  At  this  point  they  were  already  far  above  the  grade  o^ 
the  spiral  bridge,  so  that  they  soon  left  the  excessive  slopes  of  the  valley  and 
struck  comparatively  easy  work  on  the  narrow  ridge  lying  between  the  valleys 
of  the  two  parallel  streams  shown. 

Nevertheless,  the  work  on  all  three  of  the  lines  was  excessive,  while  the 
low  grade  required  a  great  amount  of  otherwise  unnecessary  development  and 
curvature.  Two  of  these  lines  were  located  on  paper  and  profiles  made,  but 
no  accurate  estimates  were  ever  made  of  them,  as  the  work  was  very  forbid- 


CH.  XX.— REDUCING  RATE  AND  COST  OF  HIGH  GRADES.  ^77 

ding,  involving,  in  spite  of  the  use  of  17°  curves,  a  number  of  tunnels  and 
many  retaining-walls  and  small  viaducts. 

These  facts  made  it  clear,  if  it  had  not  been  before,  that  the  attempt  to  find 
a  line  by  starting  from  the  summit  as  a  controlling  point,  and  letting  it  fall 
thence  where  it  would,  must  be  abandoned  and  a  line  chosen  lying  in  the  bot- 
tom of  the  valley  as  a  fixture  and  worked  from  at  each  end  ;  that  being  the 
only  place  where  a  really  economical  line  could  lie  for  the  entire  distance  down 
to  C,  Fig.  207. 

A  random  line  in  the  bed  of  the  stream  showed  that  a  2.6  per  cent  grade 


.ATS    FROM  TePIC,   MeXICO,  ON  PACIFIC  BRANCH  OF  THE  MEXICAN    CENTRAL    RAILWAY. 

etres.    The  spiral  shov>rn  in  Fig-.  208  is  '^  shown  above.] 


(137  feet  per  mile)  was  the  lowest  adapted  to  it,  and  in  assuming  the  line  to  be 
in  this  position,  and  extended  from  each  end  (i.e.,  conceiving  the  line  fixed 
under  the  bridge  in  Fig.  208),  the  ascent  thence  up  the  upper  small  stream  was 
(for  the  country)  mere  surface  work,  and  the  extraordinarily  favorable  point 
for  the  high  crossing  (the  narrowest  for  miles)  naturally  suggested  sweeping 
the  line  around,  through  a  deep  but  narrow  cut,  into  the  lower  small  valley,  so 
as  to  cross  over  itself  by  a  high  viaduct,  and  thence  ascend  to  the  summit. 
Above  the  viaduct  it  follow's  up  the  right  slope  of  the  small  stream  shown  just 
under  the  title  to  Fig.  208,  being  on  the  opposite  side  from  the  three  previous 
lines,  which  chanced  also  to  be  somewhat  the  best  side. 

It  was  found  on  extending  the  line  up  to  the  summit  that  it  left  some  spare 
elevation,  and  this  was  properly  concentrated  within  the  spiral,  in  order  to 
make  the  bridge  as  low  as  possible. 

919i  There  was  a  possibility  of  a  direct  line  from  Tepic  to  the  head  of  the 


I 


6/8  CH.  XX.— REDUCING  RATE  AND  COST  OF  HIGH  GRADES. 

spiral,  following  approximately  the  highway  via  La  Fortuna,  but   it  was  not 
deemed  worth  survey,  for  these  reasons: 

First. — It  was  certain  that  it  could  afford  no  better  grade,  and  but  little,  if 
any,  difference  in  curvature,  distance,  and  cost. 

Second. — The  fine  water-power  of  the  Rio  de  Tepic  would  have  been  left  at 
one  side,  with  the  mills  already  on  it,  and  the  others  which  were  very  likely  to 
be  placed  there — water-power  being  very  scarce  in  Mexico. 

Third. — There  was  considerable  local  traffic  from  La  Escondida  and  points 
beyond  it  to  the  west,  which  would  be  lost. 

Fourth. — A  dull,  uninteresting  ride  would  have  been  substituted  for  one  of 
the  greatest  scenic  attractions.  A  chief  dependence  for  the  traffic  of  the 
Pacific  Branch  (and  for  the  main  line  of  the  Mexican  Central  as  well)  being 
tourist  traffic,  and  much  of  the  re-mainder  of  the  line  being  of  great  scenic 
beauty,  this  alone  was  deemed  a  decisive  consideration. 

920,  The  leading  dimensions  of  the  spiral  and  viaduct  were  as  follows: 

Length  of  spiral,  2,637  metres =  8,652  feet  =      1.64  miles» 

(405  -|-  60  =  669  +  30,  with  lo-metres  station). 

Descent  in  spiral,  actual 53.00  metres  =  173.9    ^eet. 

Descent  in  spiral,  on  2.6  grade 68.56      " 

Loss  of  elevation  in  do 15.56  metres. 

Utilized  as  follows: 
For  curve  compensation,  303  degrees  (at  0.06  per 

degree) 5-56  metres. 

Spare  elevation,  utilized  for  a  station  ground  and 

water  station  at  south  end  of  spiral 10.00      " 

Viaduct :  Length,  200  metres =  656       feet. 

Height,     53      "       =173.9      " 

The  height  is  above  the  grade-line.  Above  low-water  it  was  some  7  feet 
more. 

Other  resources  for  reducing  the  rates  of  long  ascents  are  : 
921.  2.  Zigzag  developments,  obtained  by  finding  a  favorable 
point  for  the  line  to  turn  a  half-circle  and  return  upon  itself,  often  im- 
mensely facilitate  a  favorable  result,  enabling  the  possibilities  of  any  fa- 
vorable section  of  a  long  descent  to  be  utilized  to  the  utmost,  or  enabling 
the  line  to  keep  away  from  the  more  serious  difficulties.  The  develop- 
ment on  the  Jalapa  line,  Appendix  C,  is  a  good  example  of  this  device. 
The  privilege  of  using  a  sharp  curve  occasionally  is  a  great  assistance  to 
this  end,  and  often  a  sine  qua  non. 


6^zcH 

spiral,  f 
deemed 

First 
any,  difl 

Secoi 
one  side 
be  place 

Thh 
beyond 

F0U7 

the  gre; 
Pacific 
tourist 
beauty, 
920 

Length 

(40! 

Descent 

Descem 


Uti 
For  cur 

de§ 
Spare  e 

wa 
Viaduci 

The 
more, 
Otl 
921 

point  \ 
mense 
vorabl 
the  lir 
ment  < 
The  p 
this  ei 


CH.  XX.— REDUCING  RATE  AND  COST  OF  NIGH  GRADES.  679 


SAN     JUAN 


Fig.  209  is  another  example  to  scale  of  such  zigzag  or  horseshoe  develop- 
ment, on  the  Lima  &  Oroya  Railway,  in  Peru.  The  distance  from  ^  to  ^  hori- 
zontally is  570  feet, 
and  vertically  is  365 
feet.  The  horizontal 
distance  from  C  to  Z> 
is  495  feet,  vertical  dis- 
tance 360  feet;  length 
of  line  from  A  to  Z?  is 
4  miles.  The  usual 
rule  on  this  road  was 
to  use  switchbacks  for 
such  developments,  as 

shown  in  Figs.  218-21.     In  all  these  cuts  the  dotted  lines  represent  tunnels. 
The  curve  at  Sacrape  is  14°  30'. 

922.  3.  Spirals  might  be  used  to  great  advantage  much  oftener  than 


SACRAPE 


Fig.  210. 


-Bridge  Spiral, 


Fig.  211.— Tunnel  Spiral. 


they  are.     A  spiral,  also  sometimes  called  a  "loop,"  is  a  doubling  back 

of  the  line  upon  itself  so  that  it  returns  under  itself  at  a  lower  elevation. 

They  are  of  two  classes  :  bridge  spirals,    Fig.  210,   in  which  the 

upper  end  of  the  spiral  is  carried  over  the  lower  on  a  high  viaduct,  and 


6S0  CH.  XX.— REDUCING  RATE  AND  COST  OF  HIGH  GRADES. 


CH,  XX— REDUCING  RATE  AND  COST  OF  HIGH  GRADES.  68 1 


TUNNEL  SPIRALS,  Fig.  211,  in  which  the  lower  end  of  the  spiral  passes 
under  the  upper  end  with  a  tunnel.  Figs.  215-217  show  one  of  the  most 
extensive  applications  of  the  principle  of  spiralling  (made  possible  only 
by  very  peculiar  topographical  conditions)  which  was  ever  attempted, 
but  a  better  line  was  afterwards  found.  In  the  typical  bridge  spiral  the 
line  swings  around  the  slopes  of  a  valley  or  basin,  and  in  the  typical 
tunnel  spiral  the  line  swings  around  the  slopes  of  a  central  hill.  The 
tunnel  spirals  of  the  St.  Gothard  line  (Figs.  202-206)  are  also  tunnel 
spirals,  in  a  sense,  but  of  a  third  class,  which  does  not  swing  around  any- 
thing. 

923.  The  bridge  spiral  on  the  descent  to  Tepic,  Figs.  207,  208,  illus- 
trates the  advantage  gained  by  them,  which  is  to  make  a  sudden  and 
great  drop  at  one  spot.  They  are,  when  well  laid  out,  not  costly  feat- 
ures, and  bridge  spirals  especially  facilitate  that  most  important  end  of 


Fig.  213. — Map  of  Spiral  on  Union  Pacific  Railway,  shown  in  Fig.  212. 

getting  down  into  the  bed  of  a  stream  as  soon  as  it  has  descended  so  far 
from  its  source  that  it  may  be  said  to  have  a  bed.  It  is  to  be  remem- 
bered in  laying  out  bridge  spirals  that  the  height  of  iron  viaducts  is  a 
minor  factor  in  their  cost  (par.  102).  They  are  a  rare  feature  in  location, 
and  must  always  remain  so,  but  might  sometimes  be  used  to  advantage 
where  they  are  not.  Figs.  212-214  show  the  only  bridge  spiral  in  the 
United  States. 


682  CH.  XX.—REDUCnVG  RATE  AND  COST  OF  HIGH  GRADES, 


2-Sogo 


K 
Q 

< 

ind  75  feet  above  the 
lile,  exclusive  of  brid 
us  system  of  switcht 
preferable  in  every 
wo  thirds  the  cost  of 
operate.] 

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—  4_  0  t;  rt 

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sk^fc 

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'^ 

924.  4.  In  making  a 
descent  into  a  river  val- 
ley it  is  an  almost  invari- 
able rule  to  DESCEND 
against  THE  SLOPE  OF 
THE  VALLEY,  even  at  the 
cost  of  turning  a  half- 
circle  as  soon  as  the  bot- 
tom IS  reached.  The 
length  of  the  side-hill 
descent  is  much  de- 
creased. It  is  still  bet- 
ter, if  possible,  for  the 
same  reasons,  to  descend 
against  the  slope  of  some 
tributary  valley,  turn  a 
half-circle,  and  then  de- 
scend in  its  bed  to  the 
main  valley.  Figs.  215- 
217  give  an  actual  in- 
stance on  a  large  scale. 

In  Fig.  215  a  descent 
was  to  be  made  from  E,  at 
an  elevation  above  sea  of 
about  3000  ft.  (910  m.),  to 
A,  into  the  valley  of  the 
Ameca  River,  at  an  eleva- 
tion of  1120  feet  (340  m.) 
above  sea,  a  drop  of  some 
1880  feet,  to  be  made  within 
an  air-line  distance  from  E 
to  A  of  only  5  miles.  The 
Ameca  River  lies  along  the 
bottom  of  Fig.  215,  flowing 
to  the  left  with  a  sharp 
descent  of  over  one  per 
cent,  so  that  beneath  the 
spirals  EG,  shown  in  detail 
in  Figs.  216,  217,  the  bed 
of  the  river  was  only  1020 
feet  (310  m.)  above  sea. 
The  tributary  AB  had  a 


CH.  XX.— REDUCING  RATE  AND  COST  OF  HIGH  GRADES.  683 

still  sharper  descent  of  over  2  per  cent,  and  the  circumstances  of  the  location 
made  it  clear  that  the  ruling  grade  on  the  descent  must  be  at  least  2f  per  cent. 
The  location  shown  in  Fig.  216  is  3  per  cent  compensated,  about  2,6  per  cent 
actual. 

At  the  left  of  Fig.  215  was  another  tributary,  EG,  falling  far  too  fast  for  any 
line  to  follow  it  directly,  but  making  a  very  high  and  steep  backbone  or  knife- 
edge  at  EG  of  solid  basaltic  rock,  overlaid  for  the  most  part  with  a  thick  surface 
deposit  of  volcanic  tufa,  or  tepetate.  This  knife-edge  had  excessively  steep 
slopes  on  both  sides,  as  will  be  seen  from  Fig.  216,  extending  down  to  the  river- 
bed 1000  feet  below,  and  had  the  further  remarkable  peculiarity  that  the  sides 
swelled  in  and  out,  making  it  very  thin  at  points  and  thicker  at  others. 
These  unusual  topographical  features  made  conveniently  possible  such  an 
unparalleled  series  of  spiral  developments  as  are  shown  in  Figs.  216,  217, 
which  took  very  kindly  to  the  natural  surface,  so  that  they  could  be  executed 
at  very  moderate  cost,  as  the  minutely  accurate  topography  of  Fig.  216  will 
shovv\ 

925.  Under  these  circumstances  there  were  two  possibilities  for  the  de- 
scent from  E\o  A:  First,  the  line  EDCBA,  which  subsequently  proved  to  be 
by  far  the  best;  and,  secondly,  the  line  EFGHA.  Influenced  by  the  ease 
with  which  great  development  could  be  obtained  in  a  small  space  and  at 
small  cost  at  EG,  Fig.  215,  as  shown  in  detail  in  Figs.  216,  217,  the  latter 
line  was  examined  first;  the  only  useful  result  of  this  work  having  been  that 
it  is  possible  to  present  to  students  the  instructive  study  in  location  shown 
in  Figs.  216,  217,  where  six  successive  spirals  are  shown  (the  lowest  one 
finally  abandoned),  accomplishing  a  descent  of  613  feet  (187  m.)  within  a  hori- 
zontal distance  of  about  1800  feet,  measuring  from  the  highest  to  the  lowest 
points  shown  on  the  map.  The  developed  distance  between  these  same  points 
was  4.45  miles  (7.18  kilos.).  Measuring  from  the  nearest  points  of  the  first 
and  fifth  spiral,  a  descent  of  426  feet  and  a  development  of  nearly  2)k  miles 
was  obtained  between  points  only  558  feet  apart  horizontally.  The  lowest 
(abandoned)  spiral  gave  a  further  development  of  .855  mile  and  a  descent  of 
125  feet  within  a  horizontal  distance  of  263  feet.  A  striking  feature  of  the 
development  was  the  two-story  iron  viaduct  outlined  on  Fig.  216;  a  precipice 
over  200  feet  high  for  a  short  distance  at  one  point  enabling  the  line  to  pass 
twice  over  the  same  viaduct  at  elevations  100  feet  apart. 

The  value  of  such  a  feature  as  an  advertisement  and  attraction  to  trave. 
for  a  line  which  must  in  any  case  be  largely  dependent  on  tourist  travel,  was 
an  element  not  to  be  despised;  but  it  was  all  but  certain  that  the  true  loca- 
tion must  have  been  by  the  northerly  route,  as  was  found  to  be  the  case: 
for  (i)  the  stretch  ED  lay  along  the  natural  surface;  (2)  the  stretch  AB,  accom- 
plishing nearly  one  fourth  of  the  rise,  lay  in  the  bed  of  a  tributary  stream 
rising  nearly  as  fast  as  the  desired  grade.  All  that  was  necessary  by  this 
route,  therefore,  was  to  find  ground  on  which  the  descent  from  D  to  B,  and  the 


684  CH.  XX.— REDUCING  RATE  AND  COST  OF  HIGH  GRADES. 

turn  at  B,  could  be  made.  In  other  words,  granting  that  a  turn  at  B  could 
be  made,  more  than  half  the  descent  could  be  made  on  very  easy  ground.  Ex- 
amination showed  favorable  points  at  B  and  C  for  the  turn,  and  a  very  favor- 
able location  was  obtained  for  the  entire  descent.  This  line  also  had  engi- 
neering and  scenic  features  of  great  interest;  chief  among  the  latter  being  a 
gigantic  natural  obelisk  of  stone,  produced  by  erosion,  572  feet  high,  and 
pierced  through  the  centre  of  its  base  by  a  tunnel  279  feet  long. 

926.  Besides  these  four,  which  may  be  called  normal  expedients,  there 
are  the  following,  as  difficulties  multiply  : 

5.  Switchbacks:  the  proper  laying  out  of  which,  and  the  arguments 
in  favor  of  using  them  when  so  laid  out,  are  described  in  Appendix  C. 


Fig.  215. 


When  descents  of  over  1000  feet  are  to  be  grappled  with,  and  often  with 
less,  the  writer  believes  they  should  be  used  much  more  freely  than  they 
are,  if  laid  out  in  the  way  described,  so  that  the  stop  and  reversal  of  the 
direction  of  motion  involves  no  loss  of  time  or  power,  either  theoretically 
or  practically.  If  laid  out  in  the  ordinary  way  they  are  far  more  objec- 
tionable. Their  effect  to  reduce  the  cost  of  construction  is  very  great,  and 
there  is  no  necessar}^  loss  of  time  or  power  from  the  stop.  Figs.  212-214 
show  a  locality  where  well  laid  out  switchbacks  would  have  been  vastly 
more  economical,  and  have  given  better  results  in  other  ways. 


">< 


217  —Tht  l^i^"-  line-,  for  the  topography  (which  is  minutely  ac- 

r    I  nnt;  the  hill      The  whole  body  of  the  ridge  was 

1  at  crocks  on  the  surface  in  cooling  into  loose 

ti         I  ns    eaps  in  them.     The  degrees  of  the  curves 

_o-m(  tn  ir,r  It  i  chords  They  should  be  increased  about  one 
corrLCt  fur  [oo-ft  chords  The  facilities  which  a  judicious  sys- 
,  offLfS  for  conducting  location  is  apparent  from  Fig.  216.  The 
at  an  offset  for  introducing  transition  cur\xs.  making  no  effort 
r  offset  and  an\  curve  or  tangent  on  the  map  can  be  shifted,  re- 
he  line 

s  shown  throughout  the  map,  from  which  it  can  be  seen  at  once 
■nts  are  possible  at  t  number  of  points.  Including  the  lower 
I   hii.  s  a  45  miles  of  development  and  6t3  ft.  of  elevation  were 


68z! 

turr 
be  I 
ami 
able 
nee 

gigi 
pie] 


m 


CH.  XX.— REDUCING  RATE  AND  COST  OF  HIGH  GRADES.  685 


927.  The  following  Figs.  2i8  to  221  are  examples  of  switchbacks  from  the 
Lima  &  Oroya  Railway  in  Peru.  They  give  an  idea  of  the  advantage  which 
they  give  for  location, 


Fig.  218. 


From  A 


but  they  were  not 
properly  laid  out  to 
reduce  the  disadvan- 
tage of  a  stop  to  a 
minimum.  Fig.  218 
shows  a  rather  unusu- 
al and  unfavorable 
method  of  laying  them 
out,  the  switchbacks 
being  usually  in  pairs, 
as  in  Figs.  219-221, 
and  as  near  together 
as    possible,  so  as  to 

reduce  the  distance  on  which  the  train  runs  backward  to  a  minimum, 
to  B  is  34-  miles  by  the  line.     In  an  air-line  they  are  855  feet  apart  horizontally, 
and  545  feet  apart  vertically. 

From  I  to  2,   Fig.   219,  is  5  miles  by  the  line  and  i-J- 

miles  in  an  air-line.     The  horizontal  distance  between 

A  and  B  is  985  feet,   vertical    distance  625  feet.     The 

horizontal  distance  between  E  and  F  is  465  feet,  vertical 

distance  535  feet,  showing  an  average  slope  steeper  than 

I  to   I.      Many  such    places 

were  entirely  inaccessible  to 

bipeds,  and  the  line  was  only 

located  by  making  as  careful 

topographical  maps  as  possi- 

aC  hie,  projecting  a  location,  and 

pjO    ^^  triangulating  in  points  on  it 

for  beginning  construction. 

At  the  "Infiernillos,"  or  "Little  Hells,"  Fig. 

220,  the  river  passes    for  some    distance,  with  a 

succession  of  falls,  between  two  walls  of  rock  that 

rise  perpendicularly  to  a  height  of  2000  to  250c 

feet.     In  passing  under  these  high  points  the  line 

leaves  one  tunnel,  crosses  the  river  on  a  bridge 

of  160  feet  span  at  a  height  of  165  feet  above  the 

water,  and  enters  another  tunnel. 

From  I  to  2,  Fig.  220,  by  line  of  road  is  4f 
miles,  comprising  eight  tunnels.  An  air-line  from 
I  to  2  is  i|  miles.  The  horizontal  distance  from  A  \.o  B  '\s  445  feet,  vertical 
distance  310  feet. 


Fig.  2ig. 


6S6  en.  XX.— REDUCING  RATE  AND  COST  OF  HIGH  GRADES. 


Fig.  221  shows    another   very   peculiar    development — a    combination    of 
switchbacks  and  horseshoes.     From  A  Xo  B  \)^  line  of  road  is  4.9  miles,  by 

air-line  1.6  miles.  This  portion  of  the 
line  has  1776°  of  curvature— an  aver- 
age of  362°  to  the  mile.  From  C  to  Z> 
the  horizontal  distance  is  730  feet,  ver- 
tical distance  570  feet.  The  profile  in 
this  vicinity  was  not  inappropriately 
known  as  "  Gothic." 

These  maps  taken  together  will  in- 
dicate, what  is  the  fact,  that  even  in 
the  roughest  country  there  are  certain 
locations  where  zigzag  developments 
are  more  economical  than  switchbacks, 
and  others  where  switchbacks  alone 
are  practicable,  without  the  heroic  ex- 
pedient of  spiral  tunnels. 

928.  6.  Inclined  Planes  and 
Cable  Traction. — This  device,  in 
a  crude  form,  antedates  the  loco- 
motive itself,  and  was  at  first  the 
almost  universal  resort  for  dealing 
with  what  were  then  considered 
high  grades.  It  is  still  used  to  some 
extent,  but  early  passed  out  of  gen- 
eral use  as  an  accredited  auxiliary 
to  railway  transportation.  We  may 
admit  that  this  at  the  time  was  wise 
and  right,  and  still  regard  the  device  as  one  deserving  of  a  recognized 
standing  at  the  present  day.     In  all  probability,  within  a  few  years,  it  will 

be  much  more  used 
than  it  is  now  for 
moving  large  traffic 
over  high  eleva- 
tions. 

929.    The    argu- 
ments   against    the 
use    of    planes    are 
these : 
It  introduces  a  break  in  the  continuity  of  the  movement  of  traffic — 
an  argument  of  minor  importance  which  must  always  exist  in  some  degree. 


Fig. 


Fig.  221. 


I. 


CH.  XX.— REDUCING  RATE  AND  COST  OF  HIGH  GRADES.  68/ 

2.  The  power  and  working  force  necessary  to  operate  the  planes  must 
always  be  on  hand  and  available,  at  nearly  the  same  cost  whether  work- 
ing or  idle,  and  possibly  a  good  part  of  the  time  idle. 

This  was  a  very  serious  matter  in  early  days  when  traffic  was  light, 
but  it  grows  less  so  as  the  movement  of  traffic  becomes  so  great  as  to 
approximate  to  a  steady  stream  of  cars — a  condition  which  exists  on 
many  lines  now  operating  steep  grades  with  locomotive  power.  It  was  a 
leading  factor  in  causing  the  abandonment  of  planes  in  the  early  days  of 
railways  ;  hardly  subordinate  to  the  following,  which  was  perhaps  alone 
decisive : 

3.  Formerly,  planes  operated  by  stationary  power  were  necessarily 
short,  straight,  and  on  a  uniform  gradient.  This  made  it  essential  topo- 
graphically, even  if  it  had  not  been  mechanically,  that  the  planes  should 
not  be  long,  but  that  a  number  of  them,  separated  by  intervening  stretches 
of  "  level,"  should  be  used,  greatly  increasing  the  awkwardness,  delay, 
and  expense  of  the  process. 

4.  A  certain  element  of  danger  from  runaways  and  breakages  existed 
and  still  exists,  which  was,  however,  not  a  serious  nor  governing  consid- 
eration, even  when  the  only  cable  was  a  hemp  rope,  as  in  the  early  planes 
at  the  Alleghany  Portage  on  the  Pennsylvania  State  canal  and  railway 
system,  and  it  is  still  less  so  now. 

930.  On  the  other  hand,  besides  the  advantage  of  the  vast  increase  of 
traffic  which  would  enable  stationary  power  to  be  constantly  employed  at 
many  points,  the  perfection  to  which  the  cable  system  has  been  brought 
in  recent  years  has  greatly  changed  the  conditions  of  the  problem,  and 
favored  the  use  of  well-designed  inclined  planes  in  connection  with 
railways.  Passing  the  question  of  how  they  should  be  designed  for  the 
moment,  the  arguments  favoring  the  use  of  inclined  planes  of  whatever 
type  are  these : 

I.  The  great  expense  is  saved  of  lifting  the  ponderous  motor  itself 
up  and  down  hill.  Assuming  every  engine  to  be  fully  loaded,  and  assum- 
ing a  light  Consolidation  engine  with  tender  and  caboose  to  weigh  80 
tons,  we  may  deduce  from  Table  170  the  following  Table  189,  showing 
the  proportion  of  the  total  power  exerted  which  is  thrown  away  in  non- 
productive work  on  the  motor. 

•  2.  The  power  is  not  only  wasted  in  the  proportion  shown  in  Table 
189,  but  is  more  costly  per  horse-power  for  several  reasons  : 

{a)  The  fuel  burned  per  horse-power  is  much  greater  than  in  a  good 
and  powerful  stationary  engine  (Table  168,  page  531). 

{b^  As  one  stationary  engine  does  the  work  of  from  five  to  thirty 


688  CH.  XX.— REDUCING  RATE  AND  COST  OF  HIGH  GRADES. 

locomotives,  there  is  a  corresponding  saving  in  maintenance  of  machinery 
and  in  wages  of  engine-  and  train-men. 


Table  189. 

Proportion  of  the  Dead  or  Waste  Weight  (of  Engine,  Tender,  and 
Caboose)  to  the  Total  Paying  Weight  (of  Cars  and  Freight)  on 
Various  Grades. 

[An  addition  of  5  tons  has  been  made  to  the  weight  of  an  average  Consolidation  in 
Table  170,  as  better  corresponding  to  the  more  recent  practice  (Table  129),  and  a  corre- 
sponding subtraction  of  5  tons  from  the  load  given.  In  addition,  a  deduction  of  20  per 
cent  has  been  made  from  the  load  given,  as  an  allowance  for  the  lighter  winter  loads,  the 
scant  loading  of  many  trains,  and  light  trains  in  one  direction.  As  an  average,  this  allow- 
ance should  be  larger.] 


Weight  in  Tons, 

Per  Cent 

Grade 

Weight  Engine 

Per  Cent. 

Engine, 

Train 

Do.  Average 

to  Average 

Tender,  and 

by 

of 

Paying  Weight. 

Caboose. 

Table  170. 

All  Trains. 

I.O 

80 

706 

565 

14. 1 

1-5 

499 

399 

20.0 

2.0 

378 

302 

26.5 

2.5 

299 

239 

33.4 

3-0 

244 

195 

41.0 

3-5 

202 

162 

49.4 

4.0 

170 

136 

58.8 

5-0 

124 

99 

80.8 

6.0 

92 

74 

I35-0 

{c)  The  wear  and  tear  of  track  due  to  the  locomotive  is  saved,  which 
is  about  half  of  the  whole  cost  of  running  them  (par.  780).  Against 
this  is  to  be  balanced  the  loss  of  power  by  the  friction  of  the  rope  or 
cable,  but  this  is  comparatively  a  small  percentage  on  a  grade  plane, 
although  a  very  large  percentage  on  level  cable  railways.  The  cable 
friction  being  constant  per  mile  decreases  in  relative  importance  as  the 
grade  is  higher. 

{d)  The  modern  cable  system  possesses  several  advantages,  as  notably 
that  of  being  used  on  curves,  which  none  of  the  older  and  simpler  forms 
of  inclined  planes  possessed. 

3.  Apart  from  the  cost  of  the  mechanism  for  operating  the  planes 
(which  may  be  balanced  roughly  against  the  cost  of  locomotives),  the  use 
of  inclined  planes  will  ordinarily  cheapen  the  cost  of  construction  -ma- 
terially, although  this  may  not  be  invariably  the  case. 


CH.  XX.— REDUCING  RATE  AND  COST  OF  HIGH  GRADES  689 


B 


Fig.  222. 


931.  If  we  conceive  the  normal  type  of  a  passage  over  a  summit  to  be  that 
shown  in  Fig.  222,  the  manner  of  adapting  the  same  summit  to  the  use  of  in- 
clined planes  may  be  <hat  of  either  Fig.  223  or  Fig.  224.  In  Fig.  223  the  cars 
are  hauled  directly  up  an  inclined  plane  (or,  q 

if  necessary,  up  two  or  more)  at  A  and  B  to 

some  point  a  and  b  which  is  high  enough  for 

the  cars  to  descend    thence  over  the  entire 

distance  aCB  or  bCA,  presumably  in   short 

trains  in  charge  of  one  or  more  brakesmen. 

The  power  stored  in   the  cars  is  thus  not  lost,  by  having  to  be  shortly  after 

destroyed  by  the  brakes,  but  in  great  degree  utilized  for  propulsion. 

932.  This  economy  of  power  may,  under  favorable  circumstances,  be  carried 
still  further  by  the  construction  of  the  auxiliary  lines  cd  and  ce,  Fig.  224,  so  as 
to  extend  the  plan  in  Fig.  223  to  that  shown  in  Fig.  224.  By  these  auxiliary 
lines,   after   the   cars    have  as-  _   — ^  ^i__- 

fj    X "x  ir 

A 


cended  the  planes  A  and  B  \o  a 
or  b,  they  run  by  gravity  to  the 
points  e  or  d,  where  they  de- 
scend the  plane,  thus  assisting 
by  their   gravity  to    pull   other  Fig.  223. 

cars  up  it,  and  making  the  only  motive-power  required  (in  excess  of  cable-friction) 
— that  necessary  to  lift  the  cars  through  the  distance  da  or  eb,  which  is  necessary 
to  enable  them  to  run  by  gravity  to  the  opposite  plane.  If  the  distance  ab  were 
great  enough  to  make  it  desirable,  a  nearly  level  track  might  be  laid,  and  loco- 
motive-power used,  but  this  involves  the  disadvantage  that  the  location  is  more 
difficult  and  costly,  because  the  gradients  have  to  be  considered  in  both  direc- 
tions, whereas  the  duplicate  gravity  tracks  may  be  laid  out  on  different  routes, 
each  of  which  need  be  favora- 
ble to  motion  in  one  direction  "3  ^  .6 
only. 

933.  Theoretically,  the  sys- 
tem sketched  in  Fig.  224  com- 
pletely eliminates  the  disad- 
vantage of  the  elevation  sur- 
mounted, however  high,  leaving  the  only  loss  of  power  that  which  would  result 
if  the  track  were  vertically  projected  onto  the  plane  AB.  Practically,  it  will 
of  course  fall  far  short  of  this,  but  may  be  made  to  give  some  approach  to  it,  and 
with  the  privilege  of  introducing  a  few  easy  breaks  of  line  and  grade  on  the 
plane,  which  is  practicable  by  the  cable  system,  no  great  difficulty  is  likely  to 
arise  in  laying  out  long  planes  advantageously. 

934.  The  inodern  cable  system  has  not  yet  been  used  to  any  consid- 
erable extent  as  an  auxiliary  to  ordinary  railway  traffic,  although  it  is 
tending  in  that  direction.     It  originated  at  the  city  of  San  Francisco, 
44 


Fig.  224 


690  CH,  XX,— REDUCING  RATE  AND  COST  OF  HIGH  GRADES. 

from  the  necessity  of  supplying  street-railway  transportation  on  high 
grades.  In  its  essence  it  consists  in  using  a  continuously  moving  and 
endless  wire  cable  to  which  the  cars  are  attached  by  friction-grips,  instead 
of  winding  up  on  a  large  drum  a  rope,  chain,  or  flat  band  of  metal  of  the 
length  of  the  incline,  requiring  that  the  engines  should  start  and  stop 
again  after  taking  up  each  load.  The  modern  system  has  been  brought 
to  great  perfection  for  street  use,  and  has  spread  very  rapidly  in  spite  oi 
the  difficulty  and  expense  involved  in  covering  up  the  cable  below  the 
street  level.  It  has  been  described  with  remarkable  fulness,  in  all  its 
details  of  construction  and  working,  in  various  papers  before  engineering 
societies  and  in  the  leading  technical  journals. 

935.  Circumstances  favoring  the  use  of  this  particular  form  for  rail- 
way traffic  are  :  (i)  The  cable  would  not  need  to  be  covered  up  and 
gripped  at  some  disadvantage  through  a  narrow  slit;  (2)  being  primarily  re- 
quired for  vertical  and  not  for  horizontal  transportation,  the  incline  could 
be  made  steep  at  the  expense  of  length  and  speed,  reducing  the  chief 
source  of  loss  in  street  service,  friction  and  wear  of  cables ;  (3)  the  grips 
having  to  be  applied  only  at  the  bottom  of  the  plane,  and  released  only 
at  the  top,  could  be  made  very  powerful  by  duplicating  them,  or  other- 
wise ;  the  grades  at  the  bottom  of  the  plane  could  be  made  favorable  for 
getting  the  cars  quickly  under  way,  and  with  speeds  of  not  exceeding 
three  or  four  miles  per  hour,  which  would  be  quite  fast  enough  for 
economy,  the  grips  could  be  applied  and  released  by  men  jumping  onto 
the  grip-car  for  that  purpose,  so  that  there  would  be  no  necessity  for  any 
one  riding  up  or  down  the  plane  with  the  cars. 

The  system  is  certainly  one  of  much  promise  for  such  localities  and 
conditions,  and  the  necessity  of  the  utmost  economy  in  transportation 
warrants  its  careful  study,  and  will  probably  bring  about  its  gradual 
adoption,  with  details  adapted  to  the  peculiar  requirements. 

936.  A  final  expedient  for  reducing  the  disadvantages  of  gradients  is 
the  RACK  RAILWAY,  the  most  perfect  form  of  which,  and  the  only  one 
promising  general  usefulness,  is  the  Abt  system. 

The  Mt.  Washington  Railway,  in  New  Hampshire,  designed  by  Silves- 
ter Marsh,  was  the  first  example  of  a  rack  railway.*  The  device  con- 
sists, as  its  name  implies,  in  a  pinion  operated  by  a  separate  cylinder  on 
the  locomotive,  which  engages  in  a  fixed  rack  laid  between  the  rails.     It 

*  The  Rhigi  Railway,  M.  Richenbach,  engineer,  was  an  almost  exact  copy  of 
every  essential  detail  of  the  Mt.  Washington  line,  but  in  a  not  particularly  cred- 
itable way  was  labelled  the  "  Systeme  Richenbach,"  and  is  so  known  through- 
out Europe. 


CH.  XX.— DUPLICATE   TRACKS  FOR  PUSHER  GRADES.      69 1 

thus  eliminates  what  we  have  seen  to  be  the  most  serious  theoretical 
defect  of  the  locomotive — that  its  tractive  power  cannot  be  increased  in- 
definitely at  the  expense  of  speed,  but  only  within  narrow  limits.  In  its 
original  form  it  had  many  defects  which  the  Abt  system  eliminates,  but 
its  practical  utility  as  an  adjunct  to  the  normal  operation  of  railways  has 
not  yet  been  fully  demonstrated,  and  must  for  the  present  (1886)  be  re- 
garded as  somewhat  doubtful. 

937.  The  salient  features  of  the  Abt  system  are  these :  The  ingenious  en- 
gaging rack  by  which  a  locomotive  may  approach  the  foot  of  a  rack  grade  at 
some  considerable  speed,  with  certainty  that  the  pinion  will  engage  quickly 
and  without  shock  with  the  rack  ;  the  improved  manner  of  constructing  the  rack 
of  parallel  bars  with  the  teeth  staggdred  ;  the  pinion  or  driving-wheel,  which  is 
constructed  in  sections,  each  capable  of  a  slight  spring,  so  as  to  ensure  perfect 
and  smooth  contact  with  the  rack  ;  the  use  of  the  ordinary  adhesion  cylinders 

■  continuously  to  lend  what  aid  they  can. 

On  the  other  hand,  there  is  the  complication  of  the  machine,  and  the  diflS- 
culty  of  keeping  the  rack  in  working  order,  especially  in  the  winter  in  cold  cli- 
mates.* 

938.  A  device  for  accomplishing  the  same  end  as  the  rack  railway  in  a  dif- 
ferent way,  which  has  not  proved  equally  meritorious  in  practice,  is  the  fric- 
tion-grip RAILWAY,  In  this  device  two  friction  driving-wheels  engage  with  a 
■central  rail,  being  pressed  against  it  with  any  desired  force,  regardless  of  the 
weight  on  the  engine  itself.  While  the  device  has  been  used  successfully  in 
several  special  locations,  it  possesses  no  features  to  make  it  of  general  utility. 
It  is  generally  known  as  the  Fell  System,  and  was  used  at  the  Mt.  Cenis  Rail- 
way. 

DUPLICATE  TRACKS  FOR  PUSHER  GRADES. 

939.  In  the  main,  all  climbing  done  by  trains  on  pusher  or  high 
grades  is  so  much  clear  loss.  The  power  thus  stored  in  the  train  by 
lifting  it  up  not  only  does  no  good,  but  costs  more  money  to  destroy  by 
means  of  brakes.     It 

is  a   peculiar   advan- 
tage  of    the    use    of 
pushers  that  this  need 
not  be  invariably  nor  A^'* 
necessarily  the   case,  ""■"' 

for  under  certain  fa-  „  ^  _.  ^^  t. 

Fig.  225.— Typical  Profile  of  a  Gravity  Railway. 

vormg  circumstances 

it  is  possible  to  utilize  a  portion  of  the  work  thus  wasted  by  securing 

*  The  Abt  system  is  more  fully  described  in  a  paper  by  W.  W.  Evans,  Trans. 
Am.  Soc.  C.  E.,  March,  1886. 


692   CHAP.  XX.— DUPLICATE   TRACKS  FOR  PUSHER  GRADES. 

from  it  something  of  the  advantages  of  a  GRAVITY  RAILWAY,  a  typical 
profile  of  which  is  shown  in  Fig.  225. 

The  gravity  railway  does  of  set  purpose  and  to  secure  an  advantage 
what  the  ordinary  railway  only  does  of  necessity  as  an  unmitigated  dis- 
advantage; viz.,  it  seeks  out  certain  high  elevations,  and  ascends  to  them 
as  quickly  and  by  as  steep  a  grade  as  possible. 

This  it  does  for  precisely  the  same  reason  that  coal  is  put  on  the 
tender,  viz.,  TO  store  power  in  the  train  ;  only,  in  this  case,  the 
power  is  ready  for  instant  application  without  change  of  form.  It  is 
utilized  for  propulsion  instead  of  being  thrown  away  in  wearing  out 
wheel-s  and  brake-shoes,  by  laying  out  from  the  high  elevation,  to  which 
the  train  is  lifted  by  a  plane,  a  continuous  descending  gradient,  on  a  0.7 
to  i.o  per  cent  grade,  until  the  lowest  possible  point  is  reached.  The 
train  is  then  hauled  up  to  another  high  elevation,  and  the  same  process 
continued,  giving  a  profile  like  Fig.  225.  The  ascent  is  made  by  sta-. 
tionary  power;  but  that  does  not  affect  the  principle,  which  is,  that,  as  high. 
elevations  must  at  points  be  surmounted,  it  is  better  to  do  so  by  a  sys- 
tem which  utilizes  the  work  thus  done  for  propulsion  instead  of  wasting 
it  destructively. 

940.  There  is  one  serious  drawback  to  this  system,  that  cars  can  pass 
over  the  line  in  only  one  direction,  so  that  it  necessitates  an  entirely  in- 
dependent return  track,  however  light  the  traffic.  Nevertheless,  it  has 
been  and  is  still  used  to  some  extent.  It  originated  (in  this  country)  at 
Mauch  Chunk,  before  the  locomotive  had  fairly  been  invented,  and  was 
afterward  embodied  in  two  prominent  lines  in  Pennsylvania,  and  in  a 
number  of  smaller  ones.  One  of  these  lines  has  recently  been  abandoned  ; 
but  for  reasons  largely  independent  of  the  engineering  merit  of  the  sys- 
tem ;  the  other  is  still  in  operation. 

These  two  lines  are: 

Pennsylvania  Coal  Co. — 47  miles  double  track;  4  ft.  3  in.  gauge;  36-lb.  rails; 
23  stationary-engine  houses  and  as  many  planes,  or  about  one  for  every  four 
miles.  Average  speed  of  passenger  trains,  15  miles  per  hour;  freight  trains,  10 
miles  per  hour. 

Delaware  6^  Hudson  Canal  Co. — 32  miles  of  double  track;  4  ft.  3  in.  gauge; 
45  to  56  lb.  rails;  30  stationary  engines  and  as  many  planes,  or  about  one  every 
two  miles. 

The  advantage  of  the  plan  is  that  it  puts  the  undulations  of  the  sur- 
face which  cannot  be  avoided  into  the  harness,  as  it  were,  by  making  them 
a  necessary  part  of  the  system  of  operation.  Moreover,  motion  in  only 
one  direction  has  to  be  considered,  so  that,  so  long  as  the  train  keeps  de- 


CHAP.  XX.— DUPLICATE   TRACKS  FOR  PUSHER  GRADES.  693 

scending,  we  are  in  a  measure  independent  of  the  rate  of  grade,  and  econ- 
omy of  construction  is  promoted. 

To  balance  the  disadvantage  of  having  to  construct  two  independent 
tracks  there  is  a  certain  economic  advantage  in  a  double  track  even 
when  traffic  is  light. 

941.  The  extra  cost  of  having  to  construct  two  independent  lines  has 
undoubtedly  been  in  years  past  a  leading  factor  in  impeding  a  more 
general  use  of  this  plan,  until  now  engineering  practice  seems  to  condemn 
it,  but  that  under  certain  exceptional  circumstances  it  might  still  be  ad- 
vantageously used,  hardly  admits  of  doubt.  The  merits  or  demerits  of 
the  gravity  system  in  its  entirety  depend  chiefly,  it  is  plain,  on  whether 
or  not  inclined  planes  operated  by  stationary  power  are  economical  as 
compared  with  the  locomotive.  But  whether  or  not  the  plan  as  a  whole 
be  advantageous,  it  is  plain  that,  if  we  have  lifted  a  train  by  any  kind  of 
power  to  a  high  elevation,  that  feature  of  the  gravity  plan  is  economical 
which  utilizes  the  work  thus  done  instead  of  throwing  it  away,  and  this 
may  often  be  done  with  pusher  grades,  provided  the  traffic  be  sufficient 
to  make  certain  short  sections  of  double  track  in  the  immediate  vicinity 
of  the  pusher  grades  a  desirable  feature ;  which  is  very  apt  to  be  the  case, 
since  the  mere  existence  of  those  grades  practically  doubles  the  demand 
upon  the  track. 

942.  Thus,  supposing  a  summit  is  to  be  passed  over  from  one  valley 
to  another,  or  a  plateau  of  some  width  to  be  ascended  to  and  descended 
from.     Ordinarily   the    pro-  c- 

file  over  such  a  section  would  ---'^       pr 

be  something  like  the  solid  /  _---^^i^'''^V 

line  in  Fig.  226,  there  being  jB/        "~C^  \ 

certain  natural  difficulties  in  /  \ 

getting  favorable   grades    in  Jf\  V^ 

more  than  one  direction  be- 
tween B  and  D,  so  that  the  whole  stretch  AE  is  practically  a  single 
pusher  run.  If,  in  such  case,  the  grade  AB  can  be  prolonged  to  some 
higher  point  and  from  thence  carried  on  a  favorable  grade  for  trains  go- 
ing to  ^  to  a  junction  at  some  point  D,  the  expense  of  running  pusher 
engines  both  ways  over  the  distance  BD  will  be  saved,  at  the  expense  of 
constructing  the  short  section  of  duplicate  track  BFCD. 

943.  Again,  let  us  suppose  a  common  case,  that  we  are  carrying  a  line 
through  a  valley,  a  part  or  all  of  which  has  an  irregular  descent,  so  that 
an  extremely  favorable  line  may  be  had  for  trains  running  down  the 
valley  such  as  Fig.  227,  but  favorable  grades  for  ascending  it  can  only  be 


694  CHAP.  XX.— DUPLICATE   TRACKS  FOR  PUSHER  GRADES. 

had  with  some  difficulty  and  expense.  In  some  cases — not  by  any  means 
in  all  cases — it  would  be  possible  for  a  return  track  to  make  at  once  for 
some  high  point  C  on  a  ridge  or  crest,  and  thence  to  make  for  the  point 
A  with  level  or  descending  or  but  slightly  ascending  grades,  by  a  ridge 
line  or  a  different  valley  line  which  would  be  for  the  most  part  light. 


Fig.  227. 


Not  only  is  lighter  construction  per  mile  of  track  almost  certainly  attain- 
able, when  this  is  possible  at  all,  but  economy  of  operation  is  much  pro- 
moted, because,  instead  of  having  to  run  short  trains  both  ways  between 
A  and^,  because  of  the  opposing  grades  aa,  our  motive-power  is  only 
taxed  appreciably  on  the  pusher  grade  BCy  throughout  the  round 
trip. 

Nevertheless,  if  there  be  not  traffic  enough  to  require  or  justify  two 
tracks  any  attempt  of  this  kind  w^ould  probably  be  uneconomical. 

944.  But  after  all,  a  plain  continuous  descent  from  a  summit  to  the 
plain  below  will  ever  remain  the  normal  type  for  location,  such  devices  as 
spirals,  switchbacks,  and  others  being  the  exception.  In  all  but  the 
most  rugged  country,  say  wherever  most  of  the  surface  to  be  built  over  is 
not  bare  rock,  good  and  cheap  lines  can  usually  be  obtained  by  following 
these  two  rules  : 

First.  Do  not  attempt  to  secure  too  low  a  grade-line  by  more  than 
a  moderate  amount  of  development,  remembering  that  on  pusher  planes 
the  RATE  of  grade  is  comparatively  unimportant  (par.  747  and  Table  181). 

Seco7idly.  Do  not  adopt  a  limit  of  curvature  too  easy  for  the  topog- 
raphy, unless  the  importance  of  the  line  and  its  probable  revenue  will 
certainly  warrant  it.     (See,  however,  par.  883). 

945.  The  railway  system  of  Colorado  is  a  splendid  example  of  what 
may  be  accomplished  by  the  application  of  these  two  rules.  The  fact 
that  it  was  laid  to  narrow  gauge  probably  gave  courage  for  adopting  such 
alignment,  but  it  was  not  at  all  necessary  for  its  success,  as  we  have  else- 
where seen  sufficient  grounds  to  believe  (in  Chaps.  VIII.  and  XXIII). 
In  fact,  it  is  only  a  question  of  time  when  these  lines  will  be  relaid  ta 
standard  gauge  without  any  essential  change  in  their  alignment. 


CHAP.  XX.— DUPLICATE   TRACKS  FOR  PUSHER  GRADES.  695 


696  CHAP.  XX.— DUPLICATE   TRACKS  FOR  PUSHER  GRADES 

There  is  probably  no  system  of  roads  in  the  world  which  are  so  well 
worthy  of  the  study  of  engineers,  because  of  the  marvellous  cheapness 
with  which  it  has  been  carried  through  the  most  forbidding  regions,  and 
certainly  as  good  an  illustration  as  any  of  what  has  been  done  in  this 
way  is  the  "  High  Line  to  Leadville,"  on  the  Denver,  South  Park  &  Pacific 


.I  r-i       ,-1  o 


= ■ — — — — — — ^ Distance  from-  Denvef 

Fig.  230. — Profile  of  the  Last  62  Miles  of  the  "  High  Line  to  Leadville." 

[Grades  indicated  in  feet  per  mile.    The  heavy  black  line  indicates  the  section  shown  in  Fig. 

229,  a  view  from  the  lower  end  of  which  is  shown  in  Fig.  228.] 


Railway,  now  a  part  of  the  Union  Pacific  system.  The  total  cost  of  this 
line  was,  as  nearly  as  may  be,  $20,000  cash  per  mile,  and  this  was  like- 
wise very  close  to  the  cost  of  the  short  section  shown  in  the  large  map 
in  Fig.  229,  one  of  the  most  interesting  views  on  which  is  shown  in 
228. 
For  this  sum  the  line  was  carried  over  three  summits  over  11,000  ft. 


Fig, 


y' 

■^^^^ 

"    \...Vf....'> 

■r» 

!,»        j^n        ,^        «p.        t^n.        nfx.        «!«.        S(,oo       «ofoli«»  ^ 

y 

k 

V 

^ 

4 

I 

^Z'              ^      "'^^^4:*^^^ 

'^P^^--^^!:^:::^^^:^^^^ 

OuivER,soum-PARK&PAanc  nr 

Boreal  loBrecKBnridgt 

CHAP.  XX,— DUPLICATE   TRACKS  FOR  PUSHER  GRADES.   697 


high,  two  of  which  are  shown  in  Fig.  230,  and  for  a  large  part  of  the  re- 
mainder, of  the  distance  was  carried  through  the  narrow  and  tortuous 
channel  of  the  Platte  Can- 
on, where  long  stretches 
of  the  work  are  in  solid 
rock,  and  where  fills  were 
impossible,  it  being  neces- 
sary to  support  the  line 
on  retaining-walls  when 
not  in  the  solid.  These 
retaining-walls  are  among 
the  most  interesting  en- 
gineering features  of  Col- 
orado. They  are  dry 
and  very  cheap,  but  very 
solid,  and  give  no  trouble. 
They  were  generally  the  ^ 
first  work  started,  and 
were  carried  along  as  far 
as  possible  before  the 
rock  excavation  was  be- 
gun. 

946.  The  probabilities 
are  that  in  the  hands  of 
engineers  not  driven  to 
economy  by  necessity,  and 
constructing  by  what  have 
been  regarded  as  ortho- 
dox standards,  these  works 
would  have  cost  four  or 
five  times  what  they  actu- 
ally have,  while  many  of 
them  would  have  been 
wholly  impossible  at  any 
cost.  In  Fig.  229  we  have 
clearly  before  us  the  chief 
cause  of  their  economy — 

the  comparatively  free  use   [The  section  of  line  shown  by  profile  in  Fig.  230  is  indicated 
of  very  sharp  curves.      On  ^^  '^^  heaviest  line  above.] 

the  1 1.2  miles  shown  in  Fig.  229  there  are  in  all  127  curves,  or  11.3  curves 
per  mile,  divided  as  to  degrees  as  follows  : 


Fig.  231. — Map  of  the  "High   Line' 
Leadville. 


FROM   Denver  to 


698  CHAP.  XX.— DUPLICATE   TRACKS  FOR  PUSHER  GRADES. 


Total 40 


0 

9 

6 

10 

3 

II 

6 

12 

4 

13 

7 

14 

I 

15 

13 

16 

Total. 


I 

17" 

14 

18" 

2 

19" 

4 

20 

I 

21° 

3 

22° 

4 

23" 

4 

24" 

33 

25i 

.  I 
.  o 
.  I 

•25 

.  I 
.  I 
.  o 

■24 

.  I 


Total 54 


Strike  out  all  curves  sharper  than  10°  (573  ft.  radius)  from  this  list, 
and  we  multiply  the  cost  by  at  least  four  or  five  at  once  ;  besides  which, 
this  particular  line  becomes  wholly  impossible,  since  the  turn  could  not 
have  been  made  around  "  Nigger  Hill  "  nor  in  "  Illinois  Park"  in  the 
centre  of  the  view.  A  far  steeper  grade  or  an  entirely  different  route 
would  therefore  have  had  to  be  chosen.  It  should  also  be  noted  that  one 
rides  over  these  curves  without  the  slightest  sense  of  insecurity  or 
danger,  nor  have  they  proved  to  be  especially  dangerous  in  operation. 
The  motion  around  them  is  as  smooth  as  around  any  of  the  easier 
curves. 

The  writer  has  no  definite  knowledge  as  to  whether  the  general  route 
which  gave  so  very  bad  a  profile  as  this  line  has  was  really  the  best  one, 
and  must  be  understood  to  speak  only  of  the  details  of  the  location. 

947.  Fig.  232  shows  comparatively,  on  the  same  sheet,  a  number  of 
the  great  inclines  of  the  world,*  and  Table  190,  with  its  long  foot-note, 
adds  details  of  many  others,  the  whole  not  making  a  complete  list  by  any 
means. 


■^  Only  the  lines  shown  in  comparatively  heavy  lines  on  this  plate,  viz.: 
The  Jalapa  line  from  Vera  Cruz,  the  Denver  &  Rio  Grande,  the  Pennsylvania, 
and  the  Baltimore  &  Ohio  are  of  the  writer's  compiling.  The  remainder  has 
been  reproduced  from  a  plate  prepared  by  Mr.  W.  W.  Evans,  M.  Am.  Soc.  C. 
E.,  to  show  the  Peruvian  lines,  and  he  in  turn  was  indebted  to  European  au- 
thorities for  the  admirable  presentation  of  European  railways.  Comparative 
distances  are  of  course  to  be  estimated  by  the  horizontal  distance,  since  the  ex- 
aggerated vertical  scale  exaggerates  the  slant  length  greatly. 

A  small  profile  of  the  Mexican  Railway  is  shown  on  the  map  in  Appendix  C. 
It  could  not  conveniently  be  added  to  this  plate  for  comparison  with  the  Jalapa 
line.  Its  general  nature  will  be  indicated  by  projecting  a  4  per  cent  grade  (par- 
allel with  the  Peruvian  line)  from  Las  Vigas  summit  to  the  level  of  Jalapa,  and 
then  continuing  down  to  sea-level  with  mixed  i^  to  4  percent  grades,  with  some 
lost  elevation. 


CHAP.  XX.— DUPLICATE   TRACKS  FOR  PUSHER  GRADES.  699 


Table  190. 

Various  Great  Inclines  of  the  World. 

[The  body  of  this  table  is  (with  correction  of  a  number  of  errors)  a  list  given  in  The 
Engineer  of  July  17,  1885,  as  a  complete  one.  The  notes  beneath  give  various  other  and 
much  greater  inclines  omitted  from  the  list.] 


Name  of  Incline. 


Giovi 

Semmering 

Bhore  Ghaut 

Allegheny 

Tabor  (Chili) 

Kadugannavva  (Ceylon). . . 
Ambagamuwa         " 


Length 

of 
Incline. 
Miles. 


6 

15 
12 

III 
19 


Total 
Rise. 
Feet. 


884 
1,325 
1,831 
1,690 
1,360 
1,388 
2,227 


Grade. 

Av. 

Max. 

p.  c. 

P.O. 

2.78 

3-45 

2.13 

2.50 

2.08 

2.70 

2.13 

2.15 

2.25 

2.22 

2.22 

2.22 

2.27 

Maxi- 
mum 
Curve. 


4  20 
8°  40 

5°  45 
9°  30 
9°  30 
8°  40 
19°  o 


Length  of 

Tunnels. 

Miles. 


2.25 
2.66 
2.26 


30 


[In  addition  to  this  list  there  is  to  be  an  extension  of  the  same  Ceylon  railway  which 
"will  also  involve  a  further  incline  of  12  miles  rising  1359  ft.,  on  which  an  average  gra- 
dient of  2.15  per  cent,  with  a  maximum  of  2.227  P^r  cent,  will  be  compulsory,  as  will  also 
the  adoption  of  curves  as  sharp  as  19°."] 

To  the  above  very  inadequate  list  may  be  added  the  following,  the  whole  not  making  a 
complete  list  by  any  means  : 

Mexican  Railway. — Rises  6412  ft.  in  53.9  miles,  4  per  cent  maximum  grade  (214,  aver- 
age), with  325  ft.  curves  radius  (17°  40')  and  16  tunnels.  In  this  distance  it  also  rises 
2372  ft.  in  12.58  miles,  3.57  per  cent  average  grade  and  4  or  5  tunnels. 

The  air-line  distance  between  the  extreme  points  of  this  latter  section  is  less  than  four 
miles,  but  it  includes  the  bota,  or  boot,  so  called  from  its  shape,  nearly  eight  miles  long, 
and  rising  to  a  point  on  the  slope  of  the  mountain  which  to  the  eye  seems  almost  vertically 
over  the  p'oint  at  which  the  ' '  boot"  began  1650  ft.  below,  and  which  is  certainly  not  over 
one  mile  distant  from  it  horizontally,  giving  an  outlook  which  is  even  more  startling  to  the 
engineer  than  to  the  average  traveller. 

Oroya  Railroad.,  Peru. — Rises  2352  ft.  in  26  miles  on  21^  per  cent  (i  in  40)  maximum 
grade,  to  reach  the  foot  of  the  main  grade  ;  then, — 

Rises  12,84s  ft.  in  71  miles,  on  4  per  cent  grade,  with  14}^°  curves  (396  ft.  radius),  to  an 
elevation  of  15,645  ft.,  with  42  tunnels. 

On  this  line  there  are  several  switchbacks  (Figs.  217  to  221),  but  the  first  thirteen  miles 
rises  2105  ft.  without  any  switchback. 

There  are  one  or  two  other  lines  in  Peru  of  the  same  general  character,  but  rising  to 
less  elevations. 

Among  the  European  inclines  not  included  above  are  : 

St.  Got  hard. — Rising  2750  ft.  in  203^  miles  ;  142.5  ft.  per  mile  maximum  grade  (2. 7  per 
cent)  ;  130  ft.  average  grades.  Also  rising  2090  ft.  in  1534  miles,  with  28  per  cent  of  the 
distance  tunnels,  including  (on  both  these  incHnes)  seven  spiral  tunnels  turned  into  the 
mountain  to  gain  distance  (Figs.  202  to  206). 

^r^?m^r.— Rising  2584  ft.  in  221^  miles,  132  ft.  per  mile  (2.5  per  cent)  maximum  grade ; 
1 14. 6  ft.  average. 


700  CHAP.  XX.— DUPLICATE   TRACKS  FOR  PUSHER  GRADES. 

In  the  United  States  there  are  : 

Southern  Pacific. — Rises  2674  ft.  in  25,4  miles  ;  116  ft.  per  mile  (2.20  per  cent)  maxi- 
mum grade;  10°  maximum  curve;  11  tunnels,  including  a  "loop,"  or  more  properly, 
spiral  or  helix,  3800  ft.  long  and  rising  78  ft, 

Denver  6^  Rio  Grande,  Marshall  Pass.—K\^^%  3675  ft.  in  25  miles,  4  per  cent  (211  ft. 
per  mile)  maximum  grade  ;  24°  maximum  curve.  Height  of  summit,  10,852  ft,  above  the 
sea.     Also, 

La  Vet  a  Pass.—Kxs^s  2368  ft.  in  15  miles  ;  same  grades  and  curves  as  above.  Height 
of  summit,  9339  ft. 

The  Unes  over  Fremont  Pass,  11,540  ft.  above  the  sea, — the  highest  point  reached  by 
the  locomotive  anywhere  in  the  world  except  in  Peru, — and  the  Tennessee  Pass,  10,418  ft. 
high,  are  of  the  same  general  character. 

Another  very  notable  heavy  grade  on  this  same  road  is : 

Calumet  Mine  Branch,  Denver  &=  Rio  Grande. — Rises  some  2700/?.  in  seven  miles 
on  an  eight  per  cejit  grade  (nearly  406  ft.  per  mile)  with  25°  maximum  curves. 

This  unparalleled  line  is  used  to  bring  ore  to  the  Bessemer-steel  works  at  Pueblo,  and 
is  operated  by  one  train  per  day  each  way.  It  is  undoubtedly  the  heaviest  grade  on  any 
regularly  operated  railroad  in  the  world,  although  10  per  cent  temporary  grades  (528  ft. 
per  mile)  were  successfully  operated  for  over  two  months  over  the  Kingwood  Tunnel  of 
the  Baltimore  &  Ohio  Railroad  by  the  late  Benj.  H.  Latrobe  as  early  as  1852.* 

These  latter  lines  are  narrow-gauge,  but  need  not  remain  so  unless  they  choose. 

Mexican  National. — Rises  2628  ft.  in  17  miles;  on  3.8  per  cent  (201  ft.  per  mile)  max- 
imum grade;  15°  maximum  curves;  with  a  descent  of  1325  ft.  in  nine  miles  on  a  3.5  per 
cent  grade  on  the  other  side  of  the  summit.  Laid  to  narrow-gauge,  but  expressly  built 
throughout  to  be  adapted  to  standard  gauge.     On  same  road  : 

Mexican  National,  Northern  Division. — Monterey  to  Saltillo.  Rises  3465  ft.  in  54 
miles,  at  an  average  rate  of  64  ft.  per  mile,  most  of  the  rise,  however,  concentrated  on  a 
short  portion  of  the  distance  on  grades  of  2^  per  cent. 

Less  important  inclines  which  are  for  one  reason  or  another  notable  are  : 

Tyrone  dr'  Clearfield. — A  little  branch  of  the  Pennsylvania  Railroad.  Rises  1064  ft. 
in  10  miles.     Tangent  maximum,  138  ft.  per  mile. 

Central  Pacific. — Rises  992  ft.  in  13  miles;  2  per  cent  (105.6  ft.  per  mile)  maximum 
grade;  10°  curves;  eight  tunnels. 

Northern  Pacific. — Rises  1668  ft.  at  116  ft.  per  mile  (2.2  per  cent)  in  an  air-line  dis- 
tance of  13  miles. 

Mexican  Central. — Rises  1750  ft.  in  19  miles  at  San  Juan  del  Rio  with  easy  grades  and 
curves  and  1650  ft.  at  Zacatecas. 

Among  lines  located,  but  not  yet  built,  may  be  mentioned  : 

Luckmayiier  Pass  (near  the  St.  Gothard). — Rises  on  a  development  of  29}^  miles 
betweeji  two  points  six  miles  apart,  on  a  maximum  grade  of  132  ft.  per  mile  (2.5  per 
cent)  implying  a  descent  of  something  less  than  3900  ft.,  with  maximum  curves  of  984  ft. 
radius  (5°  49'). 

Mexican  Ceyitral. — Two  lines  ascending  from  the  coast  to  the  central  plateau  of  Mex- 
ico, one  from  the  Gulf  of  Mexico  at  Tampico  and  the  other  from  the  Pacific  at  San  Bias, 
both  of  which  rise  some  4500  ft.  on  2  to  3  per  cent  grades. 

*  For  a  full  and  most  interesting  account  of  these  and  other  works  by  Mr.  Latrobe,  see 

Railroad  Gazette,  December  5,  1874. 


CHAP.  XX.— DUPLICATE   TRACKS  FOR  PUSHER  GRADES.   /OI 

Vera  Ci-uz  to  City  of  Mexico^  via  Jalapa. — The  line  more  fully  described  in  Appen- 
dix C.  Rising  7323  ft.  (2232  metres)  in  one  unbroken  2  per  cent  (average)  gradient  for 
72.64  miles  (ii6.g  kilometres)  or  from  an  elevation  of  600  ft.  to  an  elevation  of  7923  ft. 
above  the  sea. 

948.  The  great  effect  of  fluctuations  of  velocity  to  modify  the  nom- 
inal rates  of  short  gradients  may  be  illustrated  by  the  following  tests 
made  by  Mr.  C.  H.  Hudson,  a  prominent  and  able  railway  manager.  The 
tests  are  thus  described  :* 

''Recently,  for  the  purpose  of  testing  a  new  engine  of  the  Consolidation 
pattern,  just  received  by  the  East  Tennessee,  Virginia  &  Georgia  Railroad,  we 
weighed  a  train  of  30  loads,  caboose  and  private  coach,  and  took  it  with  the 
engine  to  a  heavy  grade  about  a  mile  long,  averaging  67.1  ft.  per  mile.  The 
grade  was  not  even,  but  undulating  ;  some  being  more  and  some  less  than  the 
average.  In  one  place,  100  ft.  were  at  the  rate  of  98  ft. ;  another,  spots  of 
300  ft.  at  the  rate  of  91,  and,  of  course,  to  match  it  other  spots  were  less  than 
the  average.  Before  reaching  the  grade,  there  were  about  1600  ft.  of  level; 
mostly  on  a  3°  curve  to  right,  which  curve  continued  Soo  ft.  up  the  grade.  Then 
followed  [curves  and  tangents  for  4S00  ft.  in  all]  when  the  summit  was  reached. 
The  day  was  warm  and  dry,  and  circumstances  favorable.  The  weight  of  train 
was  as  follows  : 

"Engine,  109,000  lbs.;  tender,  55,000  lbs.;  32  cars,  1,453,160  lbs.;  total, 
1,617,160  lbs.  Cylinders,  20  by  24  in.;  diameter  of  drivers,  59  in.;  weight  on 
drivers.  97,000  lbs. 

''First  Test. — The  engine  stood  at  start  at  water  tank  about  1500  ft.  from 
foot-of  grade,  and  when  grade  was  reached  was  making  about  18  miles  per  hour. 
At  a  point  3700  ft.  from  the  grade  the  engine  came  to  a  stand,  unable  to  take 
train  through.  It  was  then  backed  dov/n  and  two  cars  set  oft',  weighing  123,500 
lbs.,  leaving  weights  as  follows  : 

''Engine,  109,000  lbs.;  tender,  55,000  lbs.;  train,  1,329,660  lbs.;  total, 
1,493,660  lbs. 

Second  Test. — This  time  the  engine  started  from  the  same  place  as  before, 
struck  the  grade  making  22.3  miles  per  hour,  and  in  seven  minutes  turned  the 
summit,  making  4.5  miles  per  hour.  The  engine  averaged  145  lbs,  steam,  was 
worked  most  of  the  way  in  the  second  notch  from  bottom,  or  at  about  an 
18-inch  cut-off,  the  last  1200  feet,  being  in  lowest  notch,  or  what  was  called 
full  stroke  (22-inch  cut-off).  Very  little  sand  was  used  ;  engine  did  not  slip 
any. 

"  While  this  grade  was  undulating,  it  seemed  fair  to  take  the  average, — which 
has  been  stated  67.1  per  mile,  or  1.27  per  cent, — giving  a  resistance  due  gravity 
per  ton  of  .0127  X  2000  =  25.4  lbs. 

The  locomotive- power  indicated  by  these  records  is  then  computed  in 
the  following  manner — correct  numerically,  but  wholly  incorrect  in  its 
apparent  indications : 

Lbs.  per  ton. 

"  Train  resistance 5.0 

Curve  resistance  on  6°  curve 6.0 

Grade  resistance  (1.27  per  cent) 25.4 

Total  resistance  to  be  overcome 36.4  lbs. 

'^ Jour.  Assoc.  Eng.  Societies,  1886. 


702   CHAP.  XX,— DUPLICATE  TRACKS  FOR  PUSHER  GRADES. 

"  Weight  of  engine  and  train  being  747  tons  ;  747  X  36.4 =  27,191  lbs. 

But  about  100  ft,  of  the  train  will  be  on  a  10°  curve,  where  the 
resistance  per  degree  is  .05,  or,  for  the  10°,  .50  percent ;  the  esti 
mated  resistance  on  a  6°  curve  was  .30  per  cent  ;  here  is  an  ex- 
cess of  .20  per  cent,  or  per  ton,  4  lbs.  Now,  three  cars  are  all  of 
the  train  on  this  curve,  and  we  have  69  tons,  which  gives  69  X  4  =        276  lbs. 

Making  a  total  resistance  to  overcome  of 27,467  lbs. 

"  You  will  note  that  here  we  develop  a  tractive  force  of  28.2  per  cent  of  the 
weight  on  drivers  ;  not  so  great  as  in  other  cases,  but  much  over  ordinary  prac- 
tice. 

20  X  20  X  24. 
"The  theoretical  power  of  the  engine  would  be  as  follows: 

X  cylinder  pressure  =  192  X  130  (assumed)  =  24,960  lbs. 

"  The  estimated  resistance  per  ton  is,  including  the  correction  for  the  10° 
curve,  36.8  lbs. 

"  Divide  the  theoretical  power,  24,960,  by  this  resistance  36.8,  and  we  have  : 
24,960  -^  36.8  =  678  tons  =  1,356,000  lbs. 
Being  the  theoretical  amount  the  engine  would   move  up   this  grade,  or  about 
137,000  lbs.  less  than  the  actual  amount  moved.      The  actual  work  exceeds  the 
theoTetical  by  about  the  weight  of  the  engine  and  tender."" 

949.  The  true  explanation  of  this  apparent  anomaly  is  that  the  en- 
gine in  reality  did  no  such  thing  as  to  develop  a  tractive  force  of  27.467 
lbs.,  nor  is  there  any  real  discrepancy  between  the  actual  and  theoreti- 
cal work  done.     The  true  way  of  computing  the  tests  is  as  follows  : 

Per  cent. 

Nominal  average  rate  of  grade  (that  of  the  profile) 1.27 

Correct  for  curvature  at  0.03  to  0.05  vertical  feet  for  each  degree  of  cen- 
tral angle,  which  is  in  effect  an  addition  to  the  grade  of 0.12 

And  we  have  as  the  equivalent  nominal  grade,  including  effect  of  uncom- 
pensated curvature 1.39 

Where  the  curvature  is  makes  no  great  difference,  unless  it  stalls  the 
train,  and  we  need  not  now  go  into  that  detail. 

Then  to  compute  the  first  test  we  have  :  * 

Train  struck  foot  of  grade  at  velocity  of  18.0  miles  per  hour,  and  stalled 

in  3700  ft.  Vel. -head  for  18.0  miles  (Table   118),  11.50  ft.;  —19  z=    0.311  vert. 

37.00 
ft.  per  station  as  the  work  done  by  momentum.     1.39  —  0.311  =  1.08  per  cent 
as  the  virtual  grade,  or  the  one  up  which  the  unassisted  traction  of  the  engine 
hauled  the  train. 

Miles  per  hour.     Vel.-head. 

Second  Test. — Speed  at  foot  of  grade  (4800  ft.  long) 22.3  17.67  ft. 

"      "top  "         4.5  .73  ft. 

16.94 

*  For  strict  correctness  the  distance  travelled  up  the  grade  by  the  centre  of 
gravity  of  the  train,  and  not  the  engine,  should  be  used  in  this  test,  but  as 
the  initial  velocity  was  taken  from  the  engine  it  is  impossible  to  do  so. 


CHAP.  XX.— DUPLICATE  TRACKS  FOR  PUSHER  GRADES.   703 


16.94  vert,  ft.  _  ^         ^^^^    £j^  station  as  the  assistance  derived  from  mo- 

48.00  stations 

mentum,  and  1.39—  0.353  =  1.04  per  cent  as  the  virtual  grade  in  the  second 

test. 

All  this  is  shown  graphically  in  Fig.  233.     At  the  foot  of  the  grade 
the  vertical  head  corresponding  to  the  given  velocities  is  erected,  and 


also  at  the  head  of  the  grade,  although  it  is  so  small  as  to  be  hardly  visible. 
The  dotted  lines  show  the  virtual  grades.  The  two  tests  coincide,  it  will 
be  seen,  almost  exactly  in  the  virtual  grade  which  they  indicate,  espe- 
cially if  we  remember  that  the  engine  used  a  little  more  steam  on  the 
upper  part  of  the  second  run. 

This  virtual  grade  includes  the  effect  of  curvature,  and  for  the  power 
developed  by  the  engine  we  have : 

Lbs.  per  ton. 

Train  resistance 5-0 

Grade  worked  by  engine  power  (say  1.06  per  cent) 21.2 

Total  per  ton ■■ 26.2 

26.2  lbs.  per  ton  X  747  tons =  I9'57i  lbs. 

Against  Mr.  Hudson's  computation  of  actual  work  of 27,467 

And  of  theoretical  work  with  130  lbs.  pressure  of 24,960 

The  actual  work  done  requires  an  average  effective  piston  pressure  of 

^9' 57 1  _  a  fraction  over  100  lbs.  per  square  inch,  which  is  coming  down 

192 
within  the  bounds  of  reason  (and  barely  that)  for  a  Consolidation  engine 
carrying  140  lbs.  of  boiler  pressure  and  running  over  15  miles  per  hour. 
950.  We  may  see  how  these  variations  of  velocity  may  tend  to  in- 
crease grades,  and  how  nearly  our  process  of  computing  them  will  check, 
by  considering  what  took  place  between  the  starting-point  and  foot  of 


704  CHAP.  XX.— DUPLICATE  TRACKS  FOR  PUSHER  GRADES. 

the  grade,  1 500  ft.  off,  over  a  nominally  level  grade.     The  virtual  grade 
may  be  thus  determined  : 

In  first  test.  In  second  test. 

Speed  acquired  in  1500  ft 18.00  22.30 

Corresponding  vel. -head,  ft 11.50  17.67 

Then  we  have,  as  the  virtual  gX2i^&s  per  station.. .    • — —  =  0.77  =  1.18 

15.00  15.00 

In  other  words,  in  the  first  test  the  engine  started  off  lazily  and  did 
not  do  as  much  work  as  after  it  struck  the  grade.  In  the  second  test  the 
engine  succeeded  in  doing  somewhat  more  work  than  it  did  after  it  struck 
the  grade,  as  is  but  natural  from  the  fact  that  its  average  velocity  was 
less  and  (probably)  it  used  more  sand  and  had  a  somewhat  higher  boiler 
pressure.  But  the  correspondence  is  close  without  these  allowances  ; 
quite  sufficient  to  indicate,  what  is  beyond  question,  that  the  method  is 
essentially  trustworth)'-. 

Now,  had  this  grade,  instead  of  being  only  4800  ft.  long,  been  48,000 
ft.  long,  it  will  be  evident  that  the  same  initial  velocity  would  have  done 
very  little  to  help  out  the  engine.  To  derive  equal  aid  from  momentum 
we  should  have  needed  to  have  a  vertical  head  ten  times  as  great  in  that 
case,  or  176  ft.,  which  would  have  carried  the  necessary  initial  speed  up 
to  the  impracticable  limit  of  nearly  71  miles  per  hour.  Consequently, 
while  short  grades  and  short  sags  may  be  operated  almost  as  levels  with 
speeds  of  30  to  50  miles  per  hour,  long  grades  or  bad  sags  can  be  but 
little  helped  out  by  momentum.  In  the  one  case  the  profile  tells  the 
truth,  and  in  the  other  it  does  not. 


PART  IV 


LARGER  ECONOMIC  PROBLEMS. 


*'  The  rich  man's  wealth  is  his  strong  city :  the  destruction  of  the  poor 
is  their  poverty." — Proverbs  x.  15. 

"  For  whosoever  hath,  to  him  shall  be  given,  and  he  shall  have  more 
abundance  :  but  whosoever  hath  not,  from  him  shall  be  taken  away  even 
that  he  hath." — Matthew  xiii.  12. 

"For  which  of  you,  intending  to  build  a  tower,  sitteth  not  down  first, 
and  counteth  the  cost,  whether  he  have  sufficient  to  finish  it  ?  Lest  haply, 
after  he  hath  laid  the  foundation,  and  is  not  able  to  finish  it,  all  that  be- 
hold it  begin  to  mock  him,  saying,  This  man  began  to  build,  and  was 
not  able  to  finish." — Luke  xiv.  28-30, 
45 


PART  IV. 
LARGER  ECONOMIC   PROBLEMS. 


CHAPTER   XXL 

TRUNK    LINES    AND    BRANCH    LINES. 

951.  That  the  most  elementary  conditions  on  which  the  suc- 
cess or  failure  of  railway  enterprises  depend  are  often  radically 
misunderstood,  almost  necessarily  follows  from  the  fact  that  the 
world  is  so  full  of  examples  of  misdirected  enterprise — of  lines 
built  with  great  hopes  of  profit  which  have  proved  miserable 
failures;  while,  on  the  other  hand,  there  are  so  many  examples  of 
roads  built  for  local  purposes,  or  otherwise  without  particular 
expectation  of  a  brilliant  future,  which  have  proved  magnificent 
properties.  Among  innumerable  examples  which  might  be  men- 
tioned we  may  take  the  West  Shore  Railroad  of  New  York  as 
an  example  of  the  first  class,  and  the  parallel  New  York  Central 
of  the  last:  the  present  New  York  Central  &  Hudson  River  Rail- 
road having  been  made  up  by  the  consolidation  of  six  or  eight 
different  local  lines,  built  with  little  or  no  reference  to  the  forma- 
tion of  a  great  trunk  line.  These  two  lines  are.  in  their  different 
ways,  striking  examples  of  the  fact  that  the  conditions  which  con- 
trol the  future  prosperity  of  such  properties  are  often  wholly 
misunderstood. 

952.  It  seems  for  many  reasons  probable  that  by  far  the  larger 
part  of  this  very  general  misunderstanding — of  the  blundering 
into  unexpected  success  on  the  one  hand,  and  into  dismal  and 


708      CHAP.  XXI.— TRUNK  LINES  AND  BRANCH  LINES. 

utter  failure  on  the  other — arises  from  a  single  cause,  viz.,  an 
imperfect  understanding , of  certain  elementary  facts,  which  we 
will  now  consider,  as  to  the  effect  upon  the  productiveness  of  the 
property  of  any  increase  in  the  sources  of  traffic.  The  unex- 
pectedly good  or  bad  fortune  of  hundreds  of  properties  can  be 
traced,  in  part  or  whole,  to  this  single  cause. 

953.  Let  us  suppose  a  railway  to  be  projected,  say  loo  miles 
long,  to  connect  two  traffic  points  of  some  importance.  A,  £,  Fig. 

^  233.    We  will  assume  for 

• ^"" •    simplicity  that    there  is 

Fig.  233'.  little  or  no  intermediate 

local  traffic,  as  often  happens.  We  will  consider  A  and  B  to  be 
equal,  not  necessarily  in  population,  but  in  traffic-contributing 
capacity  to  this  particular  line.  The  traffic  which  the  railway 
has  to  support  it  may  be  then  represented  by  the  combination 
AB,  being  that  which  naturally  exists  between  two  traffic  points 
of  the  importance  of  A  and  B. 

954.  Let  us  now  suppose  that  another  alternate  route  may  be 
chosen,    which   by  a  slight   detour  will    strike   an    intermediate 

^__^_C  traffic  point  C,  Fig.  234, 

A^,^ "y^'    '     ^.rrrrrmrrrrrrrrr^^S^    of  equal  potential  mag- 
nitude   with    A    and    B: 
'  ^^^'  how    have    we    affected 

the  revenue-earning  capacity  of  the  line  ? 

A  most  natural  answer — beyond  all  question  a  very  common 
answer — is  that  we  have  increased  it  just  50  per  cent.  Instead  of 
serving  perhaps  100,000  people  in  the  two  towns  A  and  B,  we 
now  serve  150,000  people  in  the  three  towns  A,  B,  C.  Fifty  per 
cent  more  people,  fifty  per  cent  more  traffic,  fifty  per  cent  more 
earnings — seem  natural  corollaries  of  each  other. 

On  the  contrary,  it  may  be  shown  at  once  that  we  have 
doubled  our  probable  traffic,  and  really  we  have  tripled  our  traffic, 
and  rather  more  than  tripled  it.  Instead  of  having  only  Traffic 
AB,  Fig.  233,  we  have  Traffic  AB,  Traffic  AC,  Traffic  CB,  Fig.  234. 
The  value  of  the  latter  is  obviously  twice,  and  really  consid- 
erably more  than  three  times,  that  of  the  former. 


CHAP.  XXI,— TRUNK  LINES  AND  BRANCH  LINES.      709 

To  have  the  traffic  tripled  we  must  assume  that  Traffic  AB^ 
Traffic  AC,  and  Traffic  BC,  Fig.  234,  are  of  equal  financial  value 
— which  they  are,  as  nearly  as  may  be. 

955.  An  objection  to  this  statement  will  naturally  suggest  it- 
self— that  in  Fig.  234,  although  the  traffic  points  A,  B,  C  are 
equal  in  magnitude,  yet  the  haul  on  the  Traffic  AB  is  twice  that 
on  Traffic  ^Cor  CB.  Therefore,  if  the  volume  of  each  be  the 
same  and  the  rates  be  the  same,  we  apparently  have  Traffic  AB  = 
Traffic  AC  +  Traffic  CB,  so  that  we  have  only  doubled  instead  of 
tripling  our  traffic  from  a  revenue-producing  point  of  view. 

But  these  latter  assumptions  are  not  correct,  either  as  respects 
the  volume  of  or  rates  on  traffic. 

As  respects  the  effect  of  distance,  it  may  be  said  in  a  general 
ivay  that,  if  we  consider  only  great  and  decided  differences  of 
distance,  the  volume  of  traffic,  both  passenger  and  freight,  will 
be  at  least  inversely  as  the  distance  :  that  is  to  say,  if  two  given 
traffic  points,  100  miles  apart,  could  be  moved  up  to  a  distance 
of  only  50  miles  from  each  other,  and  remain  otherwise  un- 
changed, the  volume  of  traffic  between  them  will  be  at  least 
doubled.  New  York  and  Philadelphia,  for  example,  are  90  miles 
apart,  and  New  York  and  Boston  231  miles.  Could  these  cities 
,be  moved  up  to  within  45  and  115  miles  of  each  other  the  volume 
of  traffic  between  them  might  even  be  quadrupled,  and  certainly 
the  lines  connecting  them  would  be  very  much  better  properties, 
because  the  loss  of  haul  would  be  more  than  made  up  by  the 
increase  of  volume,  even  as  respects  gross  revenue,  leaving  the 
saving  in  expenses  by  the  shorter  haul  and  the  probable  higher 
rates  per  mile  almost  a  clear  gain. 

956.  As  to  rates,  it  is  an  entirely  safe  general  rule,  that  freight 
hauled  only  half  as  far  will  pay  a  materially  larger  rate  per  mile 
for  the  haulage  proper,  excluding  the  terminal  charge,  which  is 
in  effect  a  part  of  every  rate. 

The  passenger  rates  per  mile  might  well  be  the  same  or  even 
lower,  but  this  would  only  be  for  the  reason  that  it  was  profita- 
able  to  make  them  lower,  to  secure  the  far  greater  net  gain  from 
the  increase  of  volume.  The  traffic  would  in  all  such  cases  bear 
a  materially  higher  rate  per  mile  without  decreasing  its  volume 


710        CHAP.  XXI.— LA  W  OF  INCREMENT  OF   TRAFFIC. 

below  what  would  exist  with  twice  the  haul.  Taking  both  these 
considerations  together,  it  is  quite  certain  that,  whether  we  con- 
sider great  distances  or  small,  nearness  of  traffic  points  is  cer- 
tainly no  disadvantage  to  the  financial  productiveness  per  unit 
of  the  traffic  between  them.  For  example,  if  the  haul  on  wheat 
to  the  seaboard  were  only  half  as  great,  it  cannot  be  questioned 
that  it  would  be  a  more  profitable  traffic,  and  it  would  possibly 
pay  quite  as  large  gross  rates.  The  New  York-Newark  traffic, 
9  miles,  is  far  more  profitable  and  far  larger  in  the  aggregate, 
in  proportion  lo  the  size  of  the  two  places,  than  the  New  York- 
Philadelphia  traffic,  90  miles.  If  Philadelphia  were  as  near  to 
New  York  as  Newark,  both  the  volume  and  the  productive  value 
of  their  interchanged  traffic  would  be  enormously  greater  than  it 
is  now. 

957.  There  are,  of  course,  certain  possible  exceptions  to  this 
general  rule.  The  tonnage  between  the  anthracite-coal  mines 
and  New  York,  for  example,  might  not  be  much  larger  than  it  is 
if  the  haul  were  only  50  miles  instead  of  150,  for  about  so  much 
must  be  had  at  any  cost,  and  more  than  that  is  not  needed.  And 
yet  it  probably  would  be  larger,  both  because  the  more  favorable 
conditions  for  coal  supply  would  have  greatly  stimulated  manu- 
factures, and  so  the  growth  of  population  as  well,  and  because 
the  rates  per  mile  hauled  would  be  higher. 

958.  We  see,  therefore,  the  reasons  why,  assuming  the  points 
^^j^D^^  ^^^^£  A,  B,  C,  Fig.  234,  to  be  of 

^:r:7^^^^^Z^^^^l7:::T:^^^=:r:r::^7l^^^  inherently  equal  traffic- 

FiG.  236.  producing  capacity,  the 

^.C short-haul    traffics,    AC 

ll^J^-^rrrrrrrrrnrrr. ^rr^rrTrirrrrt^:^    and  CB,  should  each  one 

Fig.  234.  of  them  be  of  more  rath- 

er than  less  value  than 

{^^^^^^^-"-^-^^ *^~-^~->__5    the  long-haul  traffic,  ^^; 

^"^^^^^^^ ' """' " .,««..:rn::::7r=^  from   which    it    follows 

Fig.  235. 

that  the  aggregate  of  the 
three  traffics  AB,  AC,  CB,  Fig.  234,  will  be  worth  more  rather 
than  less  than  three  times  as  much  as  the  traffic  AB  alone. 


CHAP.  XXI.— LAW  OF  INCREMENT  OF   TRAFFIC.        J 1 1 


This  being  determined,  let  us  now  extend  the  inquiry  by  de- 
termining, in  the  same 
manner  as  above,  the 
probable  comparative 
traffic  on  five  different 
lines     of   any     common 

length,    Figs,      233-237,  Fi^.  ,3^. 

having  two,   three,  four, 

five,  and  six  traffic  points  on  them,  each  point  being  assumed, 
for  the  sake  of  simplicity,  to  be  of  equal  traffic-producing 
capacity. 

We  then  have, 


Traffic  Units. 

Comparative 
Traffic. 

In  Fig.  233, 

2  trafBc 

points 

^ 

B  only, 

I 

"      234, 

3      " 

it 

AB, 

AC, 

CB, 

3 

"      =35, 

4      " 

ii 

( 

AB, 

AD, 

■  AB, 

AC, 

BD, 

AC, 

CB, 
CD, 

CB, 

.         6 
) 

"      236, 

S      " 

"     \ 

AD, 

BD, 

CD, 

>■        10 

( 

.AE, 

BE, 

CE, 

DE,\ 

* 

'AB, 

AC, 

CB, 

" 

AD, 

BD, 

CD, 

"      237, 

6      « 

«        •< 

AE, 
DE, 

BE, 
AF, 

CE, 
BF, 

'       15 

CF, 

DF, 

EF, 

, 

Comparing  Fig.  233  with  Fig.  237,  by  multiplying  our  traffic 
points  by  three  we  have  multiplied  the  traffic  by  fifteen,  or 
have  increased  the  productiveness  of  each  separate  traffic  point 
five  times. 

959.  This  process,  with  certain  corollaries  which  follow  there- 
from, is  extended  somewhat  further  in  Table  191  and  illustrated 
graphically  in  Fig.  238. 

It  will  be  seen  from  Fig.  238  that  when  on  any  given  line  with 


712 


CHAP.  XXI.— LA  W  OF  INCREMENT  OF   TRAFFIC. 


any  given  number  of  traffic   points  of  equal  weight  on  it,  we 
have — 

No.  of  traffic  points,       2  |     3     |        4         |  ,..n, 

We  have  for  the  com-  )      i      ■      1      ■      <      i      <      ,       .  .  /         \ 

parative  traffic,        ) 

In  other  words,  the  comparative  aggregate  traffic  for  any  num- 
ber of  traffic  points  n  is  given  by  the  sum  of  the  natural  mem- 
bers to  n  —  I  inclusive.  The  sum  of  such  a  series  to  n  inclusive 
is  given  by  the  formula 

_  n{n  -\-  1)  _n^  -\-  n 
2  2     ' 


(i) 


So  that  for  the  aggregate  traffic  T,  due  to 
71  traffic  points,  we  have 


T=  >- i)'  +  (^^-  i)  __  Mn  -  i), 
2  -^        2        ' 

f  being  any  coefficient. 

L 


(2) 


£8 


,AB 


AC 


AD 


/kZ 


AF 


AG 


AH 


Bcf 


BD 


BE 


BF 


BG 


BH 


^7" 
CD 


CE 


DE 


CF 


CG 


CH 


DF 


DG 


DH 


^ 


EG 


EH 


FQ 


FH 


GK 


Fig.  238. — Illustrating  THE  Law  of  Increment  in  Traffic  result^ 

ING   FROM    the    INTERPOLATION   OF  THE   ADDITIONAL   TRAFFIC  PoiNTS 

C,  Z?,  E,  F,  ETC.,  Figs.  233  to  237. 

For  any  larger  number  of  points  N  we  have  similarly 


(3) 


CHAP.  XXL— LA  W  OF  LNCREMENT  OF   TRAFFLC. 


713 


whence  the  ratio  of  increase  is 


T 


N{N-  i) 


n{n-i) ^^ 

As  n  becomes  a  larger  number,  the  ratio oin ton  —  i  becomes 
more  and  more  nearly  unity,  until  finally  the  ratio  of  T^  to  T 
becomes  sensibly 


(5) 


which  is    THE    EQUATION    GIVING    THE    GENERAL    LAW    OF    INCREASE 
IN    EARNINGS   DUE  TOAN    INCREASE    OF    TRIBUTARY    TRAFFIC    POINTS 

ON  THE  SAME  LENGTH  OF  LINE;  i.e.,  the  productive  traffic  varies 
as  the  SQUARE  of  the  number  of  tributary  sources  of  traffic. 


Table  191. 

Showing  the   Effect  upon  Aggregate  Traffic   of   Interpolating 

Additional  Traffic  Points  in  the  Line. 

[See  Figs.  233-238.] 


Per  Cent 

Absolute 

No.  OF 

Traffic 
Points. 

Relative 
Traffic. 

Traffic 
Per  Unit  of 
Population. 

Increase  of 

Traffic 

by  Adding 

One  Traffic 

Point. 

Increase  of 

Traffic 

by  Adding 

One  Traffic 

Point. 

2 

I 

0.5 



.. 

3 

3 

I.O 

200.0 

2 

4 

6 

1-5 

100. 0 

3 

5 

10 

2.0 

66.7 

4 

6 

15 

2.5 

50.0 

5 

7 

21 

3.0 

40.0 

6 

8 

28 

3-5 

33-3 

7 

9 

36 

4.0 

28.6 

8 

10 

45 

4.5 

25.0 

9 

II 

55 

5.0 

22.2 

ID 

12 

66 

5-5 

20.0 

II 

13 

78 

6.0 

18.2 

12 

14 

91 

6.5 

16.7 

13 

15 

105 

7.0 

15.4 

14 

etc. 

etc. 

cts. 

etc. 

etc. 

It  will  be  seen  from  the  last  column  of  this  table  that  the  absohcte  gain  from  a  given 
addition  of  tributary  population  is  greater  in  proportion  to  the  amount  of  other  tributary 
population,  but  that  the  addition /^r  ce?it  is  very  much  greater  on  light-traffic  roads. 


714        CHAP.  XXL— LAW   OF  LNCREMENT   OF   TRAFFLC. 


Table  192. 
Growth  of  New  York  City  Internal  Passenger  Traffic. 

[Compare  tables  noted  below,] 


City  Passenger  Traffic 

Estimated 

(Thousands). 

Per  Inhabitant. 

Ybar. 

and  Actual 

Population. 

Elevated 
Roads. 

Horse 
Cars, 

Total. 

Elevat 

ed.      Horse. 

Total. 

1853 

581. 

None. 

6,836 

II. 8 

II. 8 

54 

605. 

" 

6,817 

II. 3 

II. 3 

1855 

629,810 

<i 

18,488 

29.4 

29.4 

56 

663. 

(( 

23,153 

35.0 

35.0 

57 

698. 

(( 

22,190 

31.9 

31.9 

58 

734. 

(( 

27,900 

38.0 

38.0 

59 

773- 

(( 

32,889 

42.7 

42.7 

i860 

813,669 

(( 

(Same  as 

36,455 

44-7 

44.7 

61 

826. 

(( 

26,272 

31  =  8 

31.8 

62 

838. 

(« 

next 

35,878 

42.8 

42,8 

63 

850. 

(< 

40,412 

47.6 

47.6 

64 

863. 

(( 

column.) 

60,900 

70.6 

70,6 

1865 

876. 

.... 

82,055 

93.8 

93.8 

66 

889. 

.... 

88,953 

100. 0 

100,0 

67 

902. 

.... 

100,542 

III.O 

III.O 

68 

915. 

.... 

105,817 

115,6 

115. 6 

69 

929. 

— 

114,349 

123.5 

123.5 

1870 

942,292 

— 

115,139 

122,0 

122,0 

71 

962. 

.... 

133,894 

139.4 

139.4 

72 

982. 

136 

143,561 

143,697 

0.] 

146,0 

146. 1 

73 

1,003. 

644 

144,715 

145,359 

o.i 

)        144,4 

145.0 

74 

1,024. 

796 

151,131 

151,927 

o.\ 

\       147.8 

148.6 

1875 

1,045,223 

921 

165,997 

166,918 

o.c 

)       158.8 

159.7 

76 

1,076. 

2,013 

166,401 

168,414 

I.C 

)       154.5 

156.4 

77 

1,107. 

3,012 

160,924 

163,936 

2." 

1       135.3 

148.0 

78...... 

1,139. 

9,291 

160,899 

170,190 

8.1 

[        131.0 

149. 1 

79 

1,172. 

46,045 

141,939 

187,984 

39.^ 

\       121. 4 

160.8 

1880 

1,206,299 

60,832 

150,390 

211,222 

50.; 

;       124.7 

175.2 

81 

1,242. 

75.586 

155,801 

231,387 

bo  A 

5       125,4 

186.2 

82 

1,278. 

86,361 

166,511 

252,872 

67. ( 

)       130.8 

198,4 

83 

1,315. 

92,125 

176,625 

268,750 

70.] 

[       134.2 

204,3 

84 

1,354. 

96,703 

187,413 

284,116 

71. i 

)       138.2 

219.7 

1885 

1,393- 

103.355 

193-762 

297,117 

74.' 

2       139.0 

213.2 

In  the  years  1871-72-73,  the  report  of  a  committee  of  the  American  Society  of  Civil 
Engineers  shows  3,000,000  to  5,000,000  more  passengers  per  year  than  above,  probably 
by  inclusion  of  some  omitted  line  above,  but  it  has  not  been  attempted  to  correct  the 
error. 


CHAP.  XXI.— LAW  OF  INCREMENT  OF   TRAFFIC        715 


Summary. 


Popula- 
tion. 

Trips  per  Inhabitant. 

No.  OF  Lines. 

No.  Trips 
per  Inhab't 

Year. 

Horse. 

Elevated. 

Total. 

Horse. 

Elevated. 

per  100,000 
of  Popula- 
tion, 

1853 

1855 

i860 

1865 

1870 

1875 

1880 

1885 

1890 

581. 
630. 
814. 
876. 
942. 

1,045. 
1,206. 

1.393- 

II 

29 
44 
93 
122 
158 
124 
139 

8 
4 
7 
8 
0 
8 

7 
0 

0.9 
50.5 
74-2 

II. 8 

29.4 

44-7 

93-8 

122.0 

159-7 

175-2 

213. 1 

2 

4 
6 
12 
12 
19 
23 
25 

I 
4 
4 

2.03 
4.67 

5-5 
10.7 
I3-0 
15-3 
14-5 
15.4 

Since  1885  a  further  and  great  increase  has  begun,  so  that  there  is  every  prospect  that 
it  will  be  more  notable  in  proportion  than  heretofore. 

While  the  growth  of  city  travel  is  in  some  respects  a  special  problem,  since  its  increase 
results  in  great  part  from  the  increasing  distances  which  larger  population  brings,  yet  it  is 
mainly  but  one  expression  of  a  general  law  brought  out  in  Chap.  XXL,  that  traffic  tends 
to  increase  about  as  the  square  of  the  population  or  sources  of  traffic  united  by  con- 
venient means  of  communication.  Quite  as  forcible  an  illustration  of  this  law  is 
obtained  by  studying  the  growth  of  traffic  of  States  and  the  United  States  as  elsewhere 
presented.     Compare  Tables  14,  15,  16;  also  Tables  2,  3,  7,  21  to  28,  34,  etc. 


960.  It  is  plain  that  we  cannot  always,  nor  ordinarily,  count 
on  any  series  of  points  A,  B,  C,  Z>,  E,  etc.,  each  of  which  is  ex- 
actly equal  to  each  other,  but  we  may  push  the  generalization  a 
little  farther. 

Taking  the  entire  population  of  a  country,  or  of  a  continent, 
or  of  the  world,  and  conceiving  it  to  be  made  up  of  a  great  num- 
ber of  units,  either  of  single  individuals  or  of  groups  of  10,  100, 
1,000,  or  1,000,000  individuals,  it  is  plain  that  each  one  of  these 
units  has  potential  traffic  relations  with  every  other  unit.  The 
components  of  each  unit  visit  those  of  the  other  socially  ;  they 
buy  and  sell  from  each  other  ;  th.ey  visit  each  other  in  the  hope 
of  buying  and  selling  ;  they  produce  more  (this  is  an  invariable 
law)  for  the  especial  purpose  of  supplying  the  necessities  of  others 
with  whom  they  have  or  finally  secure  traffic  relations.  Until 
such  traffic  facilities  exist,  these  relations  are  inchoate,  or  merely 
potential.     As  the  facilities  are  extended  they  become  actual ; 


7l6       CHAP.  XXL— LAW  OF  LNCREMENT  OF   TRAFFLC. 

and  they  should  tend  to  become  actual,  if  our  reasoning  has 
been  correct,  about  in  proportion  to  the  square  of  the  facilities 
afforded  and  of  the  population  served.  Experience  seems  to 
show  that  they  do  tend  to  increase  about  in  this  ratio,  some  evi- 
dence of  which  fact  is  contained  in  Table  192,  as  also  in  Table 
14,  15,  16,  and  others  referred  to  below  Table  192  ;  but  however 
this  may  be,  that  they  increase  in  very  much  more  than  direct 
ratio  is  beyond  all  question. 

It  is  therefore  unnecessary  to  take  each  individual  town  as 
a  traffic  unit,  as  we  have  done  heretofore.  We  may  regard 
each  individual  person  as  the  traffic  unit,  and  while  it  will  be 
by  no  means  literally  true  that  he  will  have  actual  traffic  rela- 
tions with  all  those  for  whom  the  facilities  exist,  but  only  with 
every  tenth,  hundredth,  thousandth,  or  millionth  person,  accord- 
ing to  his  character  and  occupation,  yet  practically  the  result  is 
the  same.  His  aggregate  contributions  to  railway  traffic  will 
vary  in  close  accordance  with  the  total  population  connected  with 
him  by  traffic  facilities,  and  his  payments  to  any  particular  line 
will  be  in  direct  proportion  to  that  fraction  of  the  total  of  the 
whole  population  connected  with  him  by  traffic  facilities  which  is 
reached  by  him  over  that  particular  line. 

961.  We  have  thus  only  to  consider  the  points  A,  B,  C,  D,  E, 
Figs.  233-237,  to  represent  single  individuals  instead  of  towns  or 
other  traffic  points,  and  to  consider  their  number  n  to  be  indefi- 
nitely multiplied,  when  precisely  the  same  process  of  reasoning 
we  have  just  applied  to  towns  leads  to  precisely  the  same  conclu- 
sion as  respects  individuals. 

We  then  have  n{n  —  i)  ^=^7^  [Eqs.  (4)  and  (5)]  almost  exactly; 
whence,  if  Z'  =  the  actual  tributary  population  on  the  line  and 
/  =  a  possible  additional  population,  the  percentage  of  increase 
in  traffic  Z,  all  other  things  being  equal,  will  be, 

^  =  ^^' (6) 

In  other  words,  if  we  have  1,000,000  tributary  population  and 


CHAP.  XXI— LAW  OF  INCREMENT  OF   TRAFFIC        71/ 

can  add  100,000  more,  each  unit  of  which  is  of  the  same  traffic- 
producing  capacity,  the  increase  will  be 

(lO+lV 

■i ~-^  --1  =  21  per  cent. 

10 

If  our  original  population  were  500,000,  we  should  have,  all 
other  things  being  equal, 

(5  +  i)' 

^^   \- I  =  44  per  cent. 

This  is  really  a  more  correct  way  of  arriving  at  the  theoreti- 
cal effect  of  additional  sources  of  traffic  than  that  used  in  Table 
191,  since  it  takes  each  individual  as  the  unit,  instead  of  a  group 
of  20,000  or  100,000.  It  gives  a  somewhat  smaller  percentage,  but 
the  difference  is  not  great  enough  to  make  a  material  difference 
in  what  are  at  best  merely  illustrative  computations  ;  not  sus- 
ceptible, nor  supposed  to  be  susceptible,  of  exact  application  in 
practice,  except  as  indicating  the  comparative  probable  revenue, 
all  other  things  being  equal,  of  alternate  routes  between  the  same 
termini. 

962.  In  any  actual  instance,  of  course,  all  other  things  would 
be  more  or  less  unequal,  and  hardly  any  of  them  equal,  so  that 
it  would  be  quite  impossible  to  make  any  very  precise  estimates 
by  the  formula  given.  In  the  first  place,  it  is  impossible  to  more 
than  guess  at  the  true  tributary  population.  That  which  is  ap- 
parently tributary,  from  being  on  the  line,  is  decreased  by  the 
competition  of  other  lines,  so  that  only  a  fraction  of  it  is  really 
tributary  ;  while,  on  the  other  hand,  there  may  be  an  immense 
population  beyond  the  limits  of  the  line  itself  which  is  indirectly 
tributary  to  it  through  the  medium  of  other  lines,  as  in  the  case 
of  the  trunk  lines  from  the  sea-coast  to  the  west.  In  the  second 
place,  a  mere  enumeration  of  heads  is  a  very  rude  index  of  the 
traffic  value  of  those  heads.  A  great  mining  or  manufacturing 
or  commercial  point  will  contribute  vastly  more  traffic  per  head 
than  other  more  inert  communities,  and  a  large  town,  almost  al- 
ways, more  per  head  than  a  small  town. 


7l8  CHAP.  XXL— TRUNK  LINES. 

963.  Nevertheless,  when  we  connect  Smithville  with  our  line 
we  get  the  New  York- Smithville  as  well  as  the  Smithville- 
New  York  traffic;  and  the  traffic  of  New  York  is  made  up  only  of 
the  aggregate  of  that  to  thousands  of  Smithvilles,  of  which  we 
get  those  which  we  reach  in  one  way  or  another  by  our  line. 
Thus  the  discrepancy  on  account  of  the  difference  in  the  traffic- 
producing  capacity  of  individuals  is  less  than  might  be  supposed, 
and  Tables  14,  15,  16,  and  191,  with  various  others  in  this  volume, 
show  that  the  law  holds  tolerably  well  when  applied  on  a  large 
enough  scale  to  eliminate  sources  of  irregularity,  while  there  are 
innumerable  examples  of  single  lines  whose  prosperity  or  ad- 
versity can  be  directly  shown  to  imply  the  existence  of  some 
such  law. 

These  fundamental  truths  being  granted,  therefore,  it  leads 
very  directly  to  certain  conclusions  as  to  the  proper  manner  of 
laying  out  both  trunk  lines  and  branch  lines  ;  conclusions  which, 
while  they  may  be  difficult  to  apply  so  exactly  as  to  avoid  a  con- 
siderable percentage  of  error,  will  yet  be  so  definite  that  the  radi- 
cal error  of  mistaking  black  for  white,  so  to  speak — taking  that 
for  the  best  course  which  is  rather  the  worst  course, — is  not  likely 
to  occur. 

TRUNK    LINES. 

964.  Trunk  or  main  lines  may  be  roughly  divided  into  two 
classes:  those  which  are,  and  those  which  are  not,  liable  to  be 
subjected  to  close  competition  at  almost  every  important  point. 

Almost  all  lines  in  the  United  States  belong  to  the  former 
class.  Their  only  permanent  protection  against  competition,  in 
most  cases,  is  to  throw  out  a  skirmish-line  of  branches  and  par- 
allel routes  so  as  to  cover  securely  a  considerable  territory;  and 
this  is  one  great  reason  for  the  tendency  in  that  direction  which 
is  so  notable,  and  which  has  already  gone  so  far  that  more  than 
half  the  mileage  of  the  United  States  is  controlled  by  a  dozen 
managements,  with  every  prospect  that  the  tendency  to  consoli- 
dation will  grow  still  stronger.  Table  193  shows  how  far  this 
tendency  has  already  gone.  Another  and  still  stronger  reason, 
however,  directly  results  from  what   has  preceded — that  every 


CHAP.  XXI.  — TRUNK  LINES. 


719 


Table  193. 

Length  of  Road  and  Gross  Earnings  of  Fourteen  Great  Systems  of 
Road  in  the  United  States,  1881. 


[Abstracted  from  a  Paper  by  Wm.  P.  Shinn  on  "  Increased  Efficiency  of  Railways  for 
the  Transportation  of  Freight,"  Trans.  Am.  Soc.  C.  E.,  November,  1882,  with  the  addi- 
tion of  the  Baltimore  &  Ohio,  Atchison,  Topeka  &  Santa  Fe,  and  some  minor  details.] 


Miles. 

Gross  Earnings. 

New  York  Central  &  Hudson  River 

993 

1,177 

403 

950 

3,523 

I,0£0 
3,041 
2,529 

$29,322,532 
17,880,000 
3,369,259 
8,800,486 

Lake  Shore  &  Michieran  Southern  ...    

Michigan  Central 

Total  New  York  Central  System 

SS9,372,277 
20,715,60s 
5^44,224,716 
31,058,790 

New  York.  Lake  £-rie  &^  Westeyn 

"            Western      "      

5,570 

595 
959 

75,283,506 

Baltimore  &  Ohio,  Eastern  System 

"              "       Western      "      , 

Total  Baltimore  &*  Ohio 

1,554 

18,463,877 

Total  Four  Trunk  Lines 

11,667 
12.35  P-c. 

_      ,      $173,835,265 
Per  Mile  $14,900 
23.97  p.  c. 

Per  cent  of  total  United  States 

Wabash,  St.  Louis  &  Pacific  

3,348 
3,160 

1,335 
1,320 

"^       0 
1,891 

3,276 
4,260 

1,012 

4,773 

$14,467,790 
21,176,455 
11,956,907 

Chicago,  Burlington  &  Quincy 

Chicago,  Rock  Island  &  Pacific 

New  Orleans  line 

Chicago  &  North- Western 

10,793,105 
19,334,072 

*o  ^               17,025,461 

^,640,957 

19,087,484 

Chicago,  Milwaukee  &  St.  Paul         

Leased  and  controlled  lines 

1,438  ) 
434) 
272 

27,^^8,441 

Leased  lines 

$10,911,650 

1,196,112 
2,256,186 
2,543,032 

Georgia  Railroad  System 

Atchison,  Topeka  &  Santa  F^ 

2,240 
1,821 
2,449 

4,270 
2,874 
1,281 

4,155 

12,584,509 

$24,258,817 
7,608,936 

Union  Pacific,  Proper  ...   

Lines  in  interest 

Central  Pacific ...'.   

31,867,753 
$24,094,101 
3,435,945 

Southern  Pacific 

27,530,046 

Total  Ten  Systems  other  than  N.Y.Trunk  Lines. 
Per  cent  of  total  United  States 

36,754 
38.90  p.  c. 

$211,371,519 
Per  Mile  $5,751 
29.14  p.  c. 

720 


CHAP.   XXI.— TRUNK  LINES. 


Table  193. — Continued. 

Miles. 

Gross  Earnings. 

48,421 
51.25  p.  c. 

$385,206,784 

Per  Mile  $7,956 
53.  II  p.  c. 

Total  of  Minor  Lines  of  the  United  States,  under 

46,065 
48.75  p.  c. 

$340,118,335 

Per  Mile  $7,383 
46.89  p.  c. 

Total  of  the  United  States  in  1881,  of  which  earn- 

94,486 

$725,325,119 

Per  Mile  $7,677 

Since  1881  there  have  been  many  changes  in  the  details  of  the  above  table,  but  the 
great  systems  given  probably  cover  in  the  aggregate  a  still  larger  proportion  of  the  total 
mileage  of  the  United  States.  There  were  in  1881  a  total  of  104,813  miles  reported  built, 
10,327  miles  of  which  did  not  report  earnings,  being  largely  newly  built  lines. 


addition  to  the  tributary  population  makes  the  revenue  per  head 
from  the  previously  tributary  population  greater.  This  may  not 
often,  perhaps  never,  be  more  than  dimly  felt,  but  that  it  is  the 
true  course  and  justification  for  many  such  extensions  we  cannot 
doubt. 

Nevertheless  there  are  certain  mountainous  or  sparsely  popu- 
lated and  poor  regions,  in  this  and  all  other  countries,  where 
reasonable  freedom  from  competitive  lines  is  assured,  as  in 
Mexico,  the  lines  in  which  afforded  some  instructive  examples  of 
the  right  and  wrong  way  of  laying  out  main  lines. 

965.  Bearing  in  mind  what  we  have  already  seen  as  to  the 
small  expense  of  operating  extra  distance  (par.  197),  the  appreci- 
able additions  to  revenue  which  may  be  expected  to  arise  from 
it  (par.  230),  and  the  small  effect  of  moderate  additions  of  dis- 
tance to  discourage  traffic,  there  can  be  no  question  that  the 
fundamental  rule  for  laying  out  such  lines — deviated  from  only 
for  good  special  reasons — should  be  to  link  together  the  largest 
possible  population,  regardless  of  minor  losses  of  distance,  pro- 
vided    THE    AGGREGATE     POPULATION    PER    MILE    OF    ROAD    is    UOt 

diminished  (par.  237),  or  even  sometimes  if  it  is.     An  ultimate 


CHAP.  XXI.— TRUNK  LINES.  721 

limit,  beyond  which  it  would  certainly  be  unwise  to  go,  and 
hence  which  should  not  be  closely  approached,  is  that  the  in- 
crease per  cent  of  distance  should  not  exceed  the  increase  per 
cent  of  probable  revenue,  according  to  eq.  (6),  par.  961. 

966.  The  most  marked  exception  to  this  rule  is  when  the  dif- 
ference of  distance  becomes  so  great  as  to  seriously  discourage 
traffic,  or  encourage  the  construction  of  a  more  favorably  situ- 
ated competing  line. 

A  further  exception  is  when,  by  passing  midway  between  two 
traffic  centres,  neither  of  which  can  be  reached  readily  by  the 
main  line,  both  may  be  served  fairly  well  by  branches  or  other- 
wise (par.  66). 

Any  marked  difference  in  grades  or  costs  of  construction  may 
of  course  make  a  difference  either  pro  or  con  j  but  entire  disre- 
gard of  the  rule,  by  deliberately  neglecting  intermediate  traffic 
points  for  the  sake  of  through  traffic,  usually  means  financial 
failure. 

967.  Several  instances  of  the  application  of  these  general  rules  may 
be  studied  on  any  map  of  Mexico,  showing  the  existing  railway  lines. 
The  most  pronounced  is  the  choice  between  the  route  from  the  City  of 
Mexico  to  the  United  States  {via  the  Mexican  Central  or  the  Mexico 
National  routes),  either  of  which  could  be  chosen  by  the  Central  at  the 
time  the  concessions  were  granted. 

The  longer  line,  passing  through  the  heart  of  Mexico,  and  thence  con- 
necting at  El  Paso  with  the  Atchison,  Topeka  &  Santa  Fe,  was  chosen. 
The  grounds  for  this  choice,  beyond  question,  were  that  (i)  railways  in 
Mexico  were  to  be  profitable  ;  (2)  the  more  railway  controlled  the  more 
aggregate  profit,  even  if  the  less  per  mile ;  (3)  a  long  line  through  the 
heart  of  a  country  must  in  the  long-run  be  the  best  line. 

On  the  other  hand,  the  choice  violated  two  of  the  fundamental  rules 
which  have  been  laid  down.  First,  it  seriously  discouraged  traffic  be- 
tween Mexico  and  the  United  States  by  burdening  that  which  passed 
over  it  with  nearly  500  miles  of  extra  haul :  this  practically  insuring  that 
the  National  line,  when  completed,  would  be,  or  might  easily  make 
itself,  the  leading  through  line.  Secondly,  it  very  materially  decreased 
the  average  tributary  population  per  mile  over  what  it  would  have  been 
had  the  Mexican  Central  line  been  followed  as  far  as  Celaya,  in  Central 
Mexico,  and  the  Mexican  National  from  there  north  ;  especially  had  the 
46 


722  CHAP.   XXI.— TRUNK  LINES. 

towns  of  Silao,  Guanajuato,  and  Leon  been  linked  to  this  main  line  by  a 
branch,  as  they  might  have  been  later. 

Had  the  Mexican  Central  been  built  by  this  line  there  can  be  little 
doubt  that  it  would  be  to-day  (1886)  a  most  flourishing  property,  both 
because  its  investment  would  have  been  smaller  and  its  traffic  larger. 

968.  On  the  other  hand,  leaving  the  flourishing  town  of  Durango  on 
one  side,  although  it  saved  distance  in  what  was  already  a  disastrously 
long  line,  was  probably  an  error,  although  this  cannot  be  asserted  with 
mucii  positiveness.  The  loss  of  perhaps  50  or  60  miles  more  would  have 
taken  the  line  through  a  much  better  country,  actual  and  prospective, 
for  nearly  400  miles,  the  country  through  which  the  line  was  actually 
run  having  been  almost  the  poorest  possible ;  while  saving  that  loss  of 
distance  did  not  materially  improve  its  already  bad  case  as  respects 
through  traffic. 

969.  The  National,  for  its  part,  fell  into  an  error  which  has  often 
been  committed  before,  and  never  without  loss — attempting  to  start  a 
new  terminal  port  at  Corpus  Christi,  instead  of  making  for  Galveston 
direct.  Such  projects  for  changing  the  established  course  of  trade  seem 
to  have  a  peculiar  fascination  for  sanguine  projectors,  but  it  is  always  all 
but  certain  that  they  will  end  in  failure. 

The  more  instructive  example  to  be  found  on  the  National  lines,  how- 
ever is  a  striking  instance  of  how,  when  traffic  is  at  best  thin  and  prob- 
ably non-competitive,  connecting  the  'largest  possible  population  by  the 
main  line  is  almost  surely  the  wiser  course.  Fig.  239  shows  this  instance, 
the  dotted  line  being  what  had  been  projected,  and  the  full  line  the  route 
finally  chosen  by  the  company  on  the  writer's  recommendation. 

The  full  line  seems  a  most  roundabout  course  for  a  main  line,  espe- 
cially as  the  total  mileage  to  be  constructed  was  not  diminished,  but 
rather  increased.  It  was  to  be  remembered,  however,  first,  that  the 
traffic  was  thin  and  non-competitive;  secondly,  that  the  number  of  trains 
could  not  be  great ;  thirdly,  that  reasonably  good  facilities  for  continu- 
ous traffic  between  every  one  of  the  many  points  connected  by  the  line 
was  desirable ;  and,  finally,  that  with  a  traffic  thin  at  best  the  mainte- 
nance and  separate  operation  of  branch  lines  is  very  burdensome.  It  was 
therefore  decided,  as  respects  the  line  from  Morelia  to  Zamora  and  La 
Piedad,  that  it  would  be  better  to  make  the  branch  to  Patzcuaro  a  part 
of  the  main  line,  thus  accomplishing  the  double  end  of  decreasing  the 
aggregate  mileage  to  be  operated  and  maintained,  and  facilitating  Patz- 
cuaro-Zamora  traffic  and  (by  more  trains)  Patzcuaro-Morelia  traffic, 
while  gaining  more  revenue  from  through  traffic  by  not  materially 
heavier  through  rates. 


CHAP.  XXI.— TRUNK  LINES. 


723 


970.  Beyond  La  Barca,  although  the  line  had  already  been  run  out 
of  its  course  from  Patzcuaro  to  the  Pacific,  it  was  decided  to  run  it  still 
farther  north  to  take  in  the  important  city  of  Guadalajara,  the  second 
city  in  Mexico  (about  80,000  inhabitants),  whence  the  line  started  almost 
due  south  for  Colima  and  the  coasts.  This  change  alone  much  more 
than  doubled  the  probable  traffic  per  mile  of  the  road,  and  it  would  have 
been,  from  an  economic  point  of  view,  a  very  great  error  not  to  do  it. 


Fig.  239. 

It  in  effect  cut  the  line  into  two— one  from  Guadalajara  to  the  coast,  and 
one  from  Guadalajara  to  Mexico  ;  but  all  the  more  it  was  desirable.  The 
sharply  accentuated  topographical  conditions,  which  it  is  impossible  to 
describe  with  more  detail,  made  this  particularly  clear. 

971.  Trunk  lines  open  to  destructive  competition,  and  able 
to  command  only  a  narrow  belt  on  each  side  of  them  as  their 
natural  tributary  territory,  nor  that,  unless  they  afford  almost  as 
good  accommodations  as  it  is   possible  to   give,  can   of  course 


724  CHAP.  XXI,— TRUNK  LINES. 

afford  no  such  sacrifice  as  this.  As  the  subject  is  a  large  and 
complex  one,  the  conditions  of  success  and  failure  may  perhaps 
be  more  usefully  indicated  in  a  small,  space  by  a  few  notes  from 
the  history  of  the  actual  trunk  lines,  and  notably  of  the  four 
trunk  lines/<2r  excellence — the  New  York  Central  &  Hudson  River, 
Erie,  Pennsylvania,  and  Baltimore  &  Ohio — than  by  a  more  gen- 
eral discussion. 

972.  The  New  York  Central  is  probably  the  most  striking  example  in 
the  whole  world  of  two  truths :  That  lines  connecting  the  largest  aggre- 
gate of  population  will  be  likely  to  lie  on  the  most  favorable  route  for  easy 
grades,  and  that  easy  grades  give  an  overwhelming  advantage  in  handling 
low-rate  traffic  especially.  As  a  through  line  the  New  York  Central  was 
not  made, — it  grew.  Some  fifteen  different  corporations  built  its  New 
York-Chicago  line,  each  without  a  thought  of  doing  more  than  connect- 
ing its  own  particular  termini.  Consequently  it  did  connect  them  effec- 
tually, and  the  magnificent  string  of  towns  from  which  the  New  York 
Central  has  drawn  its  chief  prosperity  was  the  result. 

Its  intended  rival,  the  West  Shore,  was  built  in  a  very  different  way. 
It  was — unfortunately — planned.  From  attaching  exaggerated  impor- 
tance to  through  traffic  and  to  the  effect  thereon  of  accommodating  way 
traffic,  or  from  other  cause,  several  of  the  most  important  local  points, 
as  notably  Albany  and  Rochester,  were  left  at  one  side,  and  others 
ill  served,  there  being  hardly  a  competitive  point  on  the  line,  not  even 
its  two  termini,  as  well  served  by  it  as  by  the  Central.  This  may  have 
been  unavoidable.  The  expense  alone  of  doing  otherwise  would  have 
been  enormous,  and  had  the  expense  been  incurred  it  might  not  have 
insured  the  success  of  the  line ;  but  the  fact  that  it  was  not,  foredoomed 
failure — for  the  two  reasons,  that  the  line  which  is  only  half  as  convenient 
as  another  does  not,  therefore,  get  half  as  much  business,  but  none  at  all 
(par.  51  <?/  al.)\  and  for  the  further  reason  (par.  959),  that  the  value  of  a 
line  is  as  the  SQUARE  of  the  population  best  served  by  it. 

973.  From  the  through  business  proper  the  New  York  Central  has 
derived  comparatively  little  benefit.  Its  greater  length  reduces  its  aver- 
age receipts  per  mile  on  competitive  traffic  materially  below  those  of  the 
Pennsylvania,  and  the  magnificent  water-way  which  is  immediately  adja- 
cent to  it  for  the  entire  distance  from  New  York  to  Chicago  has  tended 
powerfully  to  still  further  curtail  its  rates.  But  its  unequalled  grades  (by 
much  the  most  favorable  in  the  world  for  a  line  of  such  length),  and  the 


CHAP.  XXI.— TRUNK  LINES.  72$ 

indirect  benefit  of  its  immense  local  traffic,  which  alone  required  and 
supported  all  the  staff  and  plant  of  a  great  railway,  enabled  its  through 
business,  vast  as  it  was,  to  be  handled  as  so  much  extra  business,  the  only- 
expense  for  which  was  the  direct  outlay  for  wages  and  fuel  and  a  small 
amount  for  wear  and  tear  of  track. 

Of  no  other  trunk  line  was  this  so  nearly  true,  but  the  lower  rate  per 
mile,  and  high  cost  for  fuel  and  (comparatively)  raw  material  on  the  New 
York  Central,  has  united  to  produce  one  result  which  is  not  always  under- 
stood: The  per  cent  of  operating  expenses  to  receipts  is  and  has  always 
been  high  on  it,  as  shown  more  clearly  in  Table  yj,  page  no,  viz.: 

, Average , 

1876-80.  1881-85. 

New  York  Central, 61.3  67.9 

Erie - 70.0  69.7 

Pennsylvania, 55.7  58.3 

Baltimore  &  Ohio, 53.9  56.0 

This  contrast  is  immutably  fixed  by  the  nature  of  the  traffic  and  the 
operating  conditions,  and  gives  no  indication  of  relative  efficiency  of 
operation,  as  has  often  been  carelessly  assumed. 

974.  The  increase  in  the  percentage  of  operating  expenses  which  is  visible 
above  in  the  figures  for  every  one  of  the  three  lines  but  the  Erie,  is  due  simply 
to  the  enormous  reduction  in  rates  in  recent  years,  the  latter  being  at  once  a 
cause  and  effect  of  the  still  more  enormous  increase  in  volume  of  traffic.  The 
astounding  and  almost  incredible  figures  for  this  change  are  shown  in  Table  194, 
and  graphically  in  Fig.  240.  The  history  of  the  world  affords  no  parallel  to  it, 
and  it  is  one  of  the  strongest  proofs  that  we  have  not  erred  far  in  our  conclu- 
sions in  the  first  part  of  this  chapter. 

975,  The  Pennsylvania  is  in  many  respects  a  contrast  to  the  New 
York  Central.  Like  the  latter,  it  grew,  rather  than  was  made,  as  a  New 
York  and  continental  trunk  line.  Projected  to  bring  traffic  from  the 
West  to  Philadelphia  only,  it  chanced  to  lie  in  the  most  favorable  posi- 
tion for  a  short  low-grade  line  between  New  York  and  the  West.  The 
irresistible  tendency  of  events,  and  of  its  situation,  linked  with  it  a  Penn- 
sylvania-New York  line  on  the  East,  and  a  branching  network  of  lines 
through  the  West.  In  comparing  it  with  the  New  York  Central  one  is 
immediately  struck  by  the  contrast  in  this  respect  which  its  policy 
affords ,  and  while  much  of  this  may  well  be  due,  and  no  doubt  is,  to  a 
difference  in  the  "  personal  equation"  of  the  managers,  an  underlying  rea- 
son for  it — of  which,  perhaps,  no  one  was  conscious — is  that  the  Pennsyl- 


726 


CHAP.  XXL— TRUNK  LINES. 


Table  194. 

Increase  of   Traffic  and   Decrease  in  Rates  on  Various  Groups  of 
American  Lines,  1865-1885. 

[The  last  part  of  this  table  is  shown  graphically  in  Fig.  240.] 


Seven  Trunk 
Lines. 

Six  Chicago 
Roads. 

Twenty-one  Leading  Lines. 

Year. 

Ton- 
miles. 

(i  = 
1,000,000.) 

Rate. 
Cents. 

Ton- 
miles, 
(i  = 
1,000,000.) 

Rate. 
Cents. 

1  =  1,000,000. 

Freight 

Earnings. 

(1  = 

$1000.) 

Rate. 
Cents. 

Tons. 

Ton- 
miles. 

1865 . . . 

1,654 

2 

900 

~546~  1 
306 

951 
715 

513 

3.642 

22 

2,370 

$69,825 

2-945 

1866... 
1867... 

1868... 
1869... 

2,044 
2,258 

2,651 
3,159 

2 
2 

577 
768 

893 
1,054 

3-459 
3-175 

3-154 
3.026 

28 
30 

35 
39 

2,981 
3,222 

41408 

77,003 
75,381 

80,141 
87.426 

2.582 
2.338 
2.140 
1.983 

1870  . . 

3,744 

585 

1,234 

2.423 

39 

5,111 

88.488 

I -731 

1871... 
1872... 

1873... 
1874... 

4,341 
5,181 

5,782 
5,879 

478 
475 
470 
342 

1,233 
1,337 

1,749 
1,851 

2.509 
2.582 

2.188 
2.160 

50 
59 

65 

5,937 
6,972 

7,885 
8,020 

97,186 
112,408 

127,045 
108,598 

1.636 
1. 612 

1.611 
1-354 

1875- •- 

5-937 

161 

1,904 

1.979 

63 

8,380 

107,657 

1.284 

1876... 
1877... 
1878... 
1879  -• 

6,739 
6,536 

8,853 

I0,t20 

983 
971 

807 

725 

1,994 
2,211 

2,822 
3,470 

1.877 
1.664 

1.476 
1.280 

69 
73 

9,072 
9,131 

10,433 
13,033 

102,009 
100,804 

105,973 
114,255 

1.124 
1.103 

1.015 

0.876 

1880  .. 

10,544 

840 

4,544 

1.266 

106 

14.085 

139,331 

0.988 

1881... 
1882... 

1883... 
1884.  - 

ii,6S9 
11,189 

11,141 
10,719 

665 

842 
740 

4,435 
5,041 
5,768 
5,940 

1.420 
1-364 
1.308 
1.251 

126 
134 
142 
144 

16,074 
16,075 

17,307 
17,501 

146,699 
147,719 
167,564 

153,735 

0.912 
0.918 

0.968 
0.878 

1885... 

11,331 

636 

6,287 

1.200 

151 

18,837 

144,562 

0.767 

This  table  is  from  data  compiled  by  Mr.  Henry  V.  Poor.  The  seven  trunk  lines  are 
the  Pennsylvania ;  Pittsburg,  Fort  Wayne  &  Chicago  ;  New  York  Central ;  Lake  Shore; 
Michigan  Central ;  Boston  &  Albany ;  and  New  York,  Lake  Erie  &  Western.  The  six 
Chicago  lines  are  the  Illinois  Central ;  Chicago  &  Alton ;  Chicago  &  Rock  Island ; 
Chicago,  Burlington  &  Quincy ;  Chicago  &  Northwestern ;  Chicago,  Milwaukee  &  St. 
Paul. 

These  thirteen  roads,  with  eight  others  of  most  prominence,  are  included  in  the  last 
part  of  the  table,  from  which  Fig.  240  was  constructed. 


vania  had  more  to  gain  by  extending  itself  in  all  directions,  and  more  to 
lose  by  not  doing  so.  Additional  traffic  we  have  seen  (par.  41)  to  be 
that  on  which  railways  grow  rich.  With  the  greatest  city  of  the  country 
only  ninety  miles  off,  it  was  indispensable,  to  secure  the  utmost  traffic 
from  it,  to  reach  it  by  its  own  lines,  even  with  a  friendly  independent 
connection  as  an  alternative.     The  futility  of  terminating  a  line  at  any 


CHAP.  XXI.  — TRUNK  LINES. 


727 


other  than  the  largest  available  city  was  never  better  illustrated,  unless 
by  the  experience  of  the  Erie  at  Dunkirk  on  a  smaller  scale.     Perhaps 


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Fig.  241  is  as  good  an  object-lesson  as  could  be  found  as  to  the  folly  of 
such  attempts,  even  when  circumstances  seem  to  especially  favor  what 
sanguine  projectors  look  on  as  a  "  fair  divide"  of  an  enormous  traffic. 


728 


CHAP.  XXI.— TRUNK  LINES. 


976.  A  larger  reason,  which  includes  the  first,  was  that  the  Pennsyl- 
vania was  so  situated 
as  to  form  a  very  short 
line  between  almost  all 
points  on  the  West  and 
the  sea-coast.  This  in- 
sured good  average  rates 
per  mile,  while  the  abun- 
dance of  coal  and  iron 
on  the  line,  and  the 
large  amount  of  favor- 
able grades  insured  low 
operating  expenses.  The 
Pennsylvania  had  much 
to  gain,  therefore,  from 
handling  additional 
through  traffic  over  its 
OWN  LINES,  according 
to  the  law  laid  down  in 
par.  211 — that  the  only 
conditions  under  which 
a  line  could  reap  the 
full  benefit  of  being  a 
short  line  was  that  it 
should  reach  all  its  im- 
portant traffic  points  by 
its  own  lines.  The  Penn- 
sylvania was  such  a  short 
line ;  it  proceeded  to 
satisfy  the  other  half  of 
the  true,  and  too  little 

Fig.  241.— Northwestern  Grain  Receipts  AT  Various  LEAD- ••,      ^j,         ^^^jv^ 

^  iNG  Shipping  Points,  1876-1885.  considered,       conditions 

[One  of  many  illustrations  of  the  persistency  with  which  Of  prosperity,  aS  it  Was 
traffic  flows  to  leading  and  well-established  centres,  as  com-  :^„  noi-n-t-ol  -rsi^Wc-ir  \r\  Ar\ 
pared  with  the  irregularity  and  uncertainty  of  traffic  at  minor    ^^^   natural   policy  LO  UO. 

points.]  Until  it  did   so   it  was, 

by  its  existence  and  facilities,  making  the  fortunes  of  other  lines  in- 
stead of  its  own. 

Moreover,  the  additional  through  traffic,  which  it  could  secure  by 
controlling  its  connections,  was  a  great  object  to  it,  for  it  made,  and 
must  always  continue  to  make,  a  comparatively  large  profit  on  it,  while 


CHAP.  XXI.— TRUNK  LINES.  729 

to  the  New  York  Central  it  was  a  small  object,  because  it  made  a  small 
profit  out  of  it.  The  New  York  Central's  chief  reliance  has  been  on  its 
local  traffic ;  its  through  rates  per  mile  being  necessarily  low  at  best, 
even  on  that  traffic  so  situated  as  to  come  to  it  most  naturally,  while  its 
expenses  were  higher  because  of  dear  fuel.  Had  it  gone  much  out  of 
its  way  to  seek  more  through  traffic,  its  average  rates  per  mile  would  have 
been  lower  yet,  and  unremunerative.     Therefore  it  has  not  done  so. 

977.  In  part,  this  likewise  explains  why  the  unfortunate  Erie  has 
never  tended  to  ramify  throughout  the  West ;  but  the  Erie  is  an  example  of 
a  line  which  has  succeeded  in  spite  of  this  disadvantage,  for  four  reasons  : 

1.  By  terminating  at  the  greatest  city  of  the  East,  and  (after  correct- 
ing the  error  of  attempting  to  make  a  new  great  city  at  Dunkirk)  at  the 
chief  traffic  point  at  the  eastern  end  of  the  great  lakes,  making  two  ad- 
mirable termini. 

2.  By  its  skilful  location,  most  of  its  line  being  on  very  low  grades 
indeed,  although  it  has  some  high  summits  and  bad  sections. 

3.  By  its  local  coal  traffic  and  cheap  supply  of  fuel. 

4.  By  its  large  and  growing  local  traffic — less  than  the  New  York  Cen- 
tral's, but  larger  than  the  Pennsylvania's,  and  until  very  recently  little 
subject  to  competition. 

These  gave  it  great  powers  of  offence  against  the  New  York  Central, 
and  it  has  been  able  to  command  at  all  times  a  fair  proportion  of  the 
traffic  which  lines  in  the  Central  interest  brought  to  Buffalo.  But  the 
Erie's  prosperity  has  been  injured  by  three  causes  quite  as  potent : 

I.  Of  all  the  great  Eastern  cities,  the  Erie  reached  advantageously 
only  ONE,  whereas  the  New  York  Central  reached  two.  New  York  and 
Boston  (in  fact,  all  New  England  and  a  large  part  of  the  Canada  trade 
has  been  almost  monopolized  by  the  Central),  and  the  Pennsylvania 
reached  four  ;  the  two  greatest  directly,  New  York  and  Philadelphia, 
and  Boston,  Baltimore,  and  Washington  fairly  well.  This  has  been  the 
primary  difficulty  with  the  Erie.  "  To  him  that  hath  shall  be  given."  It 
might  pay  the  Pennsylvania  well  to  control  a  line  to  Smithville  in  order 
to  secure  thereby  its  traffic  with  the  whole  Atlantic  coast,  when  it  would 
not  pay  the  Erie  at  all  to  own  a  line  to  it  which  would  secure  only  its  New 
York  business.  "  Whosoever  hath  not,  from  him  shall  be  taken  away 
even  that  he  hath." 

The  Smithville-Pittsburg  traffic,  the  Smithville-Boston  traffic,  and  the 
Smithville-Jonesburg  traffic  naturally  gravitated  to  the  line  which  com- 
manded its  other  traffic  East ;  and  so  the  owners  of  lines  in  the  West 
were  naturally  drawn  most  to  that  line  which  offered  the  most  widely 


730  CHAP.  XXI.— TRUNK  LINES. 

ramifying  connections,  and  could  both  give  and  ask  better  terms.  Hence 
it  has  happened — 

2,  The  Erie  has  never  been  able  to  secure  good  Western  connec- 
tions. The  only  serious  attempt  in  that  line,  until  1881,  was  the  old  At- 
lantic &  Great  Western,  one  of  the  most  ill-judged  enterprises  which  has 
ever  been  constructed  in  this  country,  whose  failure  was  foredoomed  from 
the  beginning,  as  pointed  out  in  par.  215  et  seq.  We  may  be  tolerably  as- 
sured that  the  Erie  never  will  have  a  great  system  of  connecting  lines, 
for  it  is  not  planned  to  secure  them.  In  this  respect  the  history  of  the 
road  is  full  of  instruction. 

3.  The  Erie  has  been  peculiarly  unfortunate  in  its  past  management — 
in  part  from  lack  of  comprehension  by  its  foreign  owners  of  its  necessi- 
ties and  conditions. 

978.  The  Baltimore  &  Ohio  is  somewhat  of  a  contrary  example — 
of  a  line  whose  judicious  and  consistent  management  has  given  great 
financial  strength  to  a  property  under  many  disadvantages.  It  has 
obeyed  the  irresistible  tendency  of  the  times  by  extending  its  lines  to 
Chicago  in  the  West  (as  well  as  to  the  Ohio  River  tier  of  cities)  and  to 
Philadelphia  and  New  York  on  the  East.  The  effect  of  the  latter  it  is 
as  yet  (1886)  impossible  to  foresee;  but  unless  the  laws  of  railway  pros- 
perity which  prevail  elsewhere  are  to  fail  in  its  case,  it  will  result  in  a 
very  great  addition  to  its  traffic,  giving  it  what  it  has  never  had  before — 
what  may  be  called  a  continental  traffic. 

For  the  Baltimore  &  Ohio,  as  it  stood  up  to  about  1880,  was  merely 
an  example  of  the  financial  strength  which  may  be  secured  by  locating 
between  considerable  local  sources  of  natural  traffic,  and  holding  strictly 
to  them.  Between  Baltimore  and  Washington  on  the  East  and  Pitts- 
burg, Cincinnati,  Louisville,  and  St.  Louis  on  the  West,  the  Baltimore  & 
Ohio  was  the  natural  channel  of  communication,  and  as  good  a  one  as 
could  be  secured.  A  large  coal  traffic  was  also  assured  to  it.  On  this  it 
prospered,  avoiding  dissipation  of  its  means  on  many  branches  and  con- 
nections. Nevertheless,  it  was  economically  impossible  that  it  should  fail 
for  long  to  reach  out  to  the  other  large  cities  mentioned,  and  to  transfer 
itself  from  a  local  line  to  a  national  one. 

Had  the  Pennsylvania  chosen  to  restrict  itself  to  its  main  line  between 
Pittsburg  and  Philadelphia,  with  a  few  only  of  the  most  necessary 
branches,  it  also  would  have  been,  and  might  have  indefinitely  continued 
to  be,  a  prosperous  local  line  of  the  kind  that  the  Baltimore  &  Ohio  was. 
It  might  even  have  earned  as  good  or  better  dividends  than  now,  but  its 
cost  and  value,  and  its  earning  capacity  likewise,  would  have  been  far 


CHAP.  XXI— BRANCH  LINES.  73 1 

less,  and  its  aggregate  profits  vastly  less.     It  was  therefore  not  to  be  ex- 
pected, nor  for  the  public  interest,  that  it  should  pursue  this  policy. 

979.  In  the  history  of  these  four  trunk  lines,  could  we  afford 
space  to  consider  it  in  detail,  we  have  warning  of  almost  every 
possible  danger  which  can  arise  in  the  laying  out  of  trunk  lines 
— meaning  by  the  latter  term  not  necessarily  lines  of  enormous 
traffic  (see  par.  981),  but  lines  the  main  part  of  whose  traffic  is. 
complete  in  itself,  so  that  they  are  not  mere  branches  or  feeders 
of  other  lines.  We  may  summarize  a  few  of  the  more  important 
conditions  of  success  in  such  lines  as  follows: 

1.  They  must  reach  by  their  own  lines  the  largest  traffic 
point  at  each  end  which  is  at  all  within  reach  by  an  extension  of 
20  or  30  per  cent  of  their  length,  and  there  must  stand  on  equal 
terms  with  their  connections  as  respects  benefits  and  injuries  to 
be  given  and  received.  Failing  to  do  this  is  pretty  sure  to  result 
in  great  loss,  and  generally  in  insolvency. 

2.  They  must  reach  without  fail  every  considerable  inter- 
mediate traffic  point  along  their  line  which  can  be  reached  by 
any  reasonable  detour  or  even  sacrifice  of  grades,  their  prosper- 
ity being  about  as  the  square  of  the  tributary  population. 

3.  They  can  in  no  case  attempt  to  create  new  channels  of 
trade,  as  by  attempting  to  make  a  seaport  out  of  some  neglected 
roadstead,  without  the  greatest  risk  of  failure.  The  attempts  in 
this  direction  have  been  many  ;   the  successes  as  yet  none. 

4.  Nearly  or  quite  half  of  their  traffic  must  practically  begin 
and  end  on  their  own  lines,  either  because  it  goes  no  farther,  or 
because  it  is  delivered  at  some  great  competitive  distributing 
point. 

5.  It  is  of  little  avail  to  run  a  line  even  from  a  great  city  to 
nowhere.  The  apex  to  the  pyramid  in  Fig.  238  is  eloquent  and 
truthful  in  this  respect.  Without  a  good  traffic-point  at  each 
end  of  a  line  the  conditions. for  great  prosperity  are  not  present. 

BRANCH    LINES. 

980.  That  branches  are  in  the  main  profitable  investments  is 
evident  from  their  very  rapid  rate  of  increase,  which  is  largest, 


732  CHAP.  XXI.— BRANCH  LINES. 

up  to  a  certain  point  at  least,  on  the  most  prosperous  lines.  That 
they  are  rarely  very  profitable  when  considered  by  themselves, 
and  apart  from  the  main  line,  and  as  a  rule  do  little  more  than 
pay  operating  expenses,  is  abundantly  shown  by  the  reports  of 
almost  every  line  which  has  branches  and  reports  their  traffic  in 
detail.  This  fact  is  so  clear  and  so  generally  admitted,  that  it 
hardly  needs  statistics  to  prove  it.  As  a  rule,  the  earnings  per 
mile  of  branches  range  only  from  a  fifth  to  a  tenth  of  the 
earnings  of  the  main  stems. 

981.  The  only  considerable  exceptions  to  this  rule  are  branches 
which  are  in  reality  main  lines,  having  a  very  considerable  traf- 
fic which  is  complete  in  itself.  A  striking  example  of  this  kind 
of  branch  is  what  is  known  as  the  Mahoning  Division  or  Cleve° 
land  Branch  of  the  New  York,  Pennsylvania  &  Ohio  Railroad, 
which  runs  diagonally  across  the  main  line  from  Cleveland  to 
Youngstown.  This  nominal  ''branch"  was  really  a  subordinate 
main  line,  built  by  a  separate  company  and  projected  on  rational 
principles,  according  to  par.  979.  It  had  and  has  a  very  consider- 
able traffic,  both  freight  and  passenger,  which  is  complete  in 
itself.  On  the  other  hand,  the  nominal  "main  line"  is  in  reality 
a  mere  branch,  violating  conspicuously  every  one  of  the  condi- 
tions for  the  success  of  main  lines  specified  in  par.  979.  It  is 
not  surprising,  therefore,  that  the  "  main  line"  was  a  financial 
failure  and  the  "  branch"  a  financial  success,  which  has  largely 
helped  to  support  the  main  line  even  after  paying  a  very  heavy 
rental  (10  per  cent  dividends  per  annum)  to  the  lessor  company. 

982.  The  reason  for  the  continued  and  rapid  building  of 
branches  in  spite  of  their  apparent  unproductiveness  is  simply 
this  :  They  contribute  traffic  to  the  main  line  which,  as  it  is 
merely  an  increment,  costs  always  comparatively  little  to  move, 
and  often  nothing  at  all.  The  company,  therefore,  receives  from 
its  contributed  traffic  rates  for  a  haul  of  perhaps  500  miles  at  a 
cost  for  hauling  due  to  only  100  or  200  miles.  This  follows 
directly  from  what  we  have  seen  in  Chapter  XV.,  par.  181,  and 
elsewhere.  Rudely  speaking,  if  we  call  the  average  cost  per  ton 
or  passenger-mile  100,  we  may  say  : 


CHAP.  XXL— BRANCH  LINES.  733 

Average  cost  per  unit  of  trafSc  = loo 

Extra  passengers,  singly,  cost o  -|- 

"  "  in  car-loads  cost , 51030 

"  "  in  train-loads  cost 50 

Extra  freight  in  small  lots  costs  often  in  both  directions  and  usually 

in  one  direction o  -|- 

♦*  **      in  car-loads o 5  to  20 

**  **  in  train-loads  (and  all  car-loads  must  ordinarily  be  con- 
sidered to  be  made  up  into  extra  trains  in  the  direc- 
tion of  heaviest  traffic)  not  over 60 

Not  unfrequently  when  a  large  part  of  the  traffic  of  a  branch 
goes  over  the  main  line  in  the  direction  of  favoring  grades  it  is 
handled  over  the  main  line  at  no  appreciable  extra  cost  by  simply 
filling  up  trains,  and  the  branch  is  then  enormously  profitable. 

To  these  direct  and  evident  advantages  from  a  branch  is  to  be 
added  the  vivifying  effect  of  increasing  the  tributary  population 
from  the  causes  discussed  in  the  first  part  of  this  chapter,  the 
prosperity  of  the  line  increasing  in  something  like  the  square  of 
the  tributary  population. 

983.  It  is  not  to  be  wondered  at,  therefore,  that  branches  and 
extensions  are  much  sought  for  by  prosperous  companies,  even 
in  regions  where  there  is  not  the  likelihood  of  rapid  increase  of 
traffic  which  prevails  throughout  the  United  States.  Neither  is  it 
to  be  wondered  at  that  the  seeking  for  them  is  often  overdone, 
so  that  the  branches  become  a  burden  which  threatens  to  swamp 
the  main  line,  and  often  does  so.  For  there  is  this  to  be  said 
against  branches  :  Their  traffic  is  usually  thin,  while  they  cost  as 
much  or  more  to  build  and  not  much  less  to  keep  up  than  the 
main  line.  Therefore  it  is  easy  to  lose  all  that  is  gained  on  the 
main  line  by  the  extra  cost  of  handling  the  traffic  on  branches 
and  paying  their  rentals  ;  although  it  still  remains  universally 
true,  that  branches  are  far  more  profitable  than  appears  on  the 
face  of  their  returns,  separately  considered. 

984.  These  facts  make  it  easy  to  see  what  should  be  the  gov- 
erning rule  in  laying  out  branches.  The  one  universal  rule,  to 
be  deviated  from  only  when  special  reasons  to  the  contrary  ap- 
pear, IS  this  :  Strike  the  main   line   as  soon  as  possible.     In 


734  CHAP.  XXI,— BRANCH  LINES. 

laying  out  a  branch  to  A  from  the  main  line  ED,  Fig.  241  (which 
represents  to  scale  an  actual  instance),  B  is  in  all  ordinary  cases 
...  the  point  to  strike  the  main  line,  if  possible,  even  at 

V-^^T"^.  some  disadvantage  in  grades  and  construction.  It 
\)  is  not  correct  to  compare  the  entire  line  ABCD  with 
C\  the   alternate   ACD.     Were  we   building  a  line  to 

V^  handle  a  main-line  traffic  between  A  and  Z>,  that  would 
Fig.  241'.  be  the  proper  course  to  pursue  ;  but  with  a  branch- 
line  traffic,  when  we  have  gotten  it  to  the  main  line  we  may 
say,  for  preliminary  and  approximate  purposes,  that  Ave  shall 
handle  it  thereafter  for  nothing.  If  the  branch  traffic  be  nearly 
all  toward  D  and  the  grades  favor  it,  this  will  be  almost  literally 
true.  Therefore  the  true  question  is  :  How  will  this  traffic  be 
moved  to  the  main  line  most  cheaply  and  advantageously — via 
AB  or  via  BCl  In  nine  cases  out  of  ten  AB  will  be  the  best,  for 
these  reasons  : 

985.  Branch-line  traffic  is  light  and  fragmentary.  Grades 
and  curves  then  become  minor  considerations  within  pretty  wide 
limits,  especially  when  one,  two,  or  three  engines  must  be  kept 
on  the  branch  anyway.  On  the  other  hand,  the  extra  cost  of 
keeping  up  the  track  on  AC  instead  of  AB  is  so  much  dead  loss. 

Any  traffic  AE  is  seriously  burdened  by  the  additional  dis- 
tance via  ACE  over  ABE,  while  the  gain  to  the  traffic  AD  is  but 
trifling. 

Passenger  traffic  is  almost  invariably  better  served  if  deliv- 
ered on  the  main  line  with  the  shortest  possible  haul. 

It  is  therefore  bad  practice  to  lengthen  out  branches  to  get 
cheap  construction  and  good  grades,  even  when  the  difference 
favors  most  of  the  traffic  of  the  branch,  unless  the  extension  is 
justified  by  the  cardinal  rule  laid  down  :  By  which  route  is  the 
traffic  delivered  on  the  main  line  at  any  point,  most  cheaply 
and  advantageously,  regardless  of  where  ? 

986.  To  the  preceding  is  to  be  added  another  still  more  im- 
portant and  sometimes  conflicting  rule  :  Strike  the  main  line  at 
A  considerable  town,  if  possible.  If  there  be  a  town  of  some 
size  at  either  B  or  C,  Fig.  241,  that  will  be  the  point  to  termi- 


CHAP.  XXL— BRANCH  LINES.  735 

nate  the  branch  at,  or  to  consider  it  to  terminate  in  comparing 
the  alternate  routes,  for  the  traffic  of  the  branch  will  be  very  apt 
to  be  delivered  at  this  town  even  if  the  branch  strikes  the  main 
line  elsewhere,  if  it  does  not  add  more  than  20  per  cent  to  the 
haul. 

The  purely  local  traffic  of  two  neighboring  towns,  A  and  B 
or  A  and  C,  will  ordinarily  be  found  a  very  welcome  addition  to 
the  traffic  contributed  to  the  main  line  by  the  branch,  and  it 
depends  greatly  on  facilities.  If  a  train  has  to  be  taken  from  B 
to  C  and  then  another  from  C  to  ^  to  get  from  A  to  B,  the  A-B 
traffic  will  be  practically  killed.  Only  the  necessary  travel  (par. 
45)  will  remain. 

987.  The  preceding  has  been  on  the  assumption  that  the 
branch  is  to  reach  a  point  A.     When  the  purpose  of  the  branch 


Fig.  242. 

is  not  to  reach  any  particular  point,  but  to  develop  a  tract  of 
territory,  the  conditions  are  of  course  somewhat  changed,  but 
even  then  the  same  general  principles  apply.  It  will  as  a  rule 
be  more  economical,  and  more  convenient  to  the  traffic,  to  con- 
centrate it  upon  the  main  line  as  soon  as  possible.     Therefore  it 


Fig.  243. 

is  not  as  a  rule  good  practice,  even  when  the  purpose  of  the 
branch  is  to  develop  a  long  strip  of  parallel  territory  which  has 
traffic  relations  mostly  in  one  direction,  C,  Fig.  242,  to  construct 
branches  along  parallel  lines.     The  method  outlined  in  Fig.  243 


73^  CHAP.  XXL— BRANCH  LINES. 

is  far  more  likely  to  accomplish  its  purpose  advantageously,  even 
when  branches  like  DEF  become  necessary;  the  governing  rules 
being,  first,  to  link  together  neighboring  towns  having  natural 
traffic  relations  as  directly  as  possible,  and  secondly,  to  reach  the 
main  line  quickly. 

988.  This  policy  is  the  correct  one,  not  only  because  it  handles 
a  given  traffic  most  economically,  but  because  it  tends  to  unify 
the  district  served  by  the  railway  and  aggrandize  points  on  its 
main  line.  The  two  lines  AC  and  Z>C,  Fig.  242,  are  practically 
two  separate  roads  having  no  interrelation  with  each  other 
whatever.  A  less  amount  of  road  in  Fig.  243  gives  equal  traffic 
facilities  from  the  district  AB  to  C  at  less  cost  to  the  railway,  and 
likewise  promotes  traffic  relations  with  other  points  on  the  main 
line  and  to  the  south  of  it. 

When  the  traffic  of  the  branch  is  equally  divided  between 
East  and  West,  or  nearly  so,  as  respects  destination  on  the  main 

line,  then  Fig.   244  gives  what 

is  abstractly  by  much  the  best 

p    system  for  laying  out  branches, 

other  things  being  equal.  Other 

things  rarely  are  exactly  equal, 

and  hence  considerable  devia- 

^^^-  244-  tions  from   this  plan  are  often 

required  in  the  laying  out  of  such   branches,  but  in  all  cases 

branch  traffic  needs  to  be  quite  differently  considered  from  what 

it  would  be  if  we  were  laying  out  a  main  line  to  the  same  point. 

The  writer  is  compelled  to  omit  a  number  pf  concrete  examples  of  the  lay- 
ing out  of  branches,  especially  a  most  interesting  one  having  reference  to  the 
Pacific  branch  of  the  Mexican  Central  Railway,  in  order  to  keep  this  volume 
within  more  reasonable  size. 


7 


1     1 


CHAP.  XXII.— LIGHT  RAILS  AND   LIGHT  RAILWAYS.   737 


CHAPTER  XXII. 

LIGHT    RAILS    AND    LIGHT    RAILWAYS. 

989.  A  FACT  evident  enough  in  the  existing  railway  system  of 
this  country,  and  indeed  of  the  world,  is  that,  taking  it  as  a 
whole,  distinctively  light  railways  do  not  prosper  nor  multiply. 
The  apparent  field  for  them  is  great — many  times  greater  than  for 
railways  of  the  ordinary  type.  The  need  for  them  is  keenly  felt 
in  many  regions  where  it  would  appear  as  if  cheap  light  lines 
would  answer  every  requirement  which  the  traffic  justifies.  Such 
lines  can  admittedly  be  built,  and  in  many  cases  have  been  built, 
both  of  standard  and  narrow  gauge,  for  but  little  more  than  the 
cost  of  a  good  turnpike  ;  some  of  them  even  following  the  turn- 
pike, using  low  speed,  light  rails,  light  rolling-stock,  sharp  curves, 
and  little  or  no  grading  beyond  a  mere  smoothing  of  the  sur- 
face. 

Yet  it  is  a  significant  fact  that  out  of  the  125,000  miles  of  rail- 
way in  the  United  States  (1885)  very  little  of  it  is  of  this  charac- 
ter, or  anything  closely  resembling  it.  Absolutely  there  is  a 
large  amount,  no  doubt;  but  comparatively  there  is  very  little, 
and  that  little  shows  a  constant  and  stroitg  tendency  to  approxi- 
mate to  the  general  standard.  In  spite  of  enormous  differences 
in  traffic  there  may  still  be  said  to  be  a  certain  average  standard 
to  which  the  vast  majority  of  the  roads  approximately  conform, 
or  begin  to  do  so  almost  as  soon  as  the  track  is  laid.  Between 
the  12,000  to  14,000  miles  of  trunk  lines  or  sections  thereof, 
-which  make  nearly  half  the  earnings  and  carry  far  more  than 
half  the  traffic  of  the  country,  and  the  113,000  to  115,000  miles 
which  manage  to  live  on  the  rest  of  it,  or  on  less  than  one  tenth 
as  heavy  an  average  traffic,  there  are  indeed  considerable  differ- 
ences of  condition;  yet  the  resemblances — in  rails,  in  ties,  in  bal- 
47 


738  CHAP.  XXII.— LIGHT  RAILS  AND  LIGHT  RAILWAYS. 

last,  in  rolling-stock,  in  alignment — are  still  more  striking,  prov- 
ing almost  to  demonstration  that  the  law  (to  which  there  are  of 
course  exceptions)  is  that  distinctively  light  railways  do  not 
prosper,  or  if  they  prosper,  do  not  stay  light.  We  need  not 
search  far  to  find  some  strong  reasons  why  this  should  be  so, 
and  it  is  well  that  every  one  should  do  so  who  is  concerned  in 
projecting  a  light  line  before  finally  deciding  on  its  details  of 
construction  ;  not  because  so  doing  will  necessarily  induce  him 
to  abandon  his  intention, — very  light  lines  are  often  justifiably 
built,  and  are  the  only  alternative  to  none  at  all, — but  because  it 
is  always  desirable  that  the  consequences  of  an  intended  course 
of  action  should  be  fully  understood  in  advance. 

990.  The  first  and  greatest  question  in  connection  with  alight 
railway  is,  What  weight  of  rails  shall  be  chosen?  This  is  so  for 
two  reasons  :  First,  because  the  rail  is  the  largest  single  item  of 
expense  on  such  a  line,  and  secondly,  because  on  the  weight  of 
rail  hinges  the  character  of  the  rolling-stock,  the  ties,  the  ballast, 
and  so  to  a  greater  or  less  extent  almost  every  other  detail  of  the 
line.  The  rail  question  is  therefore  a  very  fundamental  one, 
which  we  may  well  consider  with  some  care. 

Cutting  down  the  rail  section  is  almost  the  first  point  of  at- 
tack for  a  certain  large  class  of  economists,  much  as  cutting  ten 
percent  off  salaries  is  liable  to  be  at  a  later  period  in  the  history 
of  a  railway.  There  is  probably  no  other  way  in  which  anything 
like  as  large  a  saving  can  be  effected  with  so  little  demand  upon 
the  time  or  thought  (^r  skill  of  the  manager  ;  nor  does  it  admit 
of  doubt  that  either  or  both  of  these  economies  may  at  times  be 
both  expedient  and  necessary.  Nevertheless,  they  would  not, 
we  may  be  certain,  be  resorted  to  nearly  so  often  as  they  are  if 
the  full  extent  of  the  sacrifice  made  were  realized. 

991,  That  it  is  not  more  fully  realized  as  to  rails  is  probably 
due  in  the  main  to  a  not  unnatural  impression  that  in  buying  rails 
what  one  wants  is  steel  :  That  if  light  and  heavy  sections  are 
the  same  price  per  ton,  buying  a  30-lb.  section  instead  of  a  60-lb. 
is  like  a  poor  and  hungry  man  buying  a  one-pound  loaf  at  five 
cents  instead  of  a  two-pound  loaf  at  ten  cents. 


CHAP.   XXIL— LIGHT  RAILS  AND   LIGHT  RAILWAYS.  739 

This  is  not  at  all  the  case.  In  buying  rails  we  are  not  buying 
steel  ;  at  least  we  do  not  care  to  buy  it.  We  are  buying  three  im- 
ponderable qualities:  (l)  STIFFNESS,  (2)  STRENGTH,  (3)  DURABILITY. 
If  we  get  our  money's  worth  of  these  qualities,  it  is  a  matter  of 
complete  indifference  (except  the  future  scrap  value  of  the  steel, 
which  a  poor,  light  traffic  road  cannot  afford  to  give  much  thought 
to)  whether  we  get  much  or  little  of  steel.  If  we  do  not  get  our 
money's  worth  of  what  we  want,  our  bargain  is  just  as  bad,  how- 
ever much  steel  we  get. 

992.  To  determine  whether  we  do  or  not,  one  must,  unfortu- 
nately, use  an  intelligence  somewhat  higher  than  that  of  a  hay- 
scale.  Any  absolute  measure  of  the  qualities  mentioned  is  es- 
pecially difficult.  Thus,  it  may  be  hardly  necessary  to  say  here 
that  to  estimate  exactly  our  stiffness  and  strength  we  must  de- 
termine the  position  in  the  rail  section,  Fig.  245,  of  two  little 
points  which  lie  at  a  distance  called  the  radius  of  gyration 
from  the  centre  of  the  rail  (meaning  simply  the  points 
where,  if  all  the  steel  in  base  and  head  were  concen- 
trated, it  would  have  the  same  power  to  resist  gyration, 
i.e.,  bending,  as  it  now  has)  and  we  must  then  make  a  Fig.  245. 
number  of  other  assumptions  in  regard  to  the  character  of  the 
load  and  support  which  we  well  know  are  not  only  doubtful,  but 
will  not  be  even  approximately  true  in  practice,  unless  by  ac- 
cident. 

But  for  comparative  purposes  all  this  is  unnecessary.  The 
support  given  to  the  rail  from  below  by  the  road-bed  and  ties  may 
be  assumed  the  same  for  any  section  of  rail,  whatever  it  may  be 
absolutely.  We  may  assume  that  any  two  or  more  sections  re- 
quiring to  be  compared  will  be  practically  "similar"  to  each 
other,  i.e.,  with  the  same  proportion  of  base  to  height,  etc.  etc., 
so  that  Fig.  245  may,  by  simply  varying  the  scale,  be  taken  to 
represent  a  section  of  any  weight  from  10  to  100  lbs.  per  yard, 
and  yet  be  tolerably  well  designed  even  for  these  extremes.* 
From    established    mathematical    laws   we  also    know   that  the 

*  It  is  badly  designed  in  having  a  head  flaring  outward  at  the  bottom,  but 
that  is  a  detail  we  need  not  enter  into. 


740  CHAP.  XXII.— LIGHT  RAILS  AND  LIGHT  RAILWAYS. 

weight  will,  under  these  assumptions,  vary  as  breadth  X 
and  that  the  stiffness  will  vary  as  breadth  X  cube  of  height.  That 
is  to  say,  if  we  multiply  every  dimension  by  two,  we  increase  the 
weight  of  the  section  by  2  X2  =  4,  but  the  stiffness  by  2  X2^  or 
2  X  8  =  16  or  2^\  in  other  words,  the  stiffness  in  that  case  varies 
as  the  fourth  power  of  the  increase  in  linear  dimensions,  whereas 
the  weight  varies  only  as  the  square. 

993.  An  algebraic  demonstration  of  the  simplest  character, 
which  it  is  unnecessary  to  give  here,  would  prove  this  result  to 
be  in  accordance  with  a  general  law — that  the  stiffness  in  a 

RAIL    VARIES    AS    THE    SQUARE    OF     ITS    WEIGHT    PER    YARD.        If     We 

increase  the  weight 

10  per  cent,  20  per  cent,  30  per  cent, 

we  shall  increase  the  stiffness  to 

1. 10^  =  1. 21,  i.2o"^  =  1.44,  1.30^  =  1.6^, 

or  21  per  cent,  or  44  per  cent,  or  69  per  cent. 

Mere  formulae  have  a  hazy,  indefinite  sound,  which,  it  is  evi- 
dent from  what  we  see  around  us  (for  these  general  facts  are  well 
enough  known),  do  not  produce  much  impression  on  the  mind  ; 
but  let  us  reduce  them,  in  the  accompanying  Table  195,  to  the^ 
plain,  practical  basis  of  how  much  stiffness  we  get  for  a 
DOLLAR  with  light  and  heavy  rails,  and  we  shall  have  some  more 
forcible,  because  more  readily  comprehensible,  evidence  as  to 
why  light  rails  are  sooner  or  later  avoided  as  the  plague  by  all 
railways  ;  admitting  the  evident  fact,  that  for  light  lines  especi- 
ally stiffness  is  not  only  by  much  the  most  important  quality  a 
rail  can  have,  but  (as  we  shall  see  more  fully)  by  much  the  cheap- 
est stability  to  be  had  in  the  market — far  cheaper  than  tamping- 
bar  stability,  which  roads  of  heavier  traffic  can  afford  to  rely  on 
more  extensively.  In  Table  195  a  50-lb.  rail  is  taken  as  the  unit 
of  comparison,  as  being  about  the  maximum  for  distinctively 
light  railways  and  the  minimum  for  those  of  ordinary  type,  and 
the  cost  of  rails  is  taken  at  the  even  figure  of  $30  per  ton. 


CHAP.  XXII— LIGHT  RAILS  AND  LIGHT  RAILWAYS.  741 


Table  195. 
Comparative  Amount  and  Cost  of  Stiffness  in  Light  and  Heavy  Rails. 


Weight 

Cost 

Cost 

Comparative 
Value 

of  Rails. 

Tons 

Per  Mile 

Comparative 

Per  Unit 

Lbs. 

Per  Mile. 

at  S30 

Stiffness. 

of 

Received 

Per  Yard. 

Per  Ton. 

Stiffness. 

for  Si. 

10 

16 

$480 

.04 

$12,000 

20  CtS. 

15 

24 

720 

.09 

8,000 

30  CtS. 

20 

32 

960 

.16 

6,000 

40  CtS. 

25 

40 

1,200 

.25 

4,800 

50  CtS. 

30 

48 

1,440 

.36 

4,000 

60  CtS. 

35 

56 

1,680 

.49 

3,429 

70  CtS. 

40 

64 

1,920 

.64 

3,000 

80  CtS. 

45 

72 

2,160 

.81 

2,667 

90  CtS. 

50 

80 

2,400 

1.00 

2,400 

$1.00 

55 

88 

2,640 

1. 21 

2,182 

1. 10 

60 

96 

2,880 

1.44 

2,000 

1.20 

65 

104 

3,120 

1.69 

1,846 

1.30 

70 

112 

3,360 

1.96 

1,714 

1.40 

75 

120 

3,600 

2.25 

1,600 

1.50 

80 

128 

3,840 

2.56 

1,500 

1.60 

Tons  of  rail  per  mile  taken  at  1.6  tons  per  lb.  per  yard,  allowing  for  a  certain  mini- 
mum of  side  track.     Main  track  only  requires  11. 7  or  1.571  tons  per  pound  per  yard. 

Comparative  stiffjtess  (4tli  column)  is  as  the  square  of  the  weight  per  yard,  50  lbs. 
being  taken  as  the  Umit  of  comparison.  Cost  per  unit  of  stiffness  (5th  column)  is  given 
by  dividing  column  3  by  column  4.  Comparative  value  received  for  $1  (last  column)  is 
given  by  dividing  column  5  by  $2400. 

994.  This  table  should  be  carefully  studied.  It  will  be  seen 
from  it  that  the  lighter  the  original  section  of  a  railroad,  the 
more  it  loses  by  using  a  light  section,  because  the  more  would 
be  its  proportionate  gain  from  a  given  increase  in  weight  of  sec- 
tion. The  sacrifice  of  value  in  buying  light  sections  is  precisely 
the  same  as  if  in  buying  rails  we  were,  in  fact  as  well  as  in  form, 
buying  steel  instead  of  stiffness,  and  were  to  choose  light  sec- 
tions in  spite  of  the  following  market  quotations: 

Per  ton. 

Steel  in  20-lb.  sections, $75  00 

"    30  "    "  50  00 

40  "    "  . 37  50 

"    50  "    "  30  00 

"      60  "      "       25  GO 

"      70  "      "       21  43 

80  "      "       18  75 


742    CHAP.    XXII.— LIGHT  RAILS  AND  LIGHT  RAILTVAYS. 

Or,  again,  our  loss  is  the  same  as  if  we  were  offered  a  certain 
amount  of  steel  in  25-lb.  sections  at  $30  per  ton,  but  were  told 
that  if  we  would  take  twice  as  many  tons  in  the  form  of  50-lb. 
sections  we  could  have  the  remainder  at  $10  per  ton.  That  is 
precisely  what  we  are  told  in  effect,  as  respects  the  quality  we 
are  really  buying — stiffness — when  we  are  offered  rails  of  such 
sections  at  a  uniform  price  per  ton. 

995.  The  ultimate  strength  of  rails  is  a  less  important 
quality  than  the  stiffness,  because  it  is  never  expected  to  be 
called  fully  into  use.  Nevertheless,  it  often  is  so  called  into  use 
and  even  exceeded,  especially  as  the  rail  wears  out,  and  it  is 
therefore  an  important  quality.  The  strength  is  less  affected  by 
the  weight  of  the  rail  than  the  stiffness;  for,  referring  to  Fig.  245 
once  more,  the  strength  varies  only  as  the  square  of  the  height, 
whereas  the  stiffness  varies  as  the  cube,  both  varying  directly  as 
the  width.     Therefore,  in  a  similar  way  to  that   employed  for 


Table  196. 
Comparative  Amount  and  Cost  of  Strength  in  Light  and  Heavy  Rails. 


Weight 

Cost  Per  Mile 

Cost 

Comparative 

of  Rails. 

at  $30 
Per  Ton. 

Comparative 

Per  Unit 

Value 

Lbs. 

Strength. 

of 

Received 

Per  Yard. 

Strength. 

for  $1. 

10 

$480 

.089 

$•5,365 

44-7cts. 

15 

720 

.164 

4,380 

54.8     - 

20 

960 

•253 

3,796 

63.2    - 

25 

1,200 

.354 

3,717 

70.7    " 

30 

1,440 

•465 

3,091 

77.6    " 

35 

1,680 

.586 

2,870 

83.6    " 

40 

1,920 

.716 

2,684 

89.4    " 

45 

2,160 

.854 

2,530 

94.8    " 

50 

2,400 

1.000 

2,400 

100.0    " 

55 

2,640 

1. 154 

2,288 

104.9  " 

60 

2,S8o 

1. 314 

2,191 

109.5  " 

65 

3,120 

1.482 

2,105 

114. 0   " 

70 

3-360 

1.656 

2,028 

118. 3     " 

75 

3,600 

1.838 

1,959 

122.5     " 

80 

3,840 

2.024 

1,897 

126.5     " 

The  different  columns  are  determined  in  substantially  the  same  manner  as  in  Table 
195,  except  that  the  third  column  is  as  the  f  power  of  the  weight  per  yard,  taking  50-lb. 
rails  as  the  unit  of  comparison. 


CHAP.    XXII.— LIGHT  RAILS  AND  LIGHT  RAILWAYS.    743 

determining  stiffness,  we  may  determine  that  the  strength  varies 

as  the  square  root  of  the  citbe  (or  —  power)  of  the  weight,  and  thus 

obtain  Table  196.     This  table  also  should  be  carefully  studied. 

The  loss  of  strength  obtained  with  light  sections  will  be  seen 
from  Table  196  to  be  far  less  striking  than  the  loss  of  stiffness. 
Nevertheless,  it  is  as  if  strength  were  a  ponderable  element,  and 
we  bought  it  in  spite  of  the  following  prices  per  ton: 

Per  ton. 

Rails  of  20-lb.  section, $47  50 

30  "  "  38  60 

"      40  "  "  32  30 

'•      50  "  "  30  00 

**      60  "  "  27  40 

"      70  "  "  25  30 

80  "  "  23  70 

If  steel  were  quoted  at  these  prices  per  ton,  it  is  a  tolerably 
safe  hypothesis  that  light  rail-sections  would  not  be  in  much 
favor;  yet  this  is  an  unduly  favorable  showing  even  for  the  item 
of  strength,  for  if  we  were  to  compute  the  comparative  strength 
after  the  sections  have  received  a  certain  fixed  amount  of  wear, 
we  should  find  the  apparent  disadvantage  of  light  sections  as 
given  above  very  much  increased. 

996.  It  is  a  little  difficult  to  determine  a  standard  by  which 
to  measure  durability,  because,  as  a  rule,  light  and  heavy  sec- 
tions are  chosen  for  very  different  duties,  i.e.,  are  approximately 
proportioned,  and  necessarily  must  be,  to  the  kind  of  locomo- 
tives running  over  them,  so  that  no  rational  comparison  can  be 
made  between  the  durability  in  a  10-  or  20-lb.  section  and  that 
in  a  70-  or  80-lb.  section,  as  there  can  be  in  the  items  of  stiffness 
and  strength.  What  we  can  do,  however,  is  to  compare  each 
section  with  one  5  or  10  lbs.  heavier,  since  there  is  a  rational 
and  practical  choice  between  such  sections,  for  any  one  given 
service. 

Taking  a  rude  yet  tolerably  approximate  average  of  rails  as 
jthey  are  now  designed  and  chosen,  we  may  say  (i)  that  half  the 
''total  weight  is  in  the  head,  and   (2)   that  half,  or  nearly  half,  of 


744   CHAP.   XXII.— LIGHT  RAILS  AND  LIGHT  RAIL  WA  YS. 

the  metal  in  the  head  (or  i  of  the  whole  weight  of  the  rail)  is 
expected  to  be  worn  away  before  the  rail  is  finally  condemned 
as  unsafe,  although  it  may  be  earlier  removed  to  a  less  trying 
location.  That  is  to  say,  a  40-lb.  rail  has  10  lbs.  of  wear  in  it, 
and  a  50-lb.,  i2i  lbs.,  making  their  weight  when  finally  con- 
demned 30  and  37i  lbs.  respectively. 

997.  But  when  comparing  two  rails /<?r  any  one  given  service  it  is 
obvious  that  this  is  an  unfair  basis  of  comparison,  since,  what- 
ever the  original  weight  per  yard,  a  rail  for  any  one  given 
service  may  be  so  designed  as  to  utilize  most  of  any  additional 
weight  in  wear,  leaving  the  weights  of  the  worn-out  rails  when 
scrapped  nearly  the  same.  This  is,  of  course,  not  fully  possible 
without  using  very  ugly  and  distorted  original  sections,  but  it  is 
at  least  a  moderate  statement  that,  even  if  any  two  rails  of  dif- 
ferent weights  are  designed  precisely  "similar"  to  each  other  (as, 
say,  Fig.  245),  so  that  they  have  the  same  proportion  of  waste 
metal  (as  respects  wear)  in  the  base,  yet  the  head  can  in  all 
cases,  in  any  one  given  service,  be  worn  down  to  an  equal  ulti- 
mate weight  before  condemnation,  so  that  a  40-lb.  and  50-lb. 
rail  would  compare  as  follows: 


^When  New.-^ 
Head.         Base, 

, When  Worn  Out. , 

Head.          Base.                Total. 

40-lb. 

rail,  .     , 

.     .  20  lbs.     20  lbs. 

10  lbs.     20  lbs.         30  lbs. 

50-lb. 

rail,  .     , 

.     .  25  lbs.     25  lbs. 

10  lbs.     25  lbs.         35  lbs. 

A  50-lb.  rail  worn  down  to  35  lbs.  may  fairly  be  said  to  be  at 
least  as  strong  and  safe  as  a  40-lb.  rail  worn  down  to  30  lbs., 
although  that  is  rather  an  extreme  illustration  as  respects  the 
absolute  amount  of  wear  for  either  of  the  rails  specified;  but  by 
proper  design  it  is  realizable  in  sections  sufficiently  strong  for 
their  duty. 

998.  If,  however,  we  are  practising  the  last  degree  of  economy 
m  first  cost,  choosing  the  very  lightest  section  which  is  con- 
sistent with  the  duty  laid  upon  it,  as  we  have  already  admitted 
is  sometimes  expedient,  it  is  obvious  that  we  cannot  count  on 
any  such  rate  of  wear  as  that.  Wearing  off  half  the  head  means 
reducing  its  ultimate  strength  by  something  like  45  per  cent,  and 


CHAP.    XXIL— LIGHT  RAILS  AND  LIGHT  RAILWAYS.    745 


Comparative  Cost  of  the 

Durability  in  5  Lbs.  More 

Per  Yard,  taking  the 

Durabihty  of  a  Lighter 

Section  as  worth  100  Cents 

on  the  Dollar. 

'^N  M  0   Oco  r^r~NQ5o  mmu-ivnrf 

M     M     M     M 

000000000000000 

Increase  of 

Weight  by 

Adding 

5  Lbs.  to 

Section. 

^  ^  ^^^|^^^^^l^„fX)^l3,^jO^H^P^JM^H<^^^^[2 

Times  In- 
crease of  Wear 
by  Adding 
5  Lbs.  to 
Section. 

Or^vn       cnMc^vD       xcmcoidcom 
ino  N        CO  r^vo  iTiUS  r^  <^  CO  en  c<^  CO 

CnNWMHMMMFHMMMI-lMM 

Spare  Metal  in 
Next  Heaviest 

Rail  before 

Head  becomes 

as  Light. 

cnrj-'^mmovo  r^-t»ooco  <y^  o^  o  O 

M     h-l 

Left  in 

Head 

after 

Minimum 

Wear. 

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74^    CHAP.    XXII,— LIGHT  RAILS  AND  LIGHT  RAIL  WA  YS. 

its  stiffness  by  65  to  70  per  cent  (making  merely  a  rough  estimate 
of  the  new  "  moments  of  inertia"  and  "  radius  of  gyration" 
necessary  to  determine  it  exactly).  When  we  are  selecting  a 
rail  as  light  as  we  dare,  we  have  no  such  margin  as  that;  yet  we 
must  assume  some  margin  for  wear,  for  however  light  a  section 
may  be,  it  cannot  be  expected  to  become  unserviceable  as  soon 
as  the  top  is  fairly  polished.  We  may  assume,  perhaps,  that,  in 
such  cases,  a  wear  equal  to  one  fifth  of  the  metal  in  the  head 
is  more  or  less  consciously  contemplated  and  actually  realized. 
With  these  premises,  we  may  determine  in  Table  197  how  much 
durability  we  get  for  a  dollar  with  light  and  heavy  sections,  and 
it  will  be  seen  that — of  all  the  three  qualities  we  are  buying — 
the  worst  sacrifice  by  far  is  in  buying  durability  in  light  sec- 
tions. It  is  as  if  when  buying  rails  we  were  buying  steel  in- 
stead of  durability,  and  chose  the  light  sections  in  the  face  of 
the  following  market  quotations  of  steel: 

Per  ton. 

Steel  in  20-lb.  sections, $30  00 

Additional  lots  (spot  cash  for  future  delivery,  as  needed,  at  end 

of  —  years) 2  75 

Steel  in  40-lb.  sections, 30  00 

Additional  lots, 2  31 

Steel  in  60-lb.  sections,       . 30  00 

Additional  lots, i  76 

Of  course  this  enormous  difference  is  due  not  so  much  to  the 
extraordinary  cheapness  of  the  durability  in  the  heavier  sections 
as  to  the  extraordinary  dearness  of  the  durability  in  the  lighter 
sections.  Still,  if  we  assume  that  we  get  our  money's  worth  out 
of  the  light  sections,  the  comparison  is  a  fair  one.  By  varying 
the  assumed  rates  of  wear,  the  numerical  comparison  will  be 
modified  according! 3'',  but  in  no  probable  case  enough  to  make 
the  moral  materially  different. 

999.  Of  course,  too,  it  is  to  be  remembered  that  durability  is 
a  quality  for  future  delivery  (for  light-traffic  roads,  perhaps,  in 
a  very  distant  future),  which  we  pay  down  for  now,  in  cash.  It 
is  therefore  only  the  present  worth  of  this  future  value  which 
we  ought  to  consider.     Still,  this  applies  only  to  the  durability. 


CHAP.    XXII.— LIGHT  RAILS  AND  LIGHT  RAILWAYS.    747 

The  strength  and  stillness  we  have  use  for  from  the  very  day  the 
rails  are  laid;  and  even  the  present  worth  of  the  extra  durability 
at  the  largest  probable  rate  of  interest  and  the  longest  probable 
life  of  light  rails  is  cheap  indeed  at  the  price  paid  for  it,  as  will 
appear  from  Table  18,  page  82,  or  more  directly  from  the  follow- 
ing Table  198,  which  explains  itself,  and  will  probably  make  it 
very  clear  that  whether  a  new  project  as  a  whole  will  pay  or 
not,  it  is  almost  sure  to  return  a  heavy  profit  on  the  additional 
capital  invested,  obtained  at  any  probable  cost,  to  buy  reasonably 
heavy  rail-sections,  for  the  sake  of  their  durability  alone. 

Table  198. 

Years  of  Wear  which  a  Light  Rail-Section  must  Outlast  before  the 
Durability  obtainable  by  adding  Five  Lbs.  Per  Yard  to  it  will 
BECOME  A  Losing  Bargain,  costing  more  than  that  of  the  Light 
Section.* 


Weight  of 

Present  Cost  of  Capital. 

Light  Section. 

Lbs.  Per  Yard. 

5  per  cent. 

10  per  cent. 

15  per  cent. 

20  per  cent. 

Years. 

Years. 

Years. 

Years. 

20 

45-0 

23.0 

15-7 

12.0 

30 

49.1 

25.2 

17.2 

I3-I 

40 

52.0 

26.6 

18. 1 

13-9 

50 

55.5 

28.4 

19.4 

14.8 

60 

58.1 

29.7 

20.6 

15-5 

70 

60.3 

30.9 

21. 1 

16. 1 

80 

62.4 

31.9 

21.8 

16.7 

*  For  the  ultimate  value,  U,  of  a  certain  sum  p  invested  at  compound  interest  for  n  years  at 
r  per  cent,  we  have 

whence  log  Z7  =  log/  +  log  (i  +  r)  X  «, 

_  log  Z7-  log/ 
""-     log(i  +  r)    • 

Letting  the  numerator  (i)  of  the  vulgar  fractions  in  column  9  of  Table  197  =/  (the  log  of 
which  is  o  and  may  be  dropped),  the  denominator  of  the  same  fractions  will  =  U,  and  we  have 
log  n  —  log  of  log  U  —  log  of  log  (i  -+-  r). 


and 


1000.  In  these  facts  we  have  reasons  enough,  and  to  spare, 
why  all  roads  should  tend,  as  they  do  tend,  to  use  what  project- 
ors of  new  roads  call  a  "  heavy  '  rail,  and  think  they  can't  afford. 
It  is  because,  for  a  poor  road  as  well  as  a  rich  one,  the  best  is 


748    CHAP.    XXIL— LIGHT  RAILS  AND  LIGHT  RAIL  WA  YS. 

THE  CHEAPEST,  and  a  poor  road,  even  more  than  a  rich  one,  must 
have  the  cheapest  to  live  at  all.  It  is  because,  with  railways  as 
with  men,  "the  destruction  of  the  poor  is  their  poverty,"  in  that 
there  are  not  as  many  cents  in  a  poor  man's  dollar  as  in  a  rich 
one's,  because  of  the  bad  bargains  which  his  poverty  drives  him 
to — or  he  thinks  it  does.  While  it  may  still  be  right  to  buy  the 
light  sections,  if  we  must  have  something  and  cannot  pay  more 
it  should  at  least  be  realized  how  great  a  sacrifice  is  made,  in 
order  to  make  sure  that  there  is  no  other  direction  in  which  a 
less  costly  economy  can  be  exercised. 

Of  course,  as  has  been  already  stated,  there  is  another  side  to 
this  question — a  certain  legitimate  and  advisable  use  of  light 
rails.  If  a  man  needs  but  three  yards  of  cloth  to  make  a  coat, 
and  only  needs  one  coat,  there  is  no  particular  economy  in 
his  buying  four  yards,  simply  because  he  can  get  it  cheap;  and 
then,  besides,  there  is  always  the  open  question  whether  his  great- 
est need  is  for  a  coat  or  a  pair  of  breeches.  That  part  of  the  ques- 
tion we  may  now  consider.  We  have  merely  found  so  far  that 
if  a  man  is  going  to  buy  a  coat,  there  is  a  fearful  loss  which  a 
poor  man  cannot  afford  in  buying  one  which  is  too  small  to  fit 
and  too  flimsy  to  wear.  Of  all  directions  for  economy,  cutting 
down  the  rail-section  is  the  most  costly  in  the  end. 

1001.  If  attempted  economies  in  all  other  directions  were 
equally  disastrous,  we  should  be  led  directly  to  the  conclusion 
that  it  was  not  worth  while  to  build  light  railways,  and  that  they 
could  never  reasonably  be  expected  to  prosper;  but  such  a  con- 
clusion must  be,  in  part  at  least,  fallacious;  for  there  is  evident 
need  at  many  points  for  just  such  lines,  which,  when  built,  do 
prosper,  or  at  least  answer  the  requirements.  Hence  there  must 
be  certain  directions  in  which,  within  certain  limits,  it  is  expe- 
dient to  economize  in  their  construction,  and  there  are,  in  fact, 
many  directions  where  economy  does  little  harm.  If  we  exam- 
ine in  detail  the  cost  of  even  a  moderately  important  line,  we 
shall  find  that  an  enormous  proportion  of  it  is  for  items  which  a 
light,  cheap  railway  either  has  no  use  for  at  all,  or  can  dispense 
with  at  slight  inconvenience,  in  part  or  whole,  or  can  postpone  at 
moderate  sacrifice  to  some  indefinite  date  in  the  future. 


CHAP.    XXII.— LIGHT  RAILS  AND  LIGHT  RAIL  WA  YS.    y4g 

1002.  Terminal  facilities,  for  instance,  are  an  immense  item 
in  the  investment  in  large  railways.  In  the  Buffalo  (N.  Y.)  yards 
alone  there  are  650  miles  of  track  (Table  201),  representing  an  in- 
vestment of  millions.  Station  and  other  buildings  are  other 
large  items,  which  may  be  made  small  on  a  light  road;  but  the 
chief  of  all  directions  in  which  a  rigid  yet  intelligent  economy 
may  be  exercised  to  reduce  largely  the  construction  account  with- 
out undue  effect  upon  earning  capacity  is  in  the  construction  of 
the  road  to  sub-grade. 

1003.  This  is  best  seen  by  considering  how  much  (or  rather 
how  little)  the  cost  of  5  lbs.  per  yard  extra  weight  in  the  rail, 
which  we  may  take  at  the  even  figure  of  $30  per  ton,  or  ^240  per 
mile,  will  do  to  construct  the  road  to  sub-grade.  We  have  seen 
how  very  advantageous  is  the  effect  of  this  expenditure  upon  the 
rail-section.  If  expended  on  grading  and  masonry,  the  same 
amount  will  only  do  the  following: 

Cubic  Yards. 
Earthwork,  at  20  cents  per  cubic  yard 1,200 

Equal  to  a  continuous  fill  5  in.  deep,  or  a  cut  10  ft.  deep  and 

100  ft.  long. 
Rock  cutting,  at  $1. 50  per  cubic  yard 160 

Equal  to  a  cut  100  ft.  long  and  23  ft.  deep. 
Culvert  masonry,  at  $5  per  cubic  yard 48 

Or  one  small  box  culvert. 
Bridge  masonry,  at  $10  per  cubic  yard only  24 

Far  more  than  these  quantities  can  usually  be  saved  by  aban- 
doning the  attempt  to  fit  the  line  for  high  speed  and  long  trains, 
and  judiciously  economizing  in  these  three  ways  :  (i)  By  using 
sharp  curvature;  (2)  by  using  trestling  in  place  of  masonry  and 
heavy  earthwork;  (3)  by  moderate  undulations  of  grade;  to  which 
may  be  added  (4)  sacrifice  of  distance  to  obtain  easy  work,  and 
especially  to  reach  towns. 

1004.  Whatever  conclusion  may  be  just  as  to  the  proper  stand- 
ard OF  curvature  for  lines  of  fair  traffic,  it  is  certain  that  for  a 
road  to  which  the  last  degree  of  economy  in  first  cost  is  essen- 
tial, and  which  does  not  expect  more  than  a  very  light  traffic,  the 
intelligent  use  of  sharp  curvature  offers  one  of  the  simplest,  most 


750   CHAP.   XXII.-^LIGHT  RAILS  AND   LIGHT  RAILWAYS. 

effective,  and  most  expedient  methods  of  economizing  in  first 
cost.  We  have  seen  that  since  the  introduction  of  steel  rails  and 
air-brakes  both  the  operating  cost  and  the  danger  of  sharp  curva- 
ture have  been  greatly  diminished.  The  New  York  elevated  rail- 
ways run  800  or  more  trains  of  four  cars  each  per  day  around  the 
6'^''  curves  (shown  in  Figs.  201-2)  with  perfect  ease  and  with  only 
a  moderate  slackening  of  speed.  Another  much-used  curve  of 
50  ft.  radius  is  described  on  page  326.  In  Table  116  full  details 
are  given  of  other  sharp  curves  in  use  on  standard-gauge  lines, 
ranging  from  410  to  175  ft.  radius,  over  many  of  which  a  very 
heavy  traffic  passes.  While  these  extremes  are  to  be  deprecated 
(nor  are  they  often  required),  they  do  make  it  an  absurdity  to 
say  that  a  cheap  light-traffic  railroad  may  not  use  almost  any 
curvature  which  the  nature  of  its  route  calls  for  in  order  to  re- 
duce first  cost,  whatever  its  gauge. 

In  a  country  offering  any  difficulty,  the  reduction  which  can 
be  effected  in  this  way  is  very  large  indeed,  and  it  will  in  gen- 
eral be  found  that  no  excessive  reduction  of  radius  is  needed  to 
give  a  line  closely  approximating  to  a  surface  line,  and  fitting  so 
well  that  any  further  reduction  of  radius  will  save  but  little 
(par.  883).  This  disadvantage  is  far  less  than  that  of  light  rails 
in  almost  every  instance. 

1005.  Moreover,  if  the  profile  of  almost  any  line  be  studied,  it 
will  be  found  that  the  expenditures  are  largely  concentrated 
AT  single  points.  Four  or  five  cuts  in  a  mile,  eight  or  ten  miles  in 
a  hundred,  are  what  bring  up  the  average;  so  that  in  seeking  the 
last  degree  of  economy  at  these  critical  points  the  line  as  a  whole 
is  not,  after  all,  so  seriously  modified  as  would  be  imagined.  A 
further  advantage,  or  rather  a  bright  side  to  the  disadvantage  of 
so  economizing  by  sharp  curvature  is  that  at  many  points  the 
works  may  assume  a  mere  temporary  character  for  present  ne- 
cessities, while  being  adapted  for  ready  improvement  in  the  fu- 
ture, when  and  if  means  exist  for  doing  so.  In  this  way  the  ne- 
cessities of  both  the  present  and  future  are  better  provided  for 
than  if  a  compromise  line  were  chosen  in  the  beginning  which 
did  not  fully  insure  either  present  cheapness  or  future  excellence. 
Par.  283  gives  a  notable  instance. 


CHAP.   XXII.— LIGHT  RAILS  AND  LIGHT  RAILWAYS.    75 1 

1006.  Here  the  question  of  gauge  naturally  comes  up.  Among 
the  many  advantages  which  have  been  so  loosely  claimed  for  the 
narrow-gauge  system,  perhaps  none  has  been  so  insisted  on,  or 
so  affected  the  popular  imagination,  as  this  one  of  being  able  to 
use  sharp  curves  readily  which  were  all  but  impracticable  with 
the  standard  gauge. 

A  few  years  ago,  when  the  first  edition  of  this  treatise  was  is- 
sued, no  discussion  of  the  question  of  light  railways  could  have 
been  adequate  without  entering  pretty  fully  into  the  pros  and 
cons  of  the  gauge  question.  This  is  no  longer  necessary.  The 
irresistible  logic  of  events  has  practically  settled  the  question, 
and  the  belief  in  the  narrow-gauge  as  an  expedient  and  defensi- 
ble system  of  construction,  which  was  from  the  beginning 
founded  chiefly  on  illusion  and  delusion,  is  rapidly  passing  away, 
and  all  but  gone.  We  may  therefore  merely  summarize  briefly 
the  leading  points  of  the  question. 

As  respects  curvature,  we  have  already  seen  (pars.  335-6)  that 
while  the  gain  in  curve  resistance  from  a  narrowing  of  gauge 
only,  with  no  other  change,  is  very  slight,  yet  when  the  wheel- 
base  is  reduced  correspondingly  the  curve  resistance  is  probably 
diminished  about  in  proportion  to  the  gauge.  As  this  is  what  is 
usually  done  in  practice,  we  may  consider  it  from  that  point  of 
view. 

1007.  But  the  question  then  arises:  What  is  saved  thereby  ?  If 
it  be  to  increase  the  hauling  capacity  of  engines,  a  very  slight  ad- 
ditional curve  compensation  will  neutralize  the  extra  resistance 
of  the  wider  gauge,  and  we  have  already  seen  (par.  290)  that  any 
radius  which  is  likely  to  be  desired  is  readily  practicable  for 
properly  designed  standard-gauge  engines.  If  it  be  to  save  the 
extra  wear  and  tear  and  loss  of  power,  a  small  reduction  in  an 
item  the  whole  of  which  is  so  small  (Table  115,  page  322)  is  not 
worth  any  considerable  sacrifice,  nor  can  it  be  taken  for  granted 
(nor  is  it  probable)  that  there  is  any  such  reduction. 

1008.  As  respects  rolling-stock,  there  cannot  be  a  question 
that  there  is  absolutely  no  practical  advantage  in  the  narrower 
gauge.    Any  reputable  locomotive-builder  will  contract  to  build 


752    CHAP.   XXII.— LIGHT  RAILS  AND   LIGHT  RAILWAYS. 

engines  of  the  same  weight  and  power  for  either  gauge,  which 
will  traverse  the  same  curves,  for  the  same  price.  The  standard- 
gauge  engine,  in  fact,  will  or  can  have  enough  shorter  wheel- 
base,  because  of  its  greater  width,  to  make  it  take  curves  a  little 
better — a  very  important  point  which  narrow-gauge  advocates 
and*  opponents  alike  have  almost  wholly  lost  sight  of. 

The  same  is  essentially  true  of  the  cars.  The  car-bodies  may 
be  exactly  the  same,  and  the  trifling  loss  from  the  extra  width  of 
trucks,  if  it  were  worth  discussing  at  all,  may  be  fully  made  up 
by  a  slight  increase  in  the  weight  and  capacity  of  the  car-body, 
while  car-bodies  of  the  ordinary  size  and  capacity  can  go  safely 
over  any  structures  or  track  which  will  carry  a  light  locomotive 
— whether  standard-gauge  or  narrow-gauge — and  carry  as  large 
a  proportion  of  paying  load  as  is  customary  in  narrow-gauge 
cars. 

1009.  The  bridges  and  trestles  are,  of  course,  not  affected  by 
the  width  of  the  gauge,  if  rolling-stock  of  the  same  weight  and 
width  pass  over  them;  besides  which,  we  shall  shortly  see  evi- 
dence (par.  1039)  that  the  cost  of  bridges  is  but  very  little  affected 
by  the  load  per  lineal  foot  they  are  built  to  carry,  so  that  there 
is  little  real  inducement  to  build  such  structures  to  carry  less  than 
the  common  loads. 

The  earthwork  and  masonry  is  affected  only  by  whatever  dif- 
ference there  may  be  in  the  width  of  the  road-bed,  which  cannot 
properly  be  more  than  the  difference  of  gauge.  The  ties,  we  shall 
soon  see  (par.  1056),  may  be  made  somewhat  shorter,  or  about 
three  quarters  of  the  usual  w^idth,  but  only  at  the  expense  of  de- 
creasing the  stability  of  the  track  and  increasing  the  labor  re- 
quired. 

Fencing,  right  of  way,  buildings,  frogs,  switches,  side-tracks, 
shops,  etc.,  etc.,  are  not  affected  at  all,  if  the  standard  of  excel- 
lence and  weight  of  rolling-stock  be  the  same. 

1010.  There  remains,  therefore,  as  the  net  gain  from  the  nar- 
rower gauge,  only  the  slight  saving  in  grading  and  ties,  which 
may  amount  to  one  to  four  per  cent  of  the  total  cost  of  the  line. 

On  the  other  hand,  there  are  several  very  serious  losses.    The 


CHAP.    XXII.— LIGHT  RAILS  AND  LIGHT  RAILWAYS.    753 

one  which  is  alone  of  decisive  importance  is  the  great  loss  from 
not  being  able  to  exchange  traffic  in  bulk,  but  having  to  trans- 
ship all  freight  and  passengers.  The  loss  from  this  is  far  more 
than  its  direct  cost.  The  resulting  inconvenience,  delay,  and 
damage  to  freight  drives  away  much  traffic. 

The  cost  of  maintaining  track  to  a  given  standard  of  excel- 
lence is  likewise  greater,  the  cost  for  track-labor  being  in  about 
inverse  proportion  to  the  length  of  the  ties.  The  less  bearing 
area  of  the  ties  on  the  ballast  increases  this  disadvantage  ma- 
terially. 

The  maintenance  of  rolling-stock  is  decidedly  more  costly  in 
proportion  to  work  done,  and  the  train  resistance  higher,  because 
of  the  smaller  wheels.  The  speed  is  necessarily  lower,  and  the 
passenger  cars  less  comfortable. 

These  facts  are  now  admitted  by  all  intelligent  managers, 
whether  of  broad  or  narrow  gauge,  and  the  reconstruction  of 
narrow  to  standard-gauge  is  now  going  on  with  great  rapidity, 
Several  thousand  miles  of  narrow-gauge  lines  have  already  been 
changed,  and  it  is  plainly  only  a  matter  of  a  few  years  when  prac- 
tically all  the  remaining  lines  will  be  changed. 

1011.  It  is  often  apologetically  admitted  by  those  otherwise 
opposed  to  the  narrow-gauge  that  for  certain  mountainous  re- 
gions it  is  best  adapted.  This  likewise  is  an  error,  except  for 
such  few  lines  as  are  not  likely  to  either  have  or  desire  traffic 
relations  with  other  roads. 

An  example  is  the  great  system  of  narrow-gauge  lines  in 
Colorado.  The  Denver  &  Rio  Grande  was  projected  in  the 
early  days  of  the  narrow-gauge  movement,  and  did  much  to 
extend  it,  if  indeed  it  may  not  be  said  to  have  been  the  origin  of 
it,  as  it  certainly  was  the  source  of  its  temporary  strength.  It 
is  by  much  the  most  considerable  narrow-gauge  system  in  the 
world,  and  for  many  years  was  a  great  financial  success;  nor  are 
its  later  troubles  to  be  ascribed  primarily  to  its  gauge,  but  to 
bad  judgment  in  extensions  and  other  expenditures. 

Nevertheless,  the  success  of  this  line  had  little  or  nothing  to 
do  with  its  gauge,  but  was  due  rather  to  the  fact  that  it  was 
48 


754    CHAP.    XXII.— LIGHT  RAILS  AND  LIGHT  RAILWAYS. 

cheaply  built,  and  was  assured  a  monopoly  of  a  remunerative 
and  growing  traffic  at  very  high  rates — rates  from  three  to 
eight  times  higher  than  were  usual  on  lines  farther  east.  The 
disadvantages  of  a  break  of  gauge  were  likewise  reduced  to  the 
minimum  by  its  location.  Its  narrow-gauge  system  was  com- 
plete in  itself,  and  connected  with  standard-gauge  tracks  at  but 
a  few  points,  where  transshipment  was  often  no  disadvantage. 

Yet  even  under  these  circumstances — the  most  favorable  under 
which  any  large  narrow-gauge  lines  have  ever  been  placed — the 
disadvantages  of  the  gauge  have  proved  so  serious  that  it  is 
now  (1887)  only  the  lack  of  means  which  prevents  the  immediate 
widening  of  the  gauge  on  all  the  more  important  lines.  To  do 
this  involves  little  expense.  The  ties  are  rather  short  for  the 
purpose;  but  the  20°  and  24°  curves  can,  in  the  first  place,  be 
passed  without  difficulty  by  the  standard-gauge  engines,  and,  in 
the  second  place,  the  cost  of  reconstructing  such  curves  as  are 
objectionable,  while  it  may  be  a  considerable  absolute  sum,  will 
be  a  very  trifling  one  in  proportion  to  the  total  investment,  and 
probably  far  less  than  the  present  yearly  loss  from  the  narrower 
gauge. 

1012.  The  use  of  a  narrower  gauge  to  cheapen  construction 
has  been  proved  by  actual  experience,  therefore,  to  be  in  all  cases 
inexpedient  for  any  road  handling  a  general  traffic,  or  having 
any  reasonable  chance  of  wishing  to  exchange  traffic  with  other 
lines. 

1013,  Returning  to  the  more  hopeful  directions  for  economy: 
the  free  use  of  wooden  trestling  and  the  practical  abandon- 
ment of  the  (immediate)  use  of  masonry  is  another  legitimate 
and  wise  device  for  reducing  first  cost. 

There  are  not  a  few  engineers  who  decry  the  use  of  wooden 
trestles,  nor  can  it  be  denied  that  the}^  are  often  ill  and  danger- 
ously built,  and  then  neglected  so  long  that  they  become  a  fre- 
quent source  of  accident.  But  when  properly  built  and  properly 
kept  up,  they  furnish  a  safe  and  cheap  method  of  avoiding  or 
postponing  the  more  costly  features  of  construction,  so  that, 
even  for  roads   of  considerable  traffic,  it  is  far  wiser  to  preach 


CHAP.   XXII.— LIGHT  RAILS  AND  LIGHT  RAILWAYS.    755 

the  gospel  of  sound  construction  than  to  decry  their  existence. 
Fortunately,  under  existing  conditions  in  America,  most  of  the 
localities  where  very  light  railways  only  can  be  supported  are 
near  enough  to  local  timber  supply  to  obtain  pine,  hemlock,  or 
other  suitable  trestling  timber  at  very  low  prices;  and  with 
split  stringers,  and  split  sills  and  caps,  it  is  easily  possible  (with- 
out going  into  fuller  details,  which  would  be  inappropriate  in 
this  volume)  to  erect  substantial  structures,  without  mortises,  in 
which  each  individual  stick  is  renewable  in  detail,  and  which 
will  be  as  safe  for  the  passage  of  trains  as  any  bridge,  so  long  as 
they  are  properly  maintained.  The  great  majority  of  the  trestles 
now  erected  in  this  country,  however,  are  ill-designed,  especially 
as  respects  the  floors. 

1014.  At  somewhere  from  10  to  15  feet  of  height  of  fill  such  a 
structure  becom'es  cheaper  in  first  cost  than  even  a  plain  earth  fill; 
and  when,  in  addition  to  the  fill,  there  would  have  to  be  a  ma- 
sonry structure,  or  when,  if  it  were  not  for  the  trestle,  the  grade 
would  have  to  be  dropped  or  the  line  swung  in  so  as  to  give  a 
rock  cut  (or  even  a  heavy  earth  cut)  at  each  end  of  it,  the  trestle 
becomes  very  much  cheaper,  and  its  free  use  affords  us  a  solid 
and  safe  roadway  for  immediate  use  which  can  be  continued  in 
the  same  form  indefinitely,  if  poverty  requires  it,  or  which  can 
be  advantageously  and  economically  replaced  by  more  perma- 
nent structures  at  any  time,  using  trains  to  make  the  fills  and 
supply  the  stone, 

1015.  It  is  also  allowable  to  use  wooden  box  culverts,  to  be 
replaced  in  time,  as  they  begin  to  decay,  by  iron  pipes  placed 
inside  of  them.  Many  great  roads  where  stone  is  scarce  build 
these  in  place  of  open  culverts  or  trestles  as  a  regular  practice, 
and  much  can  be  said  for  it.  No  road,  of  course,  would  use 
wood  for  box  culverts  when  stone  could  be  obtained  at  reason- 
able cost. 

1016.  The  use  of  moderate  undulations  on  gradients  affords 
another  means  by  which  the  first  cost  of  a  line  may  often  be 
largely  reduced,  and  we  have  seen  (par.  397)  that  if  the  track  be 
good  enough  to  stand  a  certain  moderate  increase  of  speed  at 


7^6   CHAP.    XXII.— LIGHT  RAILS  AND  LIGHT  RAILWAYS. 

Special  points,  it  involves  no  injury  to  the  hauling  capacity  of 
engines.  The  limits  within  which  momentum  can  be  relied  on 
in  this  manner  has  been  already  considered  (par.  441)  and  may, 
when  economy  is  urgent,  be  closely  approached,  as  in  the  in- 
stance of  par.  832,  because,  should  such  undulations  prove  seri- 
ously objectionable,  the}^  may  be  taken  out  at  any  time.  This 
is  certainly  a  far  wiser  way  of  economizing  than  cutting  down 
the  rail  so  light  that  it  will  barely  carry  the  engine,  as  is  often 
done. 

1017.  Finally,  one  remaining  device  will  complete  all  that  is 
possible,  or  probably  necessary,  in  the  way  of  reducing  the  first 
cost  of  the  road-bed.  A  great  deal  of  money  is  spent  by  many 
roads  which  can  ill  afford  the  luxury  in  getting  a  short  line.  In 
the  light  of  the  facts  brought  out  in  Chap.  VII.  it  is  unquestion- 
able that,  however  it  may  be  with  roads  of  large  or  of  fair  traffic, 
a  cheap  light-traffic  railway  which  spends  money  to  get  a  short 
line  is  burning  its  candle  at  both  ends,  and  the  engineer  of  such 
a  line  cannot  too  carefully  remember  that,  although  on  the  one 
hand  its  length  may  be  the  ruin  of  it,  because  it  has  to  operate 
it,  yet  on  the  other  hand  it  is  its  salvation,  because  its  revenue 
depends  on  it. 

1018.  Especially  is  this  true  when,  in  choosing  the  easiest 
line  regardless  of  distance,  we  not  only  obtain  an  easier  line  to 
construct,  but  one  which  will  take  us  nearer  to  the  various 
SOURCES  OF  traffic.  However  it  may  be  with  lines  of  larger 
traffic,  a  poor  railway  certainly  cannot  afford  to  pass  by  on  the 
other  side  even  quite  small  traffic  points  which,  by  going  nearer 
to  them,  will  add  a  little  more  traffic  to  the  slender  aggregate; 
not  only  because  every  little  helps,  but  because  the  revenue  per 
head  of  that  population  is  also  smaller,  as  we  have  seen  in  the 
preceding  chapter. 

1019.  The  truths  which  have  been  stated  are  not  to  be  taken 
"  neat,"  nor  recklessly  twisted  to  mean  more  than  has  been  said; 
as,  for  instance,  that  it  is  ever  expedient  to  lengthen  a  line  merely 
for  the  sake  of  lengthening  it,  or  that  it  is  not  worth  while  to  try 
to  avoid  curvature,  or  that  wooden  trestles  are  as  good  as  per- 


CHAP,   XXIL— LIGHT  RAILS  AND  LIGHT  RAIL  WA  YS.    7$/ 

manent  works.  It  has  been  merely  intended  to  show  that,  for  a 
road  which  must  practise  the  last  degree  of  economy  and  which 
has  little  more  than  a  turnpike  traffic,  the  construction  of  the 
ROAD  TO  SUB-GRADE  is  the  proper  place,  and  the  most  hopeful 
place,  for  "cutting  to  the  bone,"  because  an  amount  sufficient 
to  give  a  decently  solid  superstructure  can  usually  be  saved  out 
of  the  first  construction  with  far  less  risk  of  injury  and  loss. 
This   is  apparent  from   Table  199,  showing  the  percentages  of 

Table  199. 


Showing  the  Percentage  of  Cost  to  Sub-Grade  on  Various  Items  of 
Construction  on  Various  Lines. 


I. 

II. 

III. 

IV. 

V. 

Length,  miles 

Total  cost  per  mile..  . 
Clearing   . . 

60 

$5,073 

2.1 

71.0 

14-3 
12.6 

100 
$7,490 

61.9 

13-7 
2.0 

II. 7 
4.6 

14-5 

$18,260 

0.2 

51.0 

7.5 

II. 0 

13-5 
1.2 

?•' 

6.5 

46 
$18,920 
2.0 

15 

$83,854 

Masonry,)  §;!?--■ 

35 

5 
12 

31 
12 

I 

8 

4 

8 

9 

25.7 

50.3 

5.4 

9.8 

1-5 

7.3 

Trestling,  etc 

Fencing,  etc 

Tunnel 

100. 0 

100. 0 

100. 0 

100. 0 

100. 0 

Character  of  Lines  : 
I.  Chiefly  light,  with  sections  of  heavy  grading  ;  no  stone-work. 
II.  Moderately  light  grading,  with  sections  of  heavy  ;  many  structures. 

III.  Side-hill  line,  no  surface  work  ;  very  numerous  structures. 

IV.  Light  surface  grading,  two  costly  bridges  only  ;  much  high  trestling. 
V.  One  of  the  costliest  sections  of  mountain  line  in  the  United  States. 

The  relative  cost  of  another  light  Western  road,  several  hundred  miles  long,  was 
divided  as  follows,  including  all  items,  and  not  those  to  sub-grade  only  : 


Engmeenng-  2.3 

Grading,  including  tunnelling 23.6 

Bridge  masonry 5.6 

Culvert  masonry 2.5 

Temporary  trestling i .  i 

Superstructure,  bridges  and  trestles 4.5 

Ballast,  and  settling  of  embankments. . .  3.7 

Dressing  up  road-bed  after  winter 1.7 

Right  of  way,  fencing,  cattle-guards  and 

road-crossings 1.9 

Rails  and  track-laying,  complete 17.9 


p.  c. 

Cross-ties  (very  small) 2.5 

Engine-houses,    shops,   stations,    water 

supply,  pumps,  etc 6.9 

Locomotives  and  cars 10.2 

Interest  on  bonds  to  opening 5.8 

Discount  on  bonds 7.7 

Taxes  to  opening o.  i 

Office  expenses,  salaries,  etc.,  to  open- 
ing of  line 1.7 

Incidental  to  opening  of  line. 0.3 

Total  to  opening  of  line loo.o 


758    CHAP.   XXII.— LIGHT  RAILS  AND  LIGHT  RAILWAYS, 

the  cost  to  sub-grade  of  various  items  on  different  railroads,  all 
of  them  of  comparatively  light  (although  not  the  lightest)  traffic^ 
and  varying  in  character  of  work  from  moderately  light  to  the 
very  heaviest.  The  prices  on  all  of  them  were  from  25  to  40  per 
cent  higher  than  now  (1886)  obtain,  under  favorable  conditions; 
but  in  each  case  alike  it  will  be  seen  how  much  less  injury  a  sav- 
ing of  $240  per  mile  in  some  or  all  of  the  items  given  would 
probably  have  done  to  the  road  than  if  5  lbs.  per  yard  were  cut 
off  the  rail-section. 

1020.  Nothing  has  been  said  so  far  about  gradients,  because 
a  very  light  traffic  road  cannot  afford  to  spend  money  to  obtain 
more  favorable  gradients  than  careful  study  of  the  country  will 
afford  at  the  minimum  cost,  which  (par.  894)  will  generally  be 
quite  reasonably  favorable.  At  any  rate,  while  the  temptation 
for  the  locating  engineer  to  magnify  his  office  may  be  great,, 
until  provision  has  first  been  made  for  a  i;easonab]y  substantial 
and  well-maintained  track,  it  may  be  taken  as  a  tolerably  safe 
general  rule,  that  the  same  amount  of  money  expended  on  track 
will  add  far  more  to  the  hauling  capacity  of  the  line  than  if  ex- 
pended to  reduce  gradients. 

1021.  Cutting  the  work  down  in  the  various  ways  suggested,, 
with  due  care  to  do  the  minimum  of  injury  to  its  efficiency,  $3000 
to  $5000  per  mile  may  be  made  to  grade  a  very  light  railway 
through  tolerably  broken  country,  and  this,  of  course,  under  fa- 
vorable circumstances,  may  be  reduced  much  lower.  For  such 
lines,  intelligently  planned,  there  is  and  will  probably  always  be 
a  very  wide  field.  The  trouble  is  that  the  economy  is  too  often 
given  a  wrong  direction,  and  the  item  which  is  ordinarily  the 
first  attacked — the  rail-section — is  one  of  the  last  of  all  to  attempt 
to  economize  in. 

1022.  This  ma^^  perhaps,  be  made  still  clearer  if  we  revert  to  the  rail 
question  for  a  moment  to  consider  a  little  more  exactly  the  relations 
OF  RAIL  TO  TRACK-LABOR.  Where  is  money  for  improving  track  best 
expended — in  increasing  the  rail-section  or  in  more  track-labor  ?  The 
stiffer  the  rail  the  less  perfect  need  be  the  supports  of  the  road-bed  for 
equal  excellence ;  but  it  is  sometimes  claimed  that  this  needed  support 


CHAP.   XXII.^LIGHT  RAILS  AND  LIGHT  RAILWAYS,    759 

can  be  more  cheaply  obtained  by  putting  a  little  more  work  into  the  sur- 
facing, especially  when  extreme  economy  in  first  cost  seems  necessar^^ 
It  hardly  needs  more  than  a  few  contrasting  figures  to  see  that  this  is 
more  an  impression  than  a  well-founded  belief. 

1023.  To  increase  the  weight  of  rail  10  lbs.  per  yard  requires,  in  round 
numbers,  16  tons  per  mile,  costing,  at  the  even  figure  of  $30  per  ton,  $480 
per  mile,  the  interest  on  which  is. 

At  5  per  cent,  At  10  per  cent,  At  20  per  cent, 

$24.00.  $48.00.  $96,00. 

Equal  to  a  cost  in  cents  per  train-mile,  assuming  various  numbers  of 
trains  per  day  each  way,  of 

, Cents  per  Train-Mile , 

At  5  p.  c.  At  10  p.  c.  At  20  p.  c. 

1  train  per  day,      ......  3,29  6.58  13.16 

2  "  "  1.64  3.29  6.58 

10     "  "  0.33  0.66  1.32 

20     "  "  ....  .0.16  0.33  0.66 

1024.  The  common  expenditure  on  raising  and  surfacing,  ballast,  etc., 
is  about  10  cents  per  train-mile,  as  an  average,  and  from  that  to  15  or  18 
cents  per  train-mile  on  roads  of  very  light  traffic ;  and  contrasting  this 
sum  with  the  figures  above,  we  see  at  once  that  on  a  road  of  any  consid- 
erable traffic,  vvrhich  is  a  kind  of  road  we  are  not  now  considering,  the 
stability  gained  by  adding  10  lbs.  per  yard  to  the  weight  of  a  rail  would 
give  far  more  for  the  money  invested,  at  any  probable  rate  of  interest, 
than  the  expenditure  of  an  equivalent  sum  annually  on  additional  track- 
labor  for  lining  and  surfacing.  On  a  road  running  20  trains  per  day, 
even  if  it  cannot  get  money  at  less  than  10  per  cent,  the  interest  charge 
of  $48  per  year  per  mile  amounts  to  but  0.33  cents  per  train-mile.  There- 
fore the  extra  5  lbs.  per  yard  has  only  to  save  less  than  3^  per  cent  of 
track-labor  to  be  a  paying  investment.  It  is  unquestionable  that  far 
more  than  that  might  be  saved,  and  yet  maintain  equal  condition,  even 
when  the  rail  was  a  tolerably  heavy  one. 

1025.  As  respects  the  extreme  of  light-traffic  roads,  especially  those 
built  at  great  cost  for  capital,  it  must  be  admitted  that  the  case  is  not  so 
clear  as  that.  In  fact,  for  the  extreme  of  thin  traffic  and  scant  capital, 
say  one  train  per  day  and  20  per  cent  cost  of  capital,  it  seems  at  first  sight 
clear  that  it  will  not  pay  to  increase  the  rail-section  be3^ond  what  safety 
requires,  as  the  cost  of  interest  on  even  5  lbs.  per  yard  extra  weight  of 
rail  will  in  that  case  be  6.58  cents  per  train-mile. 


760    CHAP.   XXII.— LIGHT  RAILS  AND  LIGHT  RAIL  WA  YS.. 

1026.  But,  premising  that  this  extreme  case  can  but  rarely  be  ap- 
proached in  practice, — because  (i)  there  are  few  even  of  the  lightest-traffic 
roads  which  do  not  run  more  than  one  train  each  way  per  day;  and  (2) 
few  roads  are  so  poor  that,  if  the  case  is  properly  presented,  they  cannot 
raise  a  moderate  additio7ial  capital  for  betterments  which,  whatever  the 
profit  on  the  enterprise  as  a  whole,  will  return  20  per  cent  profit  on  their 
own  separate  cost, — it  ma}^  be  reasonably  maintained  from  the  result  of 
experience  that  even  in  this  extreme  case  the  extra  weight  of  rail  is  the 
best  use  which  can  be  made  of  the  money.  The  very  least  which  can 
possibly  be  spent  on  mere  track-surfacing  and  maintenance  (par.  124)  to 
keep  it  in  fairly  safe  condition  for  the  passage  of  one  train  per  day,  is 
from  $100  to  $125  per  mile,  with  $80  to  Sioo  additional  for  ties,  or,  say, 
$200  in  all,  excluding  perhaps  $100  more  for  yards  and  miscellaneous. 
The  cost  of  the  5  lbs.  per  yard  extra  weight,  even  at  20  per  cent  interest 
on  capital,  is  only  $48  per  year,  for  which  slight  increase  of  one  fifth  or 
one  sixth  in  the  interest  charge  on  rails  we  have  just  seen  (Tables  195, 
196,  197)  that  we  obtain  an  average  increase,  in  a  very  light  rail,  of  fully 
50  per  cent  in  the  three  elements  of  strength,  stiffness,  and  durability. 
Granting  a  road  to  be  so  poor  that  no  increase  whatever  in  total  charges 
can  be  borne  for  any  betterment,  however  great,  beyond  absolute  neces- 
sities, is  it  certain  that  so  great  a  difference  in  the  stability  of  the  rail 
will  not  enable  one  fourth  of  the  otherwise  minimum  track  expenditure 
to  be  saved,  while  yet  leaving  the  track  as  safe  and  good  as  before  ?  It 
is  fairly  even  balance,  indeed,  under  this  extreme  supposition.  Unless 
the  rails  were  very  light  indeed,  it  probably  would  not  pay  to  increase 
their  weight ;  but  it  is  difficult  to  escape  from  the  conclusion  that  under 
any  ordinary  conditions,  with  the  lightest  traffic,  it  plainly  will  pay  to 
use  a  tolerably  heavy  rail  before  relying  on  track-labor  to  make  up  by 
better  surfacing  for  its  deficiency  of  strength,  simply  to  save  a  slight  ad- 
ditional investment  of  capital. 

1027.  If  so,  then  as  the  traffic  increases  up  to  a  comfortable  average, 
as  to  six  or  eight  or  ten  trains  each  way  per  day,  there  becomes  plainly 
an  immense  economy  in  using  heavy  rails  to  save  track-labor,  so  much 
so  as  to  indicate  strongly  that  the  very  curious  similarity  in  weight  of 
rails  used  on  all  roads  in  this  country  above  the  poorest  class,  despite  the 
great  difference  in  volume  of  traffic,  is  due,  not  so  much  to  the  use  of  too 
heavy,  rails  on  light-traffic  roads,  as  the  use  of  far  too  light  rails  for  true 
economy  on  our  more  important  lines,  as,  for  instance,  60-  or  65-lb.  rails 
on  trunk  lines  which  would  be  acting  more  wisely  to  use  80-  or  90-  or 
loo-lb.  rails.     The  difference  is,  however,  that  such  lines  are  rich  enough 


CHAP.    XXII.— LIGHT  RAILS  AND  LIGHT  RAILWAYS.    76 1 

to  stand  the  resulting  loss,  whereas  a  poor  road  which  permits  its  poverty 
to  destroy  it  by  buying  an  over-light  rail,  cannot.  Some  of  our  more 
prosperous  lines  have  recently  begun  to  break  through  this  rule  by  using 
what  are  now  called  very  heavy  rails,  but  the  exceptions  are  not  yet  so 
numerous  as  to  do  more  than  prove  the  rule.  It  is  in  every  way  prob- 
able that  within  a  few  years  8o-lb.  or  90-lb.  rails  will  be  the  rule,  and 
lighter  rails  the  exception.  The  inertia  from  past  precedents,  which 
have  come  down  to  us  from  the  days  when  rails  were  several  times  more 
costly  than  now,  will  in  time  be  overcome. 

1028,  We  are,  therefore,  again  and  more  strongly  driven  to 
the  conclusion,  that  the  one  thing  on  which  it  is  dangerous  to 
economize  is  the  item  which  is  often  cut  down  first  of  all — the 
weight  of  rail.  On  the  other  hand,  we  are  led  to  these  conclu- 
sions as  respects  the  details  of  alignment: 

1.  As  respects  the  minor  details,  distance,  curvature,  and  rise 
and  fall,  their  effects  to  increase  expenses  are  at  best  small,  and 
when  the  traffic  is  very  light  become  very  small.  They  are, 
therefore,  one  of  the  first  directions  in  which  close  economy  is 
warrantable  for  very  light  roads. 

2.  In  less  degree  the  same  is  true  of  ruling  grades.  Much 
increase  of  expenditure  to  obtain  lower  grades  than  a  careful 
study  of  the  ground  shows  to  be  possible  at  a  minimum  expense 
are  not  warrantable. 

3.  Both  the  above  conclusions  are  especially  true  when  the 
objectionable  details  may  be  readily  corrected  later,  when  and  if 
the  traffic  warrants  it. 

4.  Temporary  wooden  structures  to  decrease  the  immediate 
outlay  are  the  next  most  judicious  direction  for  economy. 

5.  Economies  which  decrease  the  stability  of  the  permanent 
way  are  the  most  objectionable  of  all. 

6.  Sources  of  local  traffic  which  can  be  reached  by  any  rea- 
sonable sacrifice  should  in  no  case  be  neglected. 


762    CHAP,   XXIII.— THE  ECONOMY  OF  CONSTRUCTION. 


CHAPTER  XXIII 

THE    ECONOMY    OF    CONSTRUCTION. 

1029.  We  must  necessarily  assume,  in  considering  the  pros 
and  C071S  of  many  of  the  details  of  construction  (as  in  par.  13)^ 
that,  the  construction  of  the  road  once  entered  on,  a  little  more 
or  less  money  will  not  be  a  serious  question,  but  that  means  will 
always  be  forthcoming,  at  some  rate  of  interest  or  other,  if  only 
it  can  be  shown  that  the  additional  investment  will  be  profit- 
able. 

But  while  this  is  so  far  true  in  a  small  way  that  it  is  the 
only  proper  guide  for  planning  the  details  of  a  line,  yet  it  is 
undeniable  that,  when  extended,  to  larger  questions,  affecting 
considerable  sums  of  money,  it  does  not  in  all  cases,  nor  in  many 
very  prominent  cases,  correspond  with  the  facts ;  which  are 
rather  that  a  certain  gross  sum  only  is  available,  and  when 
that  is  exhausted,  if  it  has  not  been  so  expended  as  to  com- 
plete all  the  more  essential  details  of  the  line,  the  company  be- 
comes bankrupt,  and  the  line  passes  into  other  hands — perhaps 
for  lack  of  only  a  small  fraction  of  the  sum  which  has  been  al- 
ready lavishly  expended. 

So  many  prominent  instances  of  this  have  happened,  that  it  is 
no  more  than  common  prudence  to  assume  that  there  is  immi- 
nent danger  of  it  in  the  case  of  every  new  line,  to  the  extent  of 
guarding  against  it  so  far  as  is  legitimately  possible. 

1030.  This  is  the  more  true  because  of  the  fact  alluded  to  on 
page  34,  that  money  for  new  lines  of  importance  or  for  extensive 
additions  to  old  lines  can,  as  a  rule,  only  be  raised  in  "  good 
times."  "  Good  times"  are  times  of  high  prices,  as  Fig.  246  il- 
lustrates very  forcibly,  and  are  naturally  followed  within  two  or 
three  years  by  "bad  times."     By  that  time  the  new  line  is  per- 


CHAP.   XXIII.— THE  ECONOMY  OF  CONSTRUCTION.    763 

haps  nearly  built,  and  needs  its  last  instalment  of  money,  which 
latter  is  often  a  sum  which  it  was  not  expected  to  need,  and 
which  was  even  refused  when   offered,  for  fear  of  letting  in  too 


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Fig.  246. — Prices  of  English   Iron  and   Steel  Rails  (shown  by  Shaded  Lines)  and  of 
American  Steel  Rails,  Refined  Bar  Iron,  and  No.  i  Pig  Iron,  from  1855  to  1886. 


many  ''on  the  ground-floor" — and  this  money  very  often  indeed 
has  to  be  raised  at  great  disadvantage,  if  raised  at  all. 

Unfortunately,  the  order  of  time  in  which  the  various  expen- 
ditures are  incurred  is  such  as  to  rather  increase  this  danger. 
Many  of  the  most  essential  expenditures  come  last  of  all,  and 
many  of  those  which  may  be  most  harmlessly  curtailed  or  post- 
poned come  first. 

The  locating  engineer  is  in  particular  danger  of  overloading 
his  company  in  this  way,  because,  from  the  order  of  time  in 
which  his  work  is  done,  he  in  effect  hypothecates  a  large  part  of 
its  funds  to  meet  expenses  which  are  not  fully  defrayed  until 
near  the  very  end  of  construction.  Prudence  indicates,  there- 
fore, that  whenever  there  is  even  the  slightest  doubt  of  securing 
the  money  necessary,  the  work  should,  from  the  first  (par.   7), 


764    CHAP.   XXIII.— THE  ECONOMY  OF   CONSTRUCTION. 

be  conducted  on  the  assumption  that  only  a  given  minimum 
sum  will  be  certainly  available,  and  that  from  it  enough  should 
be  reserved  to  cover  the  most  necessary  items  at  least.  The 
question  then  arises  :  In  what  direction  will  close  economy  do 
least  harm  ? 

So  far  as  it  goes,  the  preceding  chapter  is  an  answer  to  this 
question,  for  the  economies  least  harmful  to  a  light  road  are 
likely  to  be  also  least  harmful  to  a  line  of  fair  to  large  prospective 
traffic.  It  is,  however,  not  a  complete  nor  entirely  pertinent  an- 
swer. 

1031.  Perhaps  the  first  of  all  directions  in  which  economy  should 
be  sought,  or  rather  the  last  one  in  which  expense  should  be  in- 
curred, is  in  the  building  or  purchase  of  branches  during  the 
period  of  original  construction.  There  are  exceptions  to  this 
rule,  as  there  are  to  all  rules  ;  but  as  a  rule,  a  point  so  important 
that  a  branch  to  it  cannot  be  legitimately  postponed  until  the 
main  line  is  finished,  is  so  important  that  the  main  line  should 
be  carried  through  it.  Only  in  the  event  that  all  other  expenses 
are  certainly  provided  for,  should  the  construction  of  main  line 
and  branches  be  undertaken  simultaneously. 

To  give  only  a  single  example  of  the  importance  of  this  rule,  the  Canada 
Southern  Railway  Compan)-,  while  it  was  building  its  main  line  to  Chicago, 
carried  on  simultaneously  the  construction  of  the  St.  Clair  branch,  62  miles, 
and  an  extension  into  Michigan  from  St.  Clair;  the  Toledo  and  Detroit  branch, 
52  miles;  and  also  involved  itself  in  expenses  to  control  an  existing  line  to  Ni- 
agara Falls.  Had  the  money  which  went  into  these  desirable  but  subordinate 
lines  been  concentrated  on  its  main  line,  the  latter  would  probably  have  been 
completed  to  Chicago,  and  would  then,  probably,  have  secured  enough  traffic 
to  have  saved  its  projectors  from  the  almost  total  loss  which  the  panic  of  1873 
brought  upon  them,  in  spite  of  certain  unfavorable  circumstances. 

1032.  Allied  to  the  question  of  building  branches  is  that  of 
double-tracking  during  original  construction.  If  there  is  any 
reasonable  doubt  of  securing  funds  to  carry  through  the  entire 
enterprise  successfully,  opening  a  single  track  only  at  first  is  cer- 
tainly the  next  most  reasonable  method  for  a  temporary  econ- 
omy, to  insure  that  the  means  on  hand  shall  not  give  out  before 
the  line  is  in  working  order,  and  on  a  business  footing.     If  it  be 


CHAP.    XXIII.— THE  ECONOMY  OF  CONSTRUCTION,    765 

reasonably  certain  that  a  double  track  will  be  needed  in  the  near 
future,  all  masonry  structures  may  be  built  at  once  for  double 
track,  which  will  involve  but  a  small  addition  to  the  total  cost  of 
the  road — ordinarily  not  over  five  per  cent,  and  often  much  less. 
If  it  appear  still  more  certain  that  a  double  track  will  be  speed- 
ily needed,  even  the  grading  may  be  done  in  the  first  instance 
for  double  track,  and  grading  and  masonry  together  will  not  or- 
dinarily increase  the  immediate  capital  required  more  than  10 
to  15  per  cent. 

But  as  both  the  grading  and  masonry  for  double  track  can 
ordinarily  be  done  to  somew^hat  better  advantage,  on  the  whole, 
after  the  track  is  laid  than  before,  the  expediency  of  doing  even 
this  much  immediate  work  to  provide  for  the  future  is  question- 
able, unless  the  financial  condition  of  the  line  is  very  strong;  and 
the  following  items  for  double  tracking,  at  least,  can  always  be 
postponed  to  advantage  till  the  line  is  opened, — even  if  it  is  fully 
expected  to  immediately  proceed  with  double  tracking,  and 
funds  for  it  appear  to  be  certain, — viz.,  the  bridging,  ties,  rails, 
and  ballasting. 

1033.  In  IRON  BRIDGING  there  is  not,  contrary  to  what  is  gen- 
erally imagined,  any  economy  worth  taking  the  slightest  chance 
for,  in  building  double-track  bridges  instead  of  two  parallel 
single-track  bridges.  The  weight  of  a  double-track  bridge  is 
increased  about  90  per  cent  over  a  single-track  bridge  of  the 
same  span,  and  for  the  same  live  load ;  and  although  the  cost  of 
the  structure  is  not  increased  in  quite  the  same  proportion,  yet 
when  we  take  into  consideration  (i)  even  a  year  or  two's  interest 
at  ordinary  cost  of  capital ;  and  (2)  the  depreciation  and  possi- 
ble great  need  of  the  invested  capital  in  the  dark  days  of  the 
first  operation,  the  petty  saving  is  not  to  be  considered  in  com- 
parison. 

There  is  also  a  certain  considerable  operating  advantage  in 
having  independent  bridge-spans  for  each  track,  although  the 
single  structure  is  unquestionably  the  most  pleasing  to  the  eye. 
An  accident  to  one  structure  leaves  the  other  one  available. 

The  superstructure  of  the  double  track  complete,  on  a  line 


*]66   CHAP.   XXIII.— THE  ECONOMY  OF  CONSTRUCTION. 

requiring  double  track,  will  ordinarily  cost  $10,000  per  mile — a 
sum  which  has  repeatedly  made  all  the  difference  between  suc- 
cess and  failure. 

If  any  line  could  be  justified  by  the  nature  of  its  expected  traffic  in 
laying  a  double  track  at  once,  it  was  the  West  Shore  Railroad,  but  had 
this  policy  been  adopted  by  that  line  in  respect  to  the  double  track  and 
some  similar  matters,  it  would  probably  have  saved  it  from  bankruptcy. 

1034,  In  Fig.  247  is  given  a  diagram  prepared  by  the  writer  from  va- 
rious data,  but  chiefly  from  formula  for  estimating  the  weight  of  bridges 
given  in  a  valuable  paper  by  Geo.  H.  Pegram,  C.E.,  a  bridge  engineer  of 
large  experience  (Trans.  Am.  Soc.  C.  E.  1885),  which  shows  graphically 
several  things  of  importance  in  respect  to  bridges. 

It  shows,  first,  how  nearly  a  double-track  bridge  comes  to  being 
double  the  weight ;  seco7idly,  how  little  saving  is  effected  by  building 
bridges  to  carry  light  loads ;  thirdly,  the  point  at  which  the  saving 
effected  by  using  steel  instead  of  iron  becomes  important;  -ssidi, fourthly, 
the  comparative  weight  of  various  spans  by  inspection. 

If  the  truths  which  the  eye  readily  grasps  from  this  diagram  were 
more  generally  understood  and  acted  on,  there  would  probably  be  less 
bad  practice  in  railway-bridge  construction. 

1035.  The  third  least  objectionable  direction  for  economy  is 
the  bold  adoption  of  temporary  lines  where  permanent  works 
of  great  cost  will  otherwise  be  required;  meaning  by  "tempo- 
rary lines"  not  those  intended  merely  for  construction  purposes 
or  for  use  until  the  permanent  works  can  be  completed,  but  lines 
good  enough  for  several  years'  use  at  least  without  any  great 
loss,  leaving  the  better  permanent  line  to  be  constructed  only 
when  it  is  certain  that  the  traffic  justifies  and  requires  it,  and 
means  are  available.  Considerable  amounts  of  distance,  curva- 
ture, and  rise  and  fall  will  not  cause  a  dangerous  loss  in  opera- 
tion for  a  few  years,  if  used  only  on  the  rougher  sections  as  a 
substitute  for  more  costly  works  later,  and  will  enable  the  im- 
mediate outlay  on  the  usually  short  sections  (par.  1005),  where  the 
most  costly  works  are  concentrated,  to  be  very  materially  reduced 
in  many  cases,  as  well  as  enable  the  line  to  be  opened  before  an 
impending  crash  comes.  The  same  is  true  in  less  degree  of  the 
use  of  TEMPORARY  PUSHER  GRADES  of  an  objcctionablc  character, 
but  not  so  bad  as  to  prevent  the  handling  of  through-trains. 


THE  ECONOMY  OF  CONSTRUCTION. 


767 


This  diagram  shows  the  shipping  weight  of  iron,  including  an  all- 
iron  floor,  except  ties  and  guard-rails.     The  narrow-gauge  bridges  are 
for  quite  Hght  engines,  as  shown  in  Fig,   248.     The  slight  effect  of 
rolling  load  to  increase  weight  is  perhaps  more  strikingly  shown  in 
itt^^r^     Table  200.     The  formulae  on  which  it  was  constructed  are  given  near 
the  end  of  the  last  chapter. 


Fig.  247. — Diagram  of  the  Compara- 
tive Weights  of  Iron  in  Bridges 
OF  Various  Spans  and  for  Various 
Rolling  Loads  shown  in  Fig.  248. 

(See  also  Table  200.) 
[The  base  of  the  diagram  for  spans 

of  less  than  200  feet  is  at  the  side.] 


768    CHAP.    XXIII.— THE  ECONOMY  OF  CONSTRUCTION. 

1036.  The  fourth  least  objectionable  economy,  but  one  which, 
like  the  preceding,  from  its  coming  among  the  first  in  order  of 
time,  is  apt  to  be  one  of  the  last  practised,  is  the  adoption  as  a 
standard,  for  the  entire  line,  of  a  systematic  economy  (in  money, 
but  not  in  time  or  care)  in  respect  to  the  minor  details  of  align- 
ment. The  pros  and  cons  of  this  question  have  been  discussed 
so  fully  in  the  preceding  chapter  that  we  need  not  further  en- 
large upon  it. 

In  these  five  ways  (with  which  perhaps  the  use  of  timber 
STRUCTURES,  such  as  are  shown  in  Fig.  249,  might  make  a  sixth) 
a  very  large  economy  may  be  practised  which  will  almost  assure 
that  any  project  with  any  merit  whatever  will  be  so  little  bur- 
dened by  its  capital  account  that  it  will  be  able  to  live  on  what  it 
can  get  to  live  on,  even  if,  as  it  usually  is,  it  is  far  below  its  ex- 
pectations. 

1037.  Beginning  now  at  the  other  end  of  the  question,  the 
most  objectionable  of  all  ways  of  economizing  is  much  the  com- 
monest of  all,  for  reasons  already  sufficiently  discussed  in  Chap. 
III.,  omitting  to  go  into,  as  well  as  to,  the  terminal  cities,  and 
other  important  traffic  points  on  the  line.  This  error  very  largely 
arises  from  the  fact  that  it  is  an  expenditure  which  comes  late  in 
the  history  of  construction,  or  can  be  made  to  do  so. 

Probably  the  next  most  serious  injury  which  can  happen  to  a 
line  is  neglect  to  secure  best  possible  ruling  grades,  but  this 
more  often  happens  from  a  lack  of  care  and  skill  than  from  a  de- 
sire to  economize,  since  the  expenditure  is  incurred  earl}^  in  the 
history  of  construction  and  the  importance  of  favorable  grades  is 
more  generally  understood  than  the  best  manner  of  securing  them. 

1038.  Barring  this  error,  the  next  worst  form  of  economy 
which  can  afflict  a  line  is  what  is  more  emphatically  than  ele- 
gantly called  a  "cheap  and  nasty"  style  of  construction:    Light 

RAILS,  POOR  TIES,  THIN  BALLAST,  NARROW  WOOD-BEDS,  POOR  MA- 
SONRY, and  LIGHT  BRIDGES.  Thcsc  defects  really  save  but  little 
money,  while  the  expense  and  the  bad  name  which  has  resulted 
from  them  have  sapped  the  life  of  many  a  line.  It  is  far  better 
to  economize  closely  in  all  the  details  of  location  but  the  grades, 


CHAP.    XXIIL—THE  ECONOMY  OF  CONSTRUCTION.    769 


and  sometimes  even  in  the  grades  themselves,  than  to  do  this. 
The  difference  between  a  thoroughly  adequate  and  solid  road- 
bed, and  as  inferior  a  one  as  it  will  seem  possible  to  tolerate,  will 


^€<^i. 


'dll\ 


6-rJ--  6 


Cp  Cp  (f)  rh  rh  rh  'S^ 


0^ 


'l\-5''9'A:4~c\-ff'-6*-7'j''--^'-JO'  S..8\4./0-  -^ 


Si      I 


C&^ 


T T r~^ — ^ A T   ^         '       '  J    ' 


am 


fi 

3000  'Jt^r/g. 

mMMm 


^■^^.f4^j^^//V  -<g  M-^H-'^.^^/ 


rh^n  m  OOP    rh  C)  O  O  ^p^ 


Tf'cuun 

sooo 


■6-* 


Fig.  248.— Engine  Loads  used  in  Computing  the  Weights  for  Fig,  247. 

rarely  be  more  than  $2000  to  $3000  per  mile;  and  on  work  at  all 
heavy  it  is  not  difficult  to  save  that  sum  by  economizing  in  loca- 
tion, using  temporary  but  solid  wooden  structures,  and  the  other 
expedients  noted  above.  These  latter  economies  will  not  add 
49 


770    CHAP.    XXI I  I. —  THE  ECONOMY  OF  CONSTRUCTION. 


t-3„0y^. .  jr .  a:  -^3.0' 


a'a-g^tra-a-^rtrfrBrgir'—. 


■6w.11, 


'-Q ^-^^ 0 

STAHDARO    TRESTLE    BRIDGE  .-  15'.  9"  BENTS  . 
C.  M.  &    ST.  P.    Ry. 

Scale     trf  JFeet,. 


-.^ 


h ^-■^'    — -i 

PLAN   OP  WING    PANEL. 


STANDARD    PLAN     OF    CATTLE     GUARD. 
CM.  &  S7.  P.  Rr. 

ScclIc    <re   Tejpb, 


PILE  ABUTMENT.         PlLEABUTME 


o  o 
o  o 

G  O 


Centre  Jyine    rf 


£?  .-P}"'  sf..  Sjii€s  f 


:-j-o  o 
■4-0  o  .:■ 

.-3-0  O^ 


.f-O  o  o 

:  o  o  o 

5  o  o  Q 

"   O  Q  0 


0  O  .-3-0  01  ,;    Q     O    O 

o  o  ,"f-o  o'i  i  o   o   o 

Uli  fid  Q^0 

STANDARD     PLAN    OP    PILE    PIER     AND    ABUTMENT     FOR  HOWE   TRUSS    BRID.S.-"^ 
CM.  &   sr.  P.  Rr. 

ScaU.     cf   Ftel  . 


o  t 

HI     0) 

^.     , 
^    rt  1^   iT 

<  '5;   ,,   S 

<  a:   C  o 

g  ^^^^ 

>'-''"  p 

^  ^  ij  .- 
^  ■""  .^  ^ 

mi 

^   c  0-  5 

Q    p  ir.   y 

J   c  =  ii 

[:  -p=-3 

<  0)       cr 

(^    S  a;  riS 

f-i  '^  "^     - 

r"       C/j    .u     r- 

O  <U  O  c« 

fe  S  «  rf 

C  "  o 

<  C  OJ  w 

0  ^3    .. 

1  -a  ^s 

B      I     ?^ 


CHAP.    XXIII.—  THE  ECONOMY  OF  CONSTRUCTION.    77 1 

materially  to  expenses  during  the  first  ten  or  fifteen  years  on 
operation,  whereas  a  poor  and  flimsy  superstructure  entails  a 
large  and  constant  addition  to  maintenance  expenses. 

1039.  The  loss  which  results  from  light  bridges  is  propor- 
tionately quite  as  great  as  from  light  rails,  as  is  made  evi- 
dent enough,  without  further  discussion,  from  Figs.  247-8  and 
Table  200.  The  proportionate  loss  from  poor  masonry  is  even 
greater,  it  is  far  better  to  put  up  temporary  wooden  structures 
altogether,  than  to  put  up  such  flimsy  masonry  as  is  often  built. 
That  so  very  large  a  part  of  the  masonry  put  up  on  new  Ameri- 


Table  200. 

Comparative  Weight  and  Cost  of   Bridges,  taking   Bridges  of  "  T 
(Typical  Consolidation)  Type,  Fig.  249,  as  Unit. 


Class  of  Load, 

Minor  Spans  of— 

(Fig.  249.) 

30  ft. 

50  ft. 

Soft. 

104  ft. 

150  ft. 

20ll^  ft. 

T 

c        

100 
98.74 
97-73 

100 
98.05 
96.47 

100 
97.10 
94-56 

100 

96.33 
93.16 

100 
94.98 
90-75 

100 
94.00 
88.61 

M 

(Uniform  at  75.00). 


Larger  Spans. 


20l5^  ft. 

320  Feet. 

420  Feet, 

516  Feet. 

• 

Iron. 

Steel. 

Iron. 

Steel. 

Iron. 

Steel. 

T 

c. 

100 

93-34 

100 
91. II 

100 

89-55 

100 
88.77 

100 
89-55 

100 
88.21 

100 

89-55 

The  above  shows  at  a  glance  that  the  effect  of  rolling  load  on  weight  of  bridges  is 
small,  and  the  following  will  perhaps  more  fully  show  how  petty  is  the  economy  : 


For  engines  weighing  (tons) 

Or  in  the  proportion  of 

And  for  a  load  behind  engine,  per  foot  of  (lbs.) 
Or  in  the  proportion  of 


"  Typical " 
Cons'n. 


86.0 
100. 
3,000 


Consolida- 
tion. 


80.07 
93-8 
2,240 
85-4 


Mogul. 


138.0 
80.2 

1,820 
73-0 


772    CHAP.   XXII L— THE  ECONOMY  OF  CONSTRUCTION. 


Table  200. — Contiiiued. 


Per  Cent. 

Per  Cent. 

Engine, 

6.2 

19.9 

Cars, 

14.6 

27.0 

30  ft. 

1.26 

2.27 

50  " 

1-95 

3-53 

80  " 

2.90 

5-44 

104  " 

3.67 

6.84 

^5°  '  , 

5.02 

9-25 

2013^  ft. 

6.00 

11-39 

Giving  a  loss  percent  in  rolling  load  over  the  strongest  j 
type  of  bridge  of \ 


The  saving  per  cent  in  weight  (not  cost)  of  bridge  is  J 

only  —  for  spans  of j 

I 

L 


Beyond  these  spans  the  comparative  difference  becomes  greater,  so  that  we  have  for 
the  difference  between  a  rolling  load  of  the  "  typical  "  and  ordinary  Consolidation  type 
(neglecting  the  Mogul  type)  the  following  : 

r   2oii^ft. 
Forspansof •]    S^o      ;; 

Thus  even  the  largest  spans  do  not  increase  in  weight  as  fast  as  they  increase  in 
capacity,  and  on  the  shorter  and  more  common  spans  an  increase  of  only  3  to  6  per  cent 
in  weight  gives  15  to  25  per  cent  increase  in  carrying  capacity. 


Iron. 

Steel. 

6.66 

8.89 

10 -45 

10.23 

10.4s 

11.79 

10.45 

can  lines  should  give  out  within  a  few  years,  as  it  does,  either 
because  the  foundations  were  inadequate  or  were  not  properly 
protected  against  wash,  or  the  stone  poor,  or  laid  dry,  or  the 
spans  inadequate,  reflects  little  credit  on  engineers. 

1040.  A  still  less  reasonable  and  creditable  mode  of  economy 
is  CUTTING  DOWN  THE  ROAD-BED,  especially  in  cuts.  The  saving 
is  but  trifling,  and  the  effect  on  maintenance  expenses  very  un- 
favorable, since  it  forbids  proper  ditching,  impedes  access  of  the 
sun  to  the  road-bed,  and  makes  difficult  to  apply  a  proper  coat  of 
ballast  and  leave  any  ditch  at  all.  The  narrowest  road-bed  in 
earth  should  be  20  ft.,  especially  in  light  work,  or  on  light  grades 
having  many  long  low  cuts  on  them,  which  latter  are  very  difficult 
to  drain.  In  fills,  a  15-ft.  or  i6-ft.  road-bed  is  none  too  wide,  and 
will  rarely  be  found  to  be  much  wider  than  is  necessary  to  hold 
the  ballast  when  the  track  is  laid. 

1041.  Cutting  down  the  coat  of  ballast  is  likewise  one  of  the 
most  costly  economies  in  which  a  road  can  engage.  Sometimes 
it  is  necessary,  because  ballast  is  not  readily  available,  and  to 
some  extent  good  ditching  may  be  substituted  for  it,  but  econ- 
omy requires  that  both  ditching  and  ballast  should  be  good. 


CHAP.    XXIII  — THE  ECONOMY  OF  CONSTRUCTION.    'J'/ 2, 

It  was  a  saying  of  the  late  Charles  Collins,  the  lamented  chief- 
engineer  of  the  Lake  Shore  &  Michigan  Southern  Railway,  that 
*'two  feet  of  ditch  is  worth  one  foot  of  ballast,"  and  this  has  a 
foundation  of  truth  at  least,  as  was  shown  by  the  results  of  free 
ditching  on  the  Lake  Shore  road.  It  may  plausibly  be  claimed 
that  when  a  road  is  neither  well  ditched  nor  well  ballasted  a  lim- 
ited amount  of  money  will  accomplish  more  good  if  spent  for 
ditching  than  for  ballasting,  and  there  is  a  certain  absurdity  in 
putting  on  a  thick  coat  of  clean  ballast  in  a  cut  where  the  ditch- 
ing is  so  imperfect  that  there  can  hardly  be  said  to  beany.  Nev- 
ertheless, more  and  better  ballast  is  a  crying  need  on  many  lines  of 
considerable  traffic,  if  not  on  most  lines  not  of  the  first  rank,  and 
if  it  were  more  generally  realized  how  cheaply  ballast  can  be  sup- 
plied by  improved  modern  appliances,  and  how  greatly  it  would 
decrease  wear  and  tear  and  maintenance  expenses,  both  of  track 
and  of  rolling-stock,  as  well  as  sometimes  increase  by  a  car  or 
two  the  length  of  trains,  there  would  not  be  so  many  roads  as 
there  are  practising  an  expensive  economy  in  this  item. 

1042.  One  reason  why  ballasting  is  often  so  costly,  even  with  all  the  ad- 
vantages of  steam-shovels  and  unloading  ploughs,  is  an  abuse  (or  what  is  often 
such)  in  THE  HANDLING  OF  BALLAST  TRAINS  which  may  Well  be  noted.  Fair 
average  prices  for  ballasting  with  steam-excavators  and  gravel  trains  may  be 
taken  to  be  as  follows  : 

All  expenses  connected  with  loading 3  cts.  per  cu.  yd. 

Loading  and  delivering  on  road-bed,  10  mile  haul „ .  10    "      "        " 

20    "       " 15    "       " 

"  "  "  "  "  30    "       "     20    "      " 

Not  unfrequently,  however,  the  cost  will  rise  to  two  or  three  times  these  figures, 
because  of  interruption  of  trains. 

This  results  because  the  ballast  train,  in  disregard  of  all  considerations  of 
economy,  and  without  the  excuse  of  any  real  necessity,  is  all  but  universally 
treated  as  a  kind  of  outcast  or  pariah  among  trains.  The  extent  of  its  privi- 
leges is  embodied  in  the  stereotyped  formula  that  it  "has  permission  to  work 
between  A  and  B,  keeping  out  of  the  way  of  all  regular  trains."  What  that 
means,  on  a  road  doing  any  considerable  business,  with  all  the  necessary  delays 
for  clearing  the  track  "  ten  minutes  ahead  of  all  regular  trains'  time,"  and  for 
waiting  for  them  to  arrive  when  late,  is  an  enormous  proportion  of  lost  time  per 
day,  doubling  and  trebling  the  necessary  cost  of  delivering  ballast  on  the  track, 
not  only  in  many  but  in  most  cases. 


774      CHAP.  XXIII.  — THE  ECONOMY   OF  CONSTRUCTION. 

Nevertheless,  this  limitation  of  privileges  is  natural  enough  and  well  enough 
as  a  matter  of  permanent  rule.  A  ballast  train  cannot  be  anything  else  than  an 
irregular  train,  and  cannot  safely  be  given  any  rights  whatever,  except  by  spe- 
cial order  ;  but  therein  lies  the  difficulty.  Trains  are,  as  a  matter  of  fact, 
almost  all  run  by  special  order,  and  when  giving  such  order,  it  rests  entirely 
with  the  discretion  of  the  dispatcher,  within  wide  limits,  to  favor  one  train  or 
another  as  he  sees  fit.  This  discretion,  however,  is  rarely  exercised  to  prevent 
delays  of  ballast  trains,  which  cost  money,  rather  than  delays  of  regular  trains, 
which  do  not  directly  cost  money;  but  the  ballast  train  gets  from  the  dispatcher, 
improperly  and  unwisely,  much  the  same  kind  of  treatment  that  it  necessarily 
and  properly  has  in  the  printed  rules  and  time-tables. 

Now  a  regular  freight  train  is  earning  perhaps  $1.50  per  mile  run  and  cost- 
ing $1,  but  it  will  earn  no  less  and  cost  no  more  (barring  a  slight  loss  of  fuel) 
for  being  a  quarter  or  half  an  hour  more  or  less  upon  its  trips.  On  the  other 
hand,  the  total  expenses  for  running  a  steam-excavator  with  perhaps  three  or 
four  engines  at  work  to  handle  the  cars,  are  from  $100  to  $150  per  day.  A 
delay  to  any  one  of  these  trains  is  to  a  considerable  extent  a  delay  to  all  and  to- 
the  excavator  as  well,  and  a  delay  of  three  hours  per  day  to  these  trains  (which 
is  about  a  minimum)  means  the  loss  of  $1200  to  $1500  per  month. 

Under  these  circumstances  what  ought  to  be  done,  if  true  economy  is  to  be 
considered,  is  to  prepare  something  like  a  regular  schedule  for  the  movement 
of  these  trains,  from  day  to  day  and  from  week  to  week,  for  the  use  of  the  dis- 
patcher ;  to  provide  as  good  facilities  as  possible  for  communicating  orders  to 
them,  and  to  require  that,  whenever  and  wherever  it  is  possible  without  too 
great  delay,  the  gravel  trains  shall  be  favored  at  the  expense  of  the  ordinary 
freight  train. 

1043.  Supposing  the  delays  to  gravel  trains  to  have  been  re- 
duced to  a  minimum,  there  are  few  expenditures  so  directly 
profitable  as  to  procure  a  steam-excavator  and  ballast  plows, 
and  keep  two  or  three  trains  at  work  for  a  good  part  of  several 
seasons  increasing  the  depth  of  ballast.  Half  a  cubic  yard  per 
cross-tie  will  raise  the  track  some  8  in.,  and  where  the  road-bed 
is  wet  and  the  haul  not  too  great,  this  would  not  be  so  very  bad 
an  investment,  simply  as  a  preservative  of  cross-ties. 

An  additional  economy  for  this  kind  of  work  on  many  lines, 
and  one  deserving  of  more  frequent  use,  is  the  hauling  <  ;  side- 
dump  cars  loaded  with  ballast  on  regular  trains,  especially  way 
freight,  whenever,  as  is  frequently  the  case,  eight  or  ten  addi- 
tional cars  can  be  hauled  over  a  portion  of  the  division  as  welL 
as  not,  owing  to  more  favorable  gradients.     Many  types  of  cars 


CHAP.  XXIII.—  THE  ECONOMY   OF  CONSTRUCTION.      77$ 


suitable  for  this  purpose  exist  which  are  readily  dumped  by  one 
man. 

1044.  One  of  the  very  worst  places  to  economize  in,  but  for- 
tunately not  a  common  one,  is  in  the  cross-ties.  The  number 
of  these  cannot  be  too  great  for  economy,  until  they  become  so 
close  as  to  impede  tamping,  which  is  when  about  40  per  cent  of 
the  length  of  the  rail  rests  upon  ties.  Up  to  this  point  even  the 
weight  of  rail  may  be  judiciously  sacrificed,  if  necessary,  to  in- 
crease the  tie  support,  as  may  be  speedily  shown. 

Track  is  constructed  and  made  passable  by  the  use  of  three 
agencies  :  (i)  rails,  (2)  cross-ties,  (3)  tamping  under  the  ties. 
Some  proportion  of 
each  of  these  must  be 
used  to  maintain  a  sta- 
ble track,  but  in  pro- 
portion as  the  stabil- 
ity from  one  of  them 
is  increased,  that  required  from  one  or  both  of  the  others  may 
be  decreased.  If  we  have  a  stiffer  rail,  we  may  use  less  ties  and 
less  track-labor.     If  we  have  more  or  better  ties,  we  may  use  a 


Fig. 


>  ?.,-' 


Fig.  251. 

lighter  rail.  If  we  put  more  labor  into  maintenance,  we  may 
dispense  with  some  expenditure  on  either  rails  or  ties,  or  both. 
The  different  modes  of  yielding,  outlined  in  Figs.  250  and  251, 
which  occur  more  or  less  on  all  track,  may  be  assumed  to  arise, 
and  will  arise,  from    deficiencies   in   any  one   of   these   three   re- 


77^      CHAP.  XXIII.— THE   ECONOMY   OF   CONSTRUCTION. 

quirements,  either  the  rails  or  ties  or  tamping,  and  may  be 
cured,  in  part  or  whole,  by  spending  more  money  on  either  one 
of  them.  Assuming  as  a  standard  of  comparison  a  dy^^  in.  tie  8 
ft.  long,  spaced  2  ft.  apart,  or  2640  per  mile,  the  following  com- 
binations of  spacing  and  width  will  afford  an  equal  bearing-sur- 
face of  ties  on  the  road-bed  and  of  rails,  but  will  be  seen  to 
afford  a  very  unequal  support  to  the  rail  : 

Ties  per  mile 2,640        3,000  3,168  3,520 

Distance  apart,  centre  to  centre 24  in.  21.12  in.  20       in.  18  in. 

Average  width  of  face 8  in.  7.04  in.  6.67  in.  6  in. 

Clear  space,  tie  to  tie 16  in.  14.08  in.  13.33  in.  12  in. 

Comparative  stiffness  of  same  rail  for 

each  span 1,00         1.47  1.73  2.37 

Comparative  weight  of  rail  to  give  same 

stiffness , i.ooo  0.825  0.761  0.650 

The  method  of  determining  the  comparative  stiffness  and 
comparative  weight  of  rail  in  the  last  two  lines  is  the  same  as 
used  in  par.  992  for  rails,  and  need  not  be  repeated.  Whether 
we  compute  the  comparative  stiffness  of  the  rails  for  spans  from 
centre  to  centre  of  ties,  or  for  one  clear  span  between  ties,  or  for 
spans  omitting  one  tie,  as  in  Fig.  250,  the  result  is  the  same,  al- 
though the  absolute  stiffness  will  of  course  vary  greatly. 

1045.  Taking  the  extremes  of  the  table  above,  we  see  that  the 
addition  of  880  ties,  or  one  third  increase,  gives  so  much  addi- 
tional support  to  the  rail  that  (assuming  the  support  to  each  tie 
to  be  the  same)  a  rail  only  two  thirds  as  heavy  will  distribute 
the  load  as  well  from  tie  to  tie.  Not  forgetting  that  stiffness  is 
only  one  of  the  three  qualities  in  a  rail  which  are  gained  by  in- 
creasing its  weight,  this  great  difference  still  indicates  that  in- 
creasing the  number  of  ties  to  the  extent  of  practical  possibility 
(their  dimensions  remaining  the  same)  adds  much  more  to  the 
aggregate  stiffness  of  the  track  than  the  same  amount  spent  on 
rails ;  as  thus: 

The  cost  of  880  more  cross-ties  per  milCj  more  than  doubling 
the  stiffness  of  the  same  rail,  amounts — 

At  25  cents,  to  $220  =    7.14  tons  rails  at  $30  =  4.5  lbs.  per  yard. 
''  y:>      "         "     264=    8.80     "        "         "       =5.5    "       "       " 
"  40      "         "     352  =  11.73     "        "         "       =7.3    "       "       " 
"  50      "         "     440  =  14.67    "        "         "       =9.1    "       "       " 


CHAP.  XXIII.—  THE  ECONOMY   OF  CONSTRUCTION.      777 

Comparing  this  with  the  figures  in  Table  196,  giving  the 
comparative  stiffness  of  light  and  heavy  rails,  we  have  the  fol- 
lowing comparison  for  various  light  rails — for  which  rails  only 
the  comparison  is  at  all  close: 

Original  weight  of  rail, 20  lbs.         35  lbs.         50  lbs. 

Stiffness  in  do.  taken  as i.oo  i.oo  i.oo 

Adding  4.5  lbs.  per  yard  (=  cost  of  880  ties 
at  25  cents  each,  as  above)  makes  stiff- 
ness        1. 51  1.27  1. 19 

Adding  9.1  lbs.  per  yard  (=  cost  of  880  ties 

at  50  cents  each)  makes  stiffness     .     .     .      2.12  1.57  1.40 

Whereas  the  same  sum  spent  on  ties  in- 
creases the  stiffness,  as  above,  to 2.37 

1146.  While  the  addition  of  so  large  a  number  of  ties,  without 
decreasing  their  width,  can  rarely  be  practicable,  and  while  the 
comparison  is  not  strictly  exact  for  other  reasons,  this  does  indi- 
cate clearly  the  general  fact,  that  increasing  the  number  of  ties 
to  the  limit  of  convenience  is  a  cheaper  way  of  increasing  sta- 
bility than  increasing  the  rail-section,  even  for  very  light  rails. 
On  the  other  hand,  the  total  stability  which  is  obtainable  from 
ties  is  limited  by  the  number  which  it  is  possible  to  use,  so  that 
what  thes^  figures  in  fact  indicate  is  that,  in  endeavoring  to  get 
the  utmost  stability  at  the  least  cost,  the  first  essential  is  to  use 
ties  as  freely  as  is  possible,  and  the  next  essential  is  to  decide 
between  a  heavier  rail  and  more  tamping  to  supply  the  deficit. 

1047.  The  physical  limit  to  the  increase  in  number  of  ties,  of 
ordinary  standard  width,  is  probably  2800  per  mile;  but  if,  as  in 
the  first  table  above,  we  consider  the  width  of  the  ties  to  be  di- 
minished as  their  number  is  increased,  this  limit  is  considerably 
higher.  There  are  quite  a  number  of  roads  in  the  United  States 
which  use  3100  to  3300  narrow  ties  per  mile  with  very  satisfac- 
tory results.  Remembering  that  the  stiffness  of  a  rail  decreases 
as  the  cube  of  the  span,  it  is  obvious  that  by  dividing  up  the 
bearing-surface  among  a  greater  number  of  ties,  so  that  the  ag- 
gregate area  remains  the  same,  we  measurably  obtain  two  desir- 
able ends  at  once — we  give  much  more  efi"ectual  support  to  a 
weak  rail,  and  we  in  general  reduce,  instead  of  increasing,  the 
total  cost  of  ties,  since  the  cost  of  ties  will  usuallv  increase  faster 


'J'jZ      CHAP.  XXIII.— THE  ECONOMY  OF  CONSTRUCTION. 

than  the  required  minimum  face.  As,  therefore,  the  necessary 
space  between  ties  varies  approximately  with  the  width  of  face, 
and  is  about  twice  the  face  (so  that  full-width  ties  cannot  be 
used  with  very  narrow  spacing),  the  utmost  economy  would  seem 
to  require  that  narrow  ties  spaced  close  together  should  be  given 
a  decided  preference  at  the  same  cost  for  ties  per  mile  when  a 
light  rail  is  to  be  supported,  and  there  are  few  rails  indeed  in 
this  country  which  cannot  be  said  to  be  light  in  proportion  to 
the  duty  imposed  on  them.  It  could  not  rationally  be  expected^ 
indeed,  that  6-in.  ties  spaced  i8  in.  apart,  instead  of  8-in.  ties 
spaced  24  in.  apart,  would  increase  the  stiffness  of  a  light  rail 
from  1. 00  to  2.37,  as  the  figures  above  indicate;  yet  we  may 
justly  conclude  that  it  will  be  increased  very  greatly,  with  a  pos- 
sible decrease  in  the  total  cost  of  ties  as  well,  where  the  supply 
of  large  timber  is  small.  In  not  a  few  localities  ties  of  5-  or  6-in. 
face  can  be  had  for  but  little  more  than  half  the  cost  of  ties  with 
8-in.  face. 

1048.  A  great  error  is  often  committed  in  making  ties  too 
thin.  A  cross-tie  is  an  inverted  cantilever.  In  Fig.  251  we  have 
a  tie  yielding,  as  they  all  do,  more  or  less  under  a  load;  and  by 
inverting  Fig.  251  it  will  be  seen  that  we  may  consider  the  tie 
as  a  cantilever  beam,  supported  upon  two  piers  (the  rails)  and 
loaded  with  a  more  or  less  uniformly  distributed  load.  If  the 
tie  were  perfectly  stiff,  it  would  be  an  evenly  distributed  load, 
and  the  pressure  of  the  tie  upon  the  soil  would  be  uniform  for 
every  square  inch  of  its  bearing-surface.  If  the  tie  be  very  thin^ 
the  conditions  of  the  exaggerated  sketch  will  literally  obtain. 
The  middle  and  ends  of  the  tie  will  then  be  able  to  transmit  but 
little  pressure  to  the  ballast,  and  (since  the  total  pressure  trans- 
mitted must  in  any  case  be  the  same)  an  excessive  and  destruc- 
tive pressure  will  be  thrown  upon  the  road-bed  directly  under 
the  rails,  causing  rapid  deterioration  therein.  This  may  be 
shown  by  the  load-diagram  below  Fig.  251.  Let  us  suppose 
that  a  tie  be  so  thin,  or  the  nature  of  the  support  so  unyielding^ 
that  the  load  per  square  inch  directly  under  the  rail  is  three  times 
as  great  as  at  the  ends  and  in  the  middle,  as  shown  by  the  full 


CHAP.  XXIII.  —  THE  ECONOMY  OF  CONSTRUCTION.      7/9 

line  in  the  diagram  below  Fig.  251 — a  very  common  difference, 
if  not,  indeed,  one  almost  universally  exceeded  in  occasional  in- 
stances, even  on  a  very  good  track.  An  increase  of  stiffness 
which  would  double  the  load  on  these  lightly  loaded  extremities 
would  produce,  as  will  be  seen  from  the  diagram,  an  absolutely 
uniform  distribution  of  pressure,  and  although  this  can  never  be 
fully  realized,  yet  it  is  plain  that  it  may  be  approached. 

1049.  Now  the  stiffness  of  any  beam,  however  supported  or 
loaded,  is  in  proportion  to  the  cube  of  its  depth  (or  thickness  of 
tie)  and  of  its  lengths  between  supports  (or  the  gauge).  Any 
attempt  to  compute  from  these  facts  the  absolute  requirements, 
or  distribution  of  load,  with  a  given  tie  or  gauge,  would  be  pre- 
posterous. There  is  no  absolute  requirement,  since,  however 
well  maintained  the  track,  occasional  ties  are  badly  or  unequally 
supported;  and  since  the  load  is  far  more  than  sufficient  to  break 
any  tie  in  two  at  the  middle  if  only  supported  at  that  point  (a 
dead  load  of  14,000  lbs.  per  wheel  would  probably  break  such 
ties  the  first  time  it  was  imposed),  it  is  for  these  maximum  de- 
mands, and  not  the  average,  that  we  must  provide.  Therefore, 
speaking  comparatively  only,  and  taking  a  tie  6  in.  thick  as  the 
basis  of  comparison,  we  have  the  following: 

Thickness  of  Narrow-  (3  ft.)  gauge  Tie  of— 


Thickness. 

Comparative 
Stiffness. 

Equal  Stiffness. 

Equal  Strength, 

0.58 
1. 00 

1-59 
2.37 

3.18  in. 

3.82  ;; 
4.46  " 
5.10  " 

4.30  in. 
5.16    " 
6.02    " 
6.88    " 

From  this  it  is  clear  that  although  the  nominal  bearing-sur- 
face of  a  tie  is  not  increased  by  increasing  its  thickness,  yet  that 
the  effective  bearing-surface  is  likely  to  be  very  materially  in- 
creased by  a  very  moderate  increase  of  thickness.  By  increasing 
the  thickness  from  5  to  6  in.,  we  nearly  double  the  stiffness  ;  by 
increasing  it  from  6  to  7  in.,  we  increase  the  stiffness  59  per 
cent,  giving  the  effect  outlined  below  Fig.  251,  in  which  the  full 
line  shows  the  assumed  distribution  of  pressure  with  a  tie  6  in. 
thick,  and  the  dotted  line  the  effect  on  the  latter  of  thickening 


780      CHAP.  XXIII.— THE  ECONOMY  OF  CONSTRUCTION. 

the  tie  i  in.     Economizing  in  the  thickness  of  ties,  therefore, 
would  seem  to  be  one  of  the  poorest  ways  of  saving  money. 

1050.  This  is  more  fully  seen  by  comparing  the  effect  of  differ- 
ence of  length.  It  cannot  be  attempted  to  consider  the  matter 
in  detail,  but  a  tie  which  is  under  fair  conditions  to  permanently 
fulfil  its  office  of  distributing  the  load  may  be  considered  to 
curve  into  the  three  circular  arcs  shown  in  Fig.  251,  from  which 
it  will  be  apparent  that,  under  whatever  assumptions  as  to  the 
curve  of  flexure,  there  is  a  clear  limit  to  the  useful  increase  of 
length  in  ties  at  a  point  considerably  within  a  length  of  twice 
the  gauge,//'.  If  the  tie  be  made  longer,  as,  for  instance,  ex- 
tended to//',  or,  still  worse,  to  ^  g' ,  either  the  extra  length  will 
carry  little  or  no  load  (which  is  most  likely),  or,  if  the  support 
nearer  the  rail  has  given  way  so  as  to  throw  load  upon  it,  it  will 
be  very  liable  to  break  the  tie. 

If  the  tie  be  made  shorter,  the  load  thrown  on  the  middle  of 
the  tie  will  be  disproportionately  increased  until,  if  we  conceive 
the  tie  cut  off  close  to  the  outside  edge  of  the  rail,  the  load  per 
square  inch  will,  in  the  first  place,  be  very  greatly  increased, 
and,  in  the  second  place,  the  strength  of  that  portion  of  the  tie 
between  the  rails,  considered  as  a  beam,  is  diminished  by  about 
one  half  and  its  stiffness  about  seven  eighths;  because  the  effective 
span  of  the  beam  has,  by  cutting  off  the  projecting  ends,  been 
almost  doubled,  i.e.,  increased  from  bb\  Fig.  251,  to  c  c' . 

1051.  For  the  most  efficient  service  from  ties,  therefore,  we 
have  a  certain  quite  narrow  limit  of  length,  the  minimum  being 
about  7y  ft.,  and  the  maximum  about  Z\  to  9  ft.,  for  the  ordinary 
gauge  of  4.71  ft.  It  is  clear  from  the  above  that  any  increase  of 
length  above  8  ft.  gives  a  far  less  effectual  way  of  disposing  a 
given  quantity  of  wood  (to  obtain  an  approximately  uniform 
pressure  on  the  ballast,  and  so  keep  down  the  maximum),  than 
to  increase  the  thickness,  provided  the  nature  of  the  timber  per- 
mits it.  The  apparent  gain  of  bearing-surface  by  increasing  the 
length  of  ties  from  8  ft.  to  9  ft.,  and  the  apparent  absence  of  gain 
in  bearing-surface  by  increasing  the  thickness  from  6  in.  to  7  in., 
will  be  seen  to  be  precisely  the  reverse  of  the  true  conditions, 


CHAP.  XXIII.  — THE  ECONOMY   OF   CONSTRUCTION.      78 1 

and  we  may  well  believe  that  this  deceptive  contrast  has  been 
the  chief  cause  for  such  awkward  combinations  as  an  8^-  or  9-ft. 
tie  with  only  6  in.  thickness,  which  prevails  with  6.1  per  cent  of 
the  ties  in  the  United  States. 

Neglecting  the  widths,  as  an  indeterminate  element  not  defi- 
nitely fixed,  the  percentages  for  the  entire  United  States  of  the 
various  lengths  and  thicknesses  of  ties  in  use  is  as  follows  : 


Lengths,     .     . 

8  ft. 

8  ft.  6  in. 

9  ft. 

10  ft. 

Total. 

Percentages,  . 

63.5 

27.6 

8.9 

0  + 

100. 0 

Thickness, 

6  in. 

6iin. 

7  in. 

8  in. 

Percentages,  . 

54.4 

Z'^ 

41.4 

0.4 

100. 0 

While  these  variations  are  in  part,  and  perhaps  chiefly,  gov- 
erned by  the  conditions  of  the  timber  supply,  they  arise  in  part 
at  least,  we.  may  safely  assume,  from  mistaken  views  as  to  what 
is,  abstractly  considered,  the  best  proportion  for  a  tie.  The  best 
dimensions  for  a  tie  are  about  7  in.  thick,  8  ft.  6  in.  long,  and- 
7  to  9  in.  face. 

1052.  There  is  another  side  to  the  question  of  masonry  struc- 
tures which  may  be  briefly  noted.  While  a  structure,  if  built  at 
all,  should  be  well  and  solidly  built,  it  does  not  follow  that  be- 
cause a  certain  proportion  of  the  structures  of  a  line  eventually 
wash  out  that  they  were  therefore  ill-designed.  "  The  natural 
end  of  a  tutor,"  say  the  Autocrat  of  the  Breakfast-Table,  "  is  to 
die  of  starvation.  It  is  only  a  question  of  time,  just  as  with  the 
turning  of  college  libraries."  So  in  a  certain  narrow  and  limited 
sense  we  may  say  that  the  natural  end  of  a  culvert,  and  even  of 
many  bridges,  is  to  perish  in  some  excessive  flood.  The  excep- 
tional storms  which  come  but  once  or  twice  in  a  century  can 
hardly  be  fully  provided  for,  for  the  reason  that  it  is  difficult  to 
build  any  large  number  of  structures  with  such  an  ample  margin 
of  safety  as  to  insure  that  many  of  them  will  not  eventually  wash 
out. 

For  example,  in  1886  there  came  some  unusual  storms  which 
chanced  to  fall  most  severely  on  some  of  the  Boston  roads,  which 
are  about  the  oldest  roads  in  this  country,  having  been  built 


782      CHAP.  XXIIL—THE   ECONOMY   OF   CONSTRUCTION. 

from  40  to  50  3rears,  and  had  rarely  suffered  much  from  floods 
and  washouts  heretofore.  As  a  consequence  structures  were 
washed  out  in  considerable  numbers  (on  the  Old  Colony  there 
were  40  washouts),  many  of  which  were  "  supposed  to  be  strong 
enough  to  resist  any  current,"  and  had  succeeded  in  doing  so 
for  half  a  century. 

1053.  Such  occurrences  will  and  ought  to  make  engineers 
cautious;  but  we  may  remember,  on  the  other  hand,  that  to  have 
insured  that  these  structures  should  not  have  washed  out,  their 
original  size  and  cost  would  have  had  to  be  nearly  if  not  quite 
doubled,  and  a  simple  computation  in  compound  interest  will 
show  that  had  this  been  done  in  the  first  instance  the  additional 
investment  would  have  amounted  at  6  per  cent  to  19.50  times 
the  actual  first  cost.  It  follows  that  in  1835  even  a  certainty  of 
saving  the  cost  of  duplicating  the  original  structure  in  1886  would 
have  warranted  barely  5  per  cent  additional  expenditure.  It  is 
true  that  the  bare  cost  of  renewal  does  not  cover  the  whole  loss, 
for  there  is  a  loss  from  delay  and  danger  of  accident  incurred 
by  the  washout  in  addition  thereto  ;  but  on  the  other  hand,  to 
guard  against  all  the  contingencies  which  might  arise  in  1886,  it 
would  have  been  necessary  in  1835  ^^  have  about  doubled  the 
cost  of  all  the  structures,  since  all  may  be  assumed  to  have  been 
laid  out  with  equal  care,  and  it  could  not  have  been  foreseen 
which  would  be  most  tried  thereafter. 

All  of  which  goes  to  show  that  when  structures  have  been 
skilfully  laid  out  to  stand  the  ordinary  contingencies  of  20  or  30 
years  it  is  about  all  that  is  either  practicable  or  justifiable,  and 
that  the  remarkable  storms  which  come  only  once  or  twice  in  a 
century  are  not  in  fact,  and  hardly  can  be,  successfully  guarded 
against.  This  is  especially  true  because  the  worst  effects  of  even 
the  greatest  storms  are  localized  within  quite  nairow  limits. 
The  storms  referred  to  were  not  by  any  means  the  worst  for  50 
years,  except  at  a  few  spots.  But  those  structures  which  washed 
out  chanced  to  be  at  those  spots,  while  the  really  greater  storms 
which  have  washed  out  others  in  past  years  did  not  chance  to 
fall  so  severely  on  these. 


CHAP.  XX III. —  THE   ECONOMY   OF   CONSTRUCTION.      'j'^l 


1054.  The  same  is,  in  substance,  true  of  inundations  of  rail- 
way lines.  Every  year  we  hear  of  miles  of  line  of  important 
roads  being  under  water,  and  every  year  it  is,  to  a  considerable 
extent  in  different  localities.  It  is  a  tolerably  safe  prediction 
that  within  reasonable 
and  justifiable  limits 
of  expenditure  no  rail- 
way can  be  carried 
for  any  long  distance 
through  that  place  of 
all  places  for  economi- 
cal operation,  a  river 
valley,  without  being 
at  some  time  and  at 
some  point  under  wat- 
er. The  conclusion 
that  whenever  this  oc- 
curs it  is  evidence  of 
bad  engineering  is  not 
justified.  There  are 
lines  in  all  parts  of 
the  country  which  are 
overflowed  for  consid- 
erable distances  every 
three  or  four  years  for 
a  few  days,  and  find 
it  cheaper  to  suffer 
the  evil  than  to  cor- 
rect it.  Prominent 
examples  among  in- 
numerable others  is 
the  main  line  of  the  Pennsylvania  Railroad  in  Trenton,  N.  J., 
various  points  on  the  Erie,  Philadelphia  &  Erie,  and  Baltimore 
&  Ohio,  and  various  roads  in  the  vicinity  of  Buffalo,  N.  Y. 

Without  going  to  the  length  of  saying  that  this  is  ordinarily 
justifiable,  which  would   be  going  too  far,  it  is  an  entirely  safe 


Fig.  252. 


-Annual  Rainfall  in  Inches  at  Lake 

CocHiTUATE,  Mass.,  1852-1883. 


784      CHAP.  XXIII.— THE  ECONOMY  OF  CONSTRUCTION. 

Statement  that  when  the  works  endangered  by  such  overflow  are 
not  of  a  very  costly  character,  it  is  far  better  to  risk  the  chances 
of  overflow  and  damage  at  a  few  points  every  eight  or  ten  or 
fifteen  years,  and  often  still  more  frequently,  than  to  sacrifice 
the  advantage  of  easy  gradients  and  light  first  cost  to  avoid  the 
risk,  especially  as  it  is  often  impossible  to  avoid  it  without  aban- 
doning the  valley  altogether.  This  latter  has  been  done  in  not 
a  few  instances,  and  by  no  means  to  the  advantage  of  the  prop- 
erty, although  of  course  there  are  many  valleys  which  are  so 
frequently  subject  to  excessive  floods  as  to  make  them  unfit  for 
any  permanent  railway  line. 

1055.  Very  great  fluctuations  in  rainfall  occur  in  successive 
years,  as  shown  in  Fig.  252,  which  likewise  strongly  indicates 
that  there  are  periods  of  great  or  small  rainfall  of  ten  or  fifteen 
years'  duration.  It  by  no  means  follows,  however,  that  the  years 
of  greatest  rainfall  are  the  years  of  greatest  floods,  but  rather 
the  contrary. 


CHAP.  XXIV.— IMPROVEMENT  OF  OLD  LINES.  785 


CHAPTER  XXIV. 

THE   IMPROVEMENT    OF    OLD    LINES. 

1056.  It  should  follow  from  what  we  have  already  seen  in 
respect  to  the  errors  which  may  be  committed  in  the  laying  out 
of  new  lines,  that  many  existing  lines,  built  in  haste  and  without 
adequate  study  of  conditions  of  greatest  economy,  should  be 
capable  of  material  improvement  at  a  cost  far  within  the  added 
value  to  the,  property.  That  this  is  so  is  a  matter  of  common 
observation  and  belief,  and  many  lines  are  already  acting  upon 
it  to  their  great  advantage.  Undoubtedly  the  number  of  such 
lines  will  continue  to  increase,  influenced  by  the  sharp  spur  of 
necessity  if  nothing  else,  and  it  is  probable  that  this  would  be 
more  generally  done  if  it  were  fully  realized  what  great  improve- 
ments may,  in  cases,  be  effected  at  very  moderate  cost,  and  how 
readily  the  possibilities  in  that  direction  may  be  determined 
without  elaborate  and  costly  surveys. 

The  subject  is  one  which  usually  requires  careful  study,  not 
so  much  for  determining  whether  or  not  improvements  can  ad- 
vantageously be  entered  on,  which  is  often  too  clear  for  doubt, 
as  for  determining  precisely  how  and  where  the  most  improve- 
ment can  be  effected  for  the  least  money,  so  as  to  avoid  the 
danger  that,  if  the  improvements  are  entered  on,  the  expenditure 
will  not  be  given  the  right  direction,  and  so  accomplish  a  part 
only  of  what  might  have  been  accomplished,  or,  on  the  other 
hand,  will  include  much  that  was  not  essential  and  so  not  return 
interest  on  the  capital  invested. 

1057,  In  attempting  to  improve  an  old  line,  as  compared  with 
a  line  which  is  still  on  paper  only,  we  are  at  once  better  and 
worse  off.  On  the  one  hand,  we  have  a  positive  knowledge  of 
its  earnings,  expenses,  and  traffic,  and  far  more  definite  premises 

50  • 


786  CHAP.  XXIV.— IMPROVEMENT  OF   OLD  LINES, 

for  estimating  the  possibilit}^  and  value  of  any  change  therein. 
We  know  or  may  know  precisely  how  much  locomotives  do  and 
can  do  on  the  line,  how  much  they  are  now  assisted  by  momen- 
tum in  passing  over  their  heavy  grades,  and  where  they  are 
most  taxed.  Above  all,  perhaps,  we  have  time  to  fully  consider 
and  investigate  all  the  conditions.  Usually,  moreover,  there  are 
certain  members  of  the  regular  staff  who  can  devote  a  moderate 
amount  of  time  to  investigations  and  minor  surveys  without 
serious  interference  with  their  regular  duties. 

1058.  On  the  other  hand,  we  have  the  disadvantage  that  any 
changes  of  line  or  grade,  or  of  positions  of  stations  or  water- 
tanks,  etc.,  etc.,  involve  the  throwing  away  of  a  certain  amount 
of  work  already  done,  instead  of  the  mere  addition  of  a  new  red 
line  to  the  maps  and  a  new  line  of  stakes  on  the  ground.  For 
this  reason,  a  change  which  might  have  been  in  every  way  ex- 
pedient in  the  beginning  may  not  be  expedient  when  loaded 
with  the  cost  of  two  lines  instead  of  one.  We  have,  moreover, 
the  disadvantage  that  the  value  of  property  and  number  of  build- 
ings are  liable  to  have  greatly  increased,  often  to  a  prohibitory 
limit,  especially  near  stations  and  large  towns,  where  changes 
are  most  likely  to  prove  expedient.  Moreover,  in  cases  of  con- 
siderable changes,  involving  the  abandonment  of  certain  sec- 
tions of  line  or  even  the  moving  of  minor  stations  or  sidings, 
legal  difficulties  may  arise,  with  expenses  of  unknown  magni- 
tude resulting,  perhaps,  from  the  mere  whim  of  a  jury,  and  re- 
quiring the  maintenance  and  operation  at  heavy  cost  of  work 
intended  to  be  abandoned.  It  has  been  successfully  disputed  in 
some  instances,  at  least  for  a  time,  whether  a  corporation  has 
the  right  in  law  to  abandon  sections  of  unprofitable  lines  to  the 
detriment  of  vested  interests  without  payment  of  heavy  damages 
as  compensation  for  contingent  as  well  as  actual  injury.  On 
the  other  hand,  instances  have  repeatedly  arisen  where  the  right 
of  such  abandonment  has  been  successfully  asserted  and  main- 
tained. Much  depends,  no  doubt,  both  on  the  importance  of 
the  case  and  the  rigor  of  the  opposition,  but  in  general  it  seems 
reasonable  to  expect  that  moderate  changes  for  which  necessity 


CHAP.  XXIV.— IMPROVEMENT  OF   OLD  LINES.  7^7 

or  good  reason  can  be  shown  will  not  be  accompanied  by  a  re- 
fusal of  legal  authority  to  make  them,  or  by  more  than  reason- 
able and  actual  damages.  It  constitutes  an  element  to  be  always 
remembered  and  weighed,  but  not  to  be  exaggerated  without 
weighing  it,  as  there  is  some  danger  that  it  may  be. 

1059.  The  disadvantage  of  having  to  build  a  line  twice  over  is 
one  which,  while  undoubted,  is  liable  to  affect  the  imagination 
far  more  than  its  real  importance  warrants.  The  constant  loss 
from  operating  a  bad  line,  on  the  other  hand,  being  so  gradual 
and  continuous  that  it  does  not  affect  the  imagination  at  all,  the 
two  causes  may  unite  to  indispose  responsible  officers  to  think 
of  entering  upon  a  policy  in  which  the  outlay  is  certain  and 
seems  larger  than  it  is,  while  the  gain  is  problematical,  and  even 
its  possibility  does  not  force  itself  upon  the  attention. 

To  construct,  say,  lo  per  cent  of  'a  long  line  over  again,  for 
■example,  inevitably  impresses  the  imagination  as  very  much  like 
adding  8  or  lo  per  cent  to  the  capital  invested;  and  as  the  ship 
is  nearly  sinking  under  the  load  it  carries,  what  may  happen  to 
it  with  that  load  added  ?  The  chances  are,  however  (Table  199 
and  14),  that  it  will  not  really  add  more  than  one  to  three  per 
cent.  On  the  other  hand,  what  can  seem  more  improbable, 
a  priori,  to  a  manager  who  is  only  hauling  25  or  30  cars  per  train, 
than  that  50  or  60  cars  can  be  drawn  over  the  same  road  with- 
^out,  say,  doubling  or  at  least  increasing  one  third  the  cost  of  the 
line  ?  Yet  this  has  been  repeatedly  accomplished,  and  can  be 
again  accomplished  on  many  thousand  miles  of  road,  at  far  less 

€OSt. 

1060.  The  defects  which  are  most  conspicuous  in  old  lines 
which  it  is  desired  to  improve  are,  in  general,  these: 

1.  The  passing  by  of  large  towns  or  other  sources  of  traffic 
which  should  have  been  approached  more  nearly.  This  defect, 
although  a  great  one  in  the  laying  out  of  old  lines,  is  ordinarily 
not  one  for  which  alone  it  is  expedient  to  change  the  main  line, 
but  it  is  often  an  element  in  considering  changes  which  are  de- 
sirable for  other  reasons. 

2.  Excessive  curvature;    a  defect  which  forces  itself  with 


788  CHAP.  XXIV.—IiMPROVEMENT  OF   OLD  LINES. 

quite  sufficient  force,  as  a  rule,  upon  the  attention  of  all  con- 
cerned, so  that  there  is  some  danger  that  expenditures  may  be 
incurred  in  efforts  to  remedy  this  evil  which  might  better  have 
been  given  some  other  direction.  Nothing  further  vi^ill  be  said 
on  this  subject  than  has  been  already  said  in  Chapter  VIII.  on 
curvature;  but  it  is  beyond  question  that  on  important  trunk 
lines  large  expenditures  may  often  be  usefully  devoted  to  this, 
as  to  almost  any  other  improvement. 

3.  Improvements  in  gradients,  which  are  generally  at  once 
the  cheapest  and  the  most  important  to  effect,  and  to  which  this 
chapter  will  hereafter  be  devoted. 

1061.  The  defects  in  gradients,  of  a  remediable  character, 
which  are  most  likely  to  exist  in  old  lines,  are  as  follows: 

1.  Stations  on  heavy  grades,  including  as  heavy  grades 
not  only  those  which  appear  heavy  on  the  profile,  but  those 
which  are  sufficient  to  prevent  starting  a  full  train,  although 
easily  enough  passed  over  by  trains  under  normal  headway. 
The  number  of  lines  is  great  on  which  several  limiting  stations 
of  this  kind  exist  on  a  single  division,  so  that,  as  the  trainmen 
put  it,  "  it  is  harder  to  start  the  trains  than  to  pull  them  up  the 
grade."  Very  frequently  these  bad  grades  at  stations  are  the 
only  obstacles  to  a  considerable  increase  of  train-load. 

2.  Grade-crossings  of  other  railroads,  which  have  often  been 
added  in  great  number  since  the  original  opening  of  the  line 
and  seriously  modified  the  handling  of  trains,  especially  in  the 
West. 

3.  Needless  undulations  of  grade,  avoidable  by  slight  de- 
tours, and  originally  introduced  only  because  the  importance  of 
low  grades  in  comparison  with  a  short  line  or  cheap  construc- 
tion was  underestimated. 

4.  Failure  to  use  pushers,  or  assistant  engines:  in  some 
cases  from  mere  oversight,  but  more  generally  because  the  line 
is  ill-suited  for  their  use  without  modifications  elsewhere.  It  is 
unfortunately  true  that  in  the  original  location  of  most  Ameri- 
can railways  this  possibility  has  been  little  considered;  partly 
because   the  amount  of  future   traffic  was  not  foreseen;  partly 


CHAP.  XXIV.—IiMPROVEMENT  OF   OLD  LIXES.  789 

because  the  grades  seemed  too  low  to  make  the  possibility  worth 
considering  (it  being  only  in  recent  years  that  the  use  of  pushers 
on  low  grades,  to  handle  very  heavy  trains,  has  become  common), 
and  partly,  in  some  instances,  from  mere  lack  of  thought. 

1062.  On  very  many  lines  it  has  happened  that  there  was 
some  one  short  stretch  on  a  division  where  a  50  or  60  ft.  per  mile 
grade  was  unavoidable.  Grades  approaching  this  limit  were  then 
used  on  other  parts  of  the  line  which  were  easily  avoidable,  and 
can  easily  be  taken  out,  from  an  idea  (correct  enough  if  the  use 
of  pushers  is  not  considered)  that  they  were  of  no  importance  if 
not  exceeding  the  maximum. 

Consequently,  when  the  line  was  opened,  trains  had  to  be 
quite  short.  Stations  were  laid  out  or  have  been  added  from 
time  to  time,  without  reference  to  the  use  of  any  other  than  the 
short  trains  then  handled,  and  new  roads  have  from  time  to  time 
put  in  grade-crossings,  at  which  all  trains  were  compelled  to 
stop,  with  similar  indifference  to  consequences,  provided  the  new 
stop  did  not  require  a  still  shorter  train  than  was  then  handled. 

1063.  Thus  it  may  have  come  about,  in  the  course  of  years, 
that  there  will  be  a  dozen  or  twenty  points  on  the  division  where 
the  demand  upon  the  power  of  the  locomotive  is  almost  as  great 
as,  and  frequently  greater  than,  the  resistance  on  the  maximum 
grade,  so  that  no  advantage,  or  very  little  advantage,  would  be 
gained  by  the  use  of  pushers  anywhere,  and  the  character  of  the 
line  seems  fixed,  without  entire  reconstruction.  Yet  the  whole 
may  be  often  remedied  by  some  among  the  following  simple 
ways,  at  very  moderate  aggregate  cost: 

I.  The  point  or  points  offering  most  original  difficulties  and 
having,  probably,  the  heaviest  work  and  grades  (say  60  feet)  may 
be  in  some  cases  avoided  altogether  by  a  detour  of  a  few  miles, 
but  in  general  can  more  advantageously  be  operated  as  it  stands 
with  a  pusher,  thus  about  doubling  the  possible  train  over  it. 

1064.  2.  The  points  of  next  heaviest  grades — there  may  be  six 
or  eight  of  them,  having  grades  of  30,  40,  and  50  to  60  feet  per 
mile — will  in  some  instances  be  so  short  that  they  are  now,  or 
can   well   be,  operated  as  momentum   grades,  with  or  without 


790  CHAP.  XXIV.— IMPROVEMENT  OF  OLD  LINES. 

some  slight  modification.  The  feasibility  of  this  can  be  deter- 
mined simply  and  easily  in  the  manner  explained  in  par.  408.  la 
other  (and  frequent)  cases  short  sections  of  new  grading  will  be 
required,  to  which  the  track  complete  can  be  removed.  In  some 
cases  the  regrading  of  considerable  sections  will  be  necessary, 
enabling  the  line  perhaps  to  strike  some  new  town  by  a  detour^ 
but  endangering  legal  complications  for  damages  unless  both 
lines  are  maintained.  Very  frequently,  however,  such  double 
construction  may  give  all  the  advantage  of  a  double  track,  for  a 
certain  distance,  since  the  objectionable  gradients  may  be  op- 
posed to  trains  going  one  way  only. 

1065.  3.  The  disadvantageous  effects  of  grade-crossings  may 
now,  happily,  be  immediately  removed  in  all  cases  by  taking  ad- 
vantage of  the  laws  already  existing  in  some  States  (see  next  chap- 
ter), and  to  be  easily  obtained  by  effort  where  they  do  not  exist,^ 
permitting  such  crossings  to  be  operated  by  interlocking  signals 
without  requiring  trains  to  stop  at  them  regularly.  It  is  now 
universally  admitted  by  intelligent  and  well-informed  men,  that 
this  is  a  much  safer  and  cheaper  safeguard  than  the  stopping  of 
trains.  Exceptional  crossings  no  doubt  exist  where  (as  some, 
trains  must  stop  when  another  happens  to  be  passing)  this  rem- 
edy would  not  be  a  perfect  one,  and  an  overhead  crossing  prefer- 
able, especially  to  effect  at  the  same  time  an  improvement  of 
grade,  but  in  general  dispensing  with  a  stop  by  interlocking 
would  be  all  that  was  practically  necessary.  The  expense  of  do- 
ing so  is  considered  more  fully  in  the  next  chapter. 

1066.  4.  The  unfavorable  gradients  at  stations — very  often  the 
chief  evil  to  be  cured,  although  none  but  the  trainmen  may  fully 
realize  the  fact — can  be  remedied  by  one  or  the  other  of  numer- 
ous ways,  as  follows: 

{a)  By  moving  the  station  or  the  freight  tracks  only  a  little 
ahead  or  back,  so  as  to  reach  a  more  favorable  point;  if  neces- 
sary, at  important  stations,  by  completely  separating  the  freight 
and  passenger  yard  and  station,  and  incurring  some  extra  ex- 
pense for  extra  operators,  switchmen,  etc. 

{h)  By  modifying  the  gradients  of  the  station,  or  of  one  or 


CHAP,  XXJV.— IMPROVEMENT   OF  OLD  LINES.  79 1 

two  tracks  thereat  in  the  manner  indicated  in  Fig.  254,  viz.,  rais- 
ing the  track  «,  at  the  lower  end  of  the  yard,  so  as  to  give  a  lower 
grade  for  starting  trains,  at  the  expense  of  a  somewhat  higher 
grade  for  stopping  them,  the  latter  having  no  other  disadvan- 


tageous effect  than  to  check  the  speed  of  a  passing  train,  acting 
in  place  of  a  brake,  to  some  extent,  if  the  train  is  to  stop. 

{c)  By  stationing  a  switchman  to  open  certain  switches,  and 
thus  saving  the  necessity  of  a  train  stopping  at  an  unfavorable 
point  to  open  or  shut  them.  On  large  roads  and  at  large  sta- 
tions this  is  not  a  difficulty,  but  at  other  points  it  is  one  which 
must  be  fully  borne  in  mind. 

1067.  {d)  By  breaking  through,  if  necessary,  general  rules  as 
to  which  trains  shall  take  the  side  track,  and  even  (in  effect  if  not 
in  form)  which  trains  shall  have  the  right  of  way.  The  latter,  of 
course,  cannot  safely  be  done  t7t  form,  but  the  desired  end  can 
be  accomplished  by  taking  care  in  despatching,  to  have  the  lightly 
loaded  trains,  or  those  which  the  grades  favor,  held  for  those 
which  cannot  well  stop  at  certain  stations  or  only  with  difficulty. 
A  general  rule  on  this  subject  is  commonly  established  and  put 
in  force  over  all  divisions  of  large  roads — as  for  instance  that  east- 
bound  trains  have  right  of  way  over  west-bound,  which  latter, 
consequently,  are  by  custom  always  obliged  to  take  the  side 
track  at  all  stations,  and  by  custom  of  the  despatchers  are  com- 
monly held  so  as  to  favor  the  east-bound  trains.  But  while  such 
a  rule  may  work  well  enough  on  most  divisions,  it  may  work 
very  unfavorably  in  others. 

1068.  For  example,  on  the  New  York,  Pennsylvania  &  Ohio 
Railroad,  the  general  rule  that  east-bound  trains  had  the  right 
of  way,  which  was  well  enough  for  the  remainder  of  the  road,  had 
(and  probably  still  has)  the  effect  on  the  Mahoning  Division  to 
compel  the  heaviest-loaded  trains  to  stop  and  take  the  side  track, 


792  CHAP.  XXIV.— IMPROVEMENT   OF  OLD  LINES. 

on  a  curve,  when  half  up  a  long  maximum  grade,  to  let  trains 
always  more  lightly  loaded  pass  down  hill  at  full  speed  past  them. 

Such  cases  are  not  infrequent,  and  come  to  be  looked  upon  as 
matters  of  course;  but  it  is  needless  to  say  that  they  can,  when 
occasion  arises  to  make  it  expedient,  be  modified  if  necessary  (i) 
b}^  reversing  on  one  division  the  usual  rule  as  to  which  trains  have 
right  of  Avay  ;  (2)  by  giving,  at  some  given  station  or  stations, 
trains  going  in  one  direction  the  right  to  hold  the  main  track  and 
require  an  opposing  train  to  take  side  track,  regardless  of  which 
has  right  of  way;  (3)  by  favoring  trains  in  dispatchers'  orders,  as 
before  suggested. 

Thus,  in  one  way  or  another,  it  may  generally  be  effected 
that  trains  passing  in  one  direction  past  some  one  station  on  a 
division,  at  least,  with  unfavorable  grades  which  cannot  other- 
wise be  remedied,  shall  not  be  compelled  to  stop  at  it. 

1069.  {/)  At  large  stations,  where  there  is  most  likely  to  be  diffi- 
culty or  great  expense  in  adopting  any  of  the  preceding  meth- 
ods, a  switch-engine  which  it  is  found  necessary  to  keep  at  the 
station,  but  which  is  not  kept  very  busy,  may  be  utilized  to  help 
trains  through  the  yard,  and  perhaps  also  over  some  unfavor- 
able grade-crossing,  which  is  particularly  likely  to  come  near 
to  such  a  station.  If  the  traffic  of  the  line  be  very  heavy  this 
may  not  be  possible;  but  in  that  case,  as  a  last  resort,  an  engine 
may  be  stationed  at  the  yard  for  the  sole  purpose  of  helping 
trains  through  it.  By  modifying  the  position  of  the  tele- 
graph office  it  may  in  general  be  arranged  that  the  use  of  such 
an  engine  shall  cause  no  extra  stoppage  of  the  train.  In  fact,  on 
many  lines  of  heavy  traffic,  as  for  instance  the  Hudson  River 
Division  of  the  New  York  Central  Railroad,  pusher  engines  are 
used  to  help  trains  over  short  grades  without  stopping  trains  at 
all,  the  pushers  coming  up  behind  the  train  as  it  passes  a  switch, 
running  two  or  three  milles,  and  returning  on  the  same  track, 
protected  by  a  flag. 

1070.  The  best  method  of  determining  how  much  can  be  ef- 
fected in  these  various  ways  is  by  observations  of  the  variations 
of  velocity  in  the  handling  of  heavy  trains  on  the  present  line  in 


CHAP.  XXIV.— IMPROVEMENT   OF  OLD  LINES.  793 

a  manner  shortly  to  be  described.  In  this  way  we  eliminate  the 
necessity  of  considering  and  allowing  for  a  long  list  of  doubtful 
elements — which  throw  a  haze  of  uncertainty  over  any  computa- 
tion in  which  they  must  be  separately  estimated  or  guessed  at — 
by  simply  determining  by  direct  observation  the  resultant,  so  to 
speak,  or  net  effect  of  them  all.  For  lack  of  definite  knowledge 
on  a  number  of  variable  elements,  it  is  difficult,  if  not  impossible, 
either  to  compute  or  to  observe,  separately,  either  the  power  of 
the  engine  or  the  whole  resistance  of  the  train,  but  we  can  de- 
termine, very  accurately  and  simply,  the  relation  which  the  one 
bears  to  the  other — which  is  all  that  really  concerns  us — in  this 
way  : 

I.  When  the  engine  at  any  given  point  on  the  open  road 
LOSES  SPEED,  it  is  proof  that  working  with  the  given  steam-pres- 
sure and  point  of  cut-off  it  is  overloaded,  and  the  amount  of 
velocity  lost  can  be  made  a  measure  of  how  much  it  is  over- 
loaded (par.  400  et  al.). 

II.  Conversely,  if  the  engine  gain  speed  at  any  point  on  the 
open  road,  under  given  conditions  of  steam-pressure  and  cut-off, 
it  is  a  proof  that  it  is  underloaded,  and  the  observed  variations 
of  velocity  can  be  made  to  accurately  indicate  how  much. 

III.  If  an  engine  acquires  speed  in  starting  very  quickly, 
under  given  conditions,  without  slipping  the  wheels  or  using 
sand,  etc.;  or,  on  the  contrary, 

IV.  If  the  engine  start  very  slowly,  or  not  at  all,  without 
slipping  the  wheels  or  using  sand,  or  both — the  observed  facts 
may  be  made  a  measure  for  accurately  determining  what  train  it 
could  start  under  similar  conditions  with  fair  working  efficiency. 

(071.  By  velocity  observations  of  the  nature  above  indicated 
under  varying  conditions  of  wind,  weather,  temperature,  long  and 
short  trains,  loaded  and  empty  cars,  etc.,  etc.  (all  of  which  can 
be  observed  on  trains  by  simply  waiting  for  suitable  opportuni- 
ties without  affecting  or  interfering  with  normal  operating  prac- 
tices), we  have  a  positive  basis  for  determining  from  what  is 
done  under  those  conditions  whether  or  not  the  comparative 
ratio  of  power  to  resistance  on  various  parts  of  the  line  is  seri- 
ously imperfect. 


794  CHAF.  XXIV.— IMPROVEMENT  OF  OLD  LINES. 

In  Other  words,  we  can,  by  the  simple  observations  suggested 
and  to  be  described,  construct  a  virtual  profile  of  the  road 
under  all  extremes  of  external  conditions.  We  can  then  com- 
pare these  virtual  profiles  and  determine  whether  or  not  a  given 
set  of  improvements  which  produce  a  desired  uniformity  of  re- 
sistance under  one  set  of  conditions,  as  fair  summer  weather  and 
heavy-loaded  trains,  will  have  as  great  comparative  value  in 
stormy  winter  weather  with  long  trains  of  empty  cars. 

Positive  determinations  of  any  one  of  the  following  doubtful 
elements  we  save  the  need  of  altogether  : 

f  The  ratio  and  amount  of  adhesion. 
I   The  cylinder-power. 

A^res'h^ctstheenirtne       \   The  steam-power. 
AS  respects  tfie  engine.  •  •  ^   ^^6  head  resistance. 

I   The  rolling-friction  and  friction  of  machinery. 

[  The  gain  from  using  sand. 

r  The  rolling-friction. 
As  respects  the  cars \   The  wind  resistance. 

[  The  effect  of  number  and  load  of  cars. 

f  The  effect  of  temperature,  state  of  rail. 
As  respects  the  train  as   \   The  extent  to  which  momentum  may  be  re- 
a  whole •  j       lied  upon  to  help  trains  over  short  heavy 

[      grades. 

1072.  To  accomplish  these  ends  the  system  of  observation 
should  in  detail  be  as  follows  : 

The  only  apparatus  or  previous  preparation  necessary  is  a  series  of 
distance-stakes  along  the  line,  a  stop-watch,  and  a  note-book,  with  an 
observer  on  the  engine  (at  times),  also  provided  with  a  note-book. 

The  stakes  are  set  at  various  governing  points  on  the  line  where 
speed  observations  are  desirable.  They  should  be  of  a  size  and  color  to 
be  easily  visible,  and  should  be  set  throughout  the  road  at  some  fixed 
and  uniform  distance  apart.  Boards  fastened  to  the  fence  may  be  more 
convenient  than  stakes.  It  is  unimportant  to  place  them  with  ref- 
erence to  mile-posts,  but  they  should  be  set  at  top  and  bottom  of  every 
doubtful  grade,  and  at  the  up-grade  starting-point  at  every  station  and 
stopping-place  which  either  is  or  may  become  in  any  way  a  difficult 
point,  requiring  consideration.  It  can  do  no  harm  to  place  them  at  all 
stations,  as  comparisons  may  be  instructive. 

A  train  moving  at  lo  miles  per  hour  passes  over  14.67  feet  per 
second.     As  our  time  observations  must  be  in  seconds,  it  will  be  more 


CHAP.  XXIV.— IMPROVEMENT   OF  OLD  LINES. 


79S 


convenient  to  set  these  stakes  at  some  multiple  of  14.67  feet  apart,  thus 
making  all  velocity  records  throughout  readily  convertible  into  miles 
per  hour  from  speed  notes  in  seconds.  A  suitable  distance  is  14.667  x  20 
or  293.33  feet.  If  set  at  that  distance  a  train  which  passes  over  the 
distance  between  any  two  stakes  in 


20  seconds  is  moving  at  10 
15         "            "          "       i3i 

13^       "            •'          "       15 
10         "            "          "       20 

mi 

es 

per  hour. 

5         "            ''          "       40 
,.            ((          ,<     200 

In  other  words,  reciprocal  of  A  seco7ids  X  200  =  vel.  in  miles  per  hour 
between  the  two  stakes  ;  a  very  simple  computation  from  a  table  01  re- 
ciprocals which  the  following  Table  201  will  save  the  need  of. 


Table  201. 
Speed  in  Miles  Per  Hour  corresponding  to  the  Time  in  Seconds  in 

PASSING   OVER   A    DISTANCE    OF    293|-    FeET. 


Seconds. 

Speed. 

Seconds. 

Speed. 

Seconds. 

Speed. 

Seconds. 

Speed. 

3 

66.7 

6i 

32.0 

9i 

21. 1 

17 

11.76 

3i 

61.6 

6i 

30.8 

9f 

20.5 

18 

II. II 

3i 

57-1 

6f 

29.6 

10 

20.0 

19 

10.53 

3f 

53-3 

7 

28.6 

lOi 

19.0 

20 

10.00 

4 

50.0 

nl 

27.6 

II 

18.2 

22 

9.09 

4i 

47.1 

7i 

26.7 

Hi 

17.4 

24 

8.33 

4i 

44.4 

7f 

25.8 

12 

16.7 

26 

7.69 

4f 

42.1 

8 

25.0 

12i 

16.0 

28 

7.14 

5 

40.0 

8i 

24.2 

13 

15-4 

30 

6.67 

5i 

38.1 

8i 

23.5 

I3i 

14.8 

35 

5-71 

5i 

36.4 

81 

22.9 

14 

14-3 

40 

5.00 

5f 

34.8 

9 

22.2 

15 

13-3 

50 

4.00 

6 

33-3 

9i 

21,6 

16 

12.5 

60 

3-33 

The  disposal  of  the  stakes  at  stations,  where  speed  is  slow, 
may  be  advantageously  modified  by  putting  in  half-stations,  so 
that  they  are  only  146.67  feet  apart,  thus  giving  more  accuracy 
to  the  observations  ;  but  this  is  unessential,  and  does  not  modify 
the  principle. 


796 


CHAP.  XXIV.— IMPROVEMENT   OF  OLD  LINES. 


1073.  Stop-watches  suitable  for  this  purpose  may  be  bought  of  any  dealer 
for  $7  to  $io  each.  They  read  to  quarter  or  fifths  of  seconds,  being  stopped 
and  the  hands  fixed  at  any  instant  by  the  movement  of  a  little  button.  Pres- 
sure on  another  button,  B,  Fig.  255,  restores  the 
hand  to  zero,  ready  for  another  start.  They  are 
generally  durable  and  reliable. 

Two  stop-watches  may  advantageously  be  pro- 
cured and  mounted  together  on  a  board,  the  starting 
buttons  being  connected  to  a  single  lever,  as  shown 
in  Fig.  255,  in  such  manner  that  a  single  motion  of 
the  lever  will  start  one  watch  and  stop  the  other 
simultaneously.  This  will  throw  the  buttons  for 
turning  the  hand  to  o  on  the  outside,  so  that  they 
can  be  readily  used  without  danger  of  mistaking  one 
for  the  other.     It  is  not,  however,  essential  that  in 


A 

> 

•< 

/f^"^ 
Vi^ 

Fig.  255. 

taking  a  series  of  say  five  or  six  observations  we  should  return  the  hand  to  zero 
each  time.  We  may  simply  start  one  watch  and  stop  the  other  at  each  station 
and  note  the  actual  readings,  as  below  noted.  The  attachment  of  the  lever 
should  be  so  devised  that  there  is  a  single  point  in  a  central  position  of  the 
lever  where  neither  watch  will  be  started,  which  is  a  simple  matter  to  do.  A 
single  "  split-second"  watch  will  answer  the  same  purpose,  but  is  more  expen- 
sive. 

Some  brass  clips,  C,  for  inserting  a  memorandum  slip  near  to  the  watches 
may  advantageously  be  placed  upon  the  board  to  which  they  are  attached,  and 
brackets  or  angle-plates  may  well  be  provided  for  readily  screwing  the  whole 
firmly  to  the  side  of  the  car.  It  is  convenient,  although  not  essential,  to  have 
an  observer  to  watch  and  call  off  the  instant  of  passing  each  stake,  so  that  the 
attention  need  not  be  distracted  from  accurately  taking  the  time  observations. 
A  little  stand  or  hook  to  carry  an  ordinary  watch  for  time  records  may  well  be 
added. 

1074.  The  records  of  a  series  of  six  or  eight  successive  observations 
at  any  desired  point  may  then  be  jotted  down  on  the  memorandum  pad, 
to  be  worked  up  later,  or  on  the  spot,  since  they  are  likely  to  be  needed 
at  infrequent  intervals  only.  It  answers  every  useful  purpose  of  a  dyna- 
mometer record,  for  the  fluctuations  of  speed  are  such  a  record. 

In  starting  out  from  a  station  the  intervals  of  time  will  be  consider- 
able, even  when  taking  half-stations  of  146.67  feet  each,  and  there  is  no 
difficulty  under  any  circumstances  in  taking  readings  with  all  essential 
accuracy, 

1075.  The  simple  preliminary  preparations  required  having  been 
made,  the  method  of  conducting  the  observations  of  the  actual  working 
of  trains  should  be  as  follows  : 


CHAP.  XXIV.— IMPROVEMENT  OF   OLD  LINES.  7gj 

Before  beginning  the  more  careful  and  accurate  work  a  series  of  com- 
paratively rude  observations  may  well  be  made  in  which  exactitude  is 
not  desired  or  attempted,  solely  for  the  purpose  of  observing  the  varia- 
tions of  velocity  in  the  ordinary  routine  of  service,  and  to  learn  what  to 
expect  and  where  to  observe  most  carefully.  No  observer  on  the  engine 
is  needed  for  this  purpose,  and  it  is  as  well,  or  perhaps  better,  that  the 
trainmen  should  know  nothing  of  the  particular  purpose  in  view. 

For  the  more  formal  and  careful  observations  an  observer  on  the 
engine  is  necessary ;  and  it  is  desirable  that  the  train  should,  in  several 
instances  at  least,  be  run  on  an  accelerated  schedule,  and  that  the  engine- 
man  should  have  full  liberty,  and  indeed  express  instructions,  to  get  over 
the  ground  (and  especially  to  pull  out  from  stations)  as  rapidly  as  is  con- 
sistent with  due  caution  and  safety  ;  in  other  words,  to  see  how  quickly 
he  can  run  over  the  division,  remembering  always  that  the  cylinder 
tractive  power  of  locomotive  is  very  different  at  high  speed  and  low 
speed  (par.  557  et  seq.). 

1076.  The  duty  of  the  observer  on  the  engine  is  to  take  notes  from 
point  to  point  of  the  following  details ;  not  for  the  purpose  of  making 
any  absolute  estimates  or  computations,  but  simply  to  have  a  full  record 
of  the  work  of  the  engine  : 

(i)  The  steam-pressure,  by  record  of  fluctuations  of  the  steam-gauge. 
It  depends  largely  on  the  skill  of  the  foreman  ;  how  much,  can  only  be 
determined  by  trial  of  different  m*en,  or  by  their  record,  if  on  a  road 
which  has  a  fuel  premium. 

(2)  The  point  of  cut-off,  or  "  notch." 

(3)  The  slipping  of  wheels  and  the  use  of  sand.  The  record  as  to  the 
last  depends  very  largely  (par.  501)  upon  the  skill — and  even  in  some 
cases  on  the  good-will — of  the  engineman.  It  should  be  remembered 
that  he  can,  if  he  chooses,  slip  the  wheels  almost  anywhere,  and  he  will 
slip  them,  whether  he  wishes  to  or  not,  if  he  have  not  the  requisite  skill,, 
or  is  not  disposed  to  be  careful.  Starting  is  ordinarily  effected  by  set- 
ting the  valves  in  full  gear  ahead  and  regulating  the  admission  of  steam 
by  the  throttle.  If  a  full  pressure  of  steam  be  admitted  too  suadenly, 
slipping  of  the  wheels  is  certain  to  ensue,  even  if  the  engine  be  hauling 
no  train  whatever. 

1077.  Too  much  importance  must  not  be  attached  to  such  slipping, 
therefore,  since  it  is  more  or  less  a  regular  incident  to  handling  heavy 
trains  by  locomotives,  which  cannot  be  wholly  avoided  without  cutting 
down  trains  to  an  uneconomical  point,  nor  perhaps  even  by  doing  so,  as  is 
witnessed  by  the  slipping  which  goes  on  constantly  in  yard  work,  result- 


79^  CHAP.  XXIV.— OLD  LINES— VIRTUAL   PROFILE. 

ing  not  from  the  excessive  load,  but  from  too  great  haste  to  get  the  load 
under  way. 

1078.  The  duty  of  the  observer  on  the  caboose  (or  at  any  other  con- 
venient point  on  the  train)  is  confined  to  taking  the  time  records.  He 
should  know  the  points  at  which  they  are  to  be  taken  very  thoroughly. 
He  should  also,  before  starting  out  on  the  trip  or  after  completing  it, 
note  the  following  details  : 

Number  and  class  of  engine  and  name  of  engineman  and  fireman. 

Number  and  gross  weight  of  loaded  and  einpty  cars,  and  whether  box 
or  flat  cars,  and  how  many  ends  of  box  cars  are  left  exposed  in  the  train, 
by  being  preceded  by  flat  cars,  to  cause  extra  air  resistance. 

Teviperature,  conditioji  of  rail,  and  direction  and  velocity  of  the  wind. 
The  latter  may  well  be  determined  by  an  anemometer  and  wind-vane  on 
the  caboose,  which  will  give  directly,  what  is  really  required,  the  resultant 
in  magnitude  and  direction  of  the  wind  caused  by  the  motion  of  the  train, 
and  that  otherwise  existing.  With  a  head  wind  the  resultant  will  lie  in  the 
direction  of  the  train  and  have  a  velocity  equal  to  the  two  combined  ; 
with  a  rear  wind,  it  will  have  a  velocity  equal  to  the  difference  of  the 
two,  which  may  be  zero ;  with  a  side  wind  equal  in  velocity  to  the  speed 
of  the  train  the  resultant  will  lie  at  an  angle  of  45°  therewith,  and  have 
a  velocity  1.414  times  greater,  etc.  It  is  not  really  essential  that  very 
accurate  wind  observations  should  be  made,  since  we  are  not  after  abso- 
lute but  comparative  results,  and  it  is  easily  estimated  whether  a  storm 
or  wind  is  or  is  not  about  as  unfavorable  as  is  often  encountered. 

1079.  The  records  having  been  taken,  the  velocities  at  various  points 
are  taken  from  Table  201  and  the  vertical  "  head  "  in  feet  corresponding 
to  that  velocity  taken  from  Table  118,  in  the  manner  which  has  been  dis- 
cussed in  par.  397  et  seq.  on  virtual  profiles,  which  we  are  now  ready  to 
construct,  preparatory  to  entering  upon  the  interpretation  of  the  obser- 
vations taken.     In  these  latter  steps  lie  the  delicate  parts  of  the  work. 

CONSTRUCTION    OF    THE    VIRTUAL    PROFILE. 

1080'  Taking  an  actual  profile  (which  need  not  necessarily 
cover  the  whole  line,  but  may  show  only  the  important  points; 
a  common  profile  to  working  scales  is  the  best),  lay  off  at  each 
point  where  time  records  have  been  taken  the  vertical  height  in 
feet  corresponding  to  the  velocity  which  the  train  had  at  that 
point.  By  an  assumption  which  is  practically  correct,  the  aver- 
age speed  which  a  train  has  between  any  two  stations  is  its  actual 


CHAP.  XXIV.— OLD   LIXES— VIRTUAL   PROFILE.  799 

speed  at  a  point  midway  between  them.  The  vertical  heights 
should  therefore  be  laid  off  at  corresponding  points  on  the 
profile. 

In  this  way  we  obtain  our  virtual  profile,  parts  of  which  may 
be  something  like  the  dotted  line  on  the  following  Fig.  256,  the 
solid  line  being  the  actual  profile. 

r 2-s 

0.4-    _. 

T 0.6 

--^/i*  _^ 

Fig.  256. 

1081.  This  virtual  profile,  as  we  have  seen,  is  that  which  alone 
needs  to  be  considered.  It  represents  a  line  over  which,  if  it 
were  actually  constructed,  a  locomotive,  exerting  at  every  point 
the  same  energy  and  overcoming  the  same  frictional  resistances, 
would  move  at  every  point  without  either  gaining  or  losing 
speed.  On  this  profile  what  appears  to  be  and  what  is  coincide, 
if  the  virtual  profile  shows  a  low  enough  rate  of  grade  we  need 
not  be  disturbed  if  the  actual  profile  below  it  shows  a  consider- 
ably higher  grade.  On  the  other  hand,  if  the  virtual  profile 
shows  a  short  heavy  grade  in  pulling  out  from  a  station,  which 
cannot  be  reduced  by  taking  more  time  in  starting  trains,  its 
disadvantage  is  no  whit  less  because  it  is  short  or  because  the 
actual  grade  below  it  is  almost  a  level. 

The  virtual  profile  will  differ  according  to  the  direction  the 
train  is  running,  as  well  as  more  or  less  with  each  record  taken; 
but  from  all  these  notes  together  a  safe  average  is  supposed  to 
have  been  determined  at  each  point. 

1082.  Studying  how  to  reduce  this  virtual  profile,  we  recog- 
nize three  ways: 

First  (and  simplest),  to  vary  the  velocity  by  increasing  it 
in  the  hollow  of  grades  and  decreasing  it  on  the  summits  and  by 
eliminating  or  taking  longer  time  for  stops.  By  carrying  this 
process  far  enough,  we  may  reduce  the  virtual  profile  of  an  un- 
dulating line  having  very  heavy  grades  to  a  level,  as  we  have 


8C0  CHAP.  XXIV.— OLD   LINES— VIRTUAL  PROFILE. 

seen  (par.  399);  but,  practically,  only  minor  variations  of  this 
kind  are  admissible. 

Secondly  (and  next  simplest),  by  using  pushers. 

Thirdly,  by  reconstruction  or  amendment  of  the  actual 
profile. 

1083.  Let  us  suppose,  as  examples  are  most  readily  followed^ 
that  these  observations  have  been  taken  and  the  virtual  profiles 
made  over  a  given  division  with  the  results  at  various  points 
outlined  on  the  following  Figs.  257  to  264. 

Some  long  hard  pull  on  a  1.2  per  cent  grade  {6t,.2,6  feet  per 
mile)  shows  that  the  given  engines  can  handle  25  cars,  more  or 
less,  on  this  grade  with  great  ease,  except  in  very  unfavorable 
weath'er.  Under  fairly  favorable  conditions  the  velocity  gained 
without  overtaxing  the  boiler  capacity  is  such  as  to  indicate  a 
virtual  maximum  grade  of  1,4  per  cent,  or  even  more. 

The  same  is  true  at  a  number  of  minor  points  on  the  same 
division. 

In  pullmg  out  at  stations,  by  comparison  of  many  observa- 
tions, it  is  found  under  average  conditions  that  the  virtual  grade 
was  1.3  to  1.5  without  using  sand  (being  somewhat  lower  be- 
cause of  the  greater  journal-friction,  and  lower  because  the  full 
adhesion  was  more  nearly  used  and  there  was  less  air  and  other 
velocity  resistance),  while  when  sand  was  used  the  virtual  grade 
was  raised  to  1,6  or  1.8.  On  the  other  hand,  with  very  unfa- 
vorable weather  and  a  bad  rail,  the  virtual  profile  in  starting  is 
1.2  to  1.4,  even  with  use  of  sand. 

1084.  Under  these  conditions  we  have,  in  the  first  place,  an 
indication  that  the  trains  now  handled  on  the  road  as  it  stands 
are  somewhat  smaller  than  they  might  be — an  indication  which 
is  alone  worth  the  trouble  of  an  investigation  of  this  kind,  and 
can  in  no  other  way  be  so  accurately  determined.  Passing  that 
question,  however,  as  not  now  under  consideration,  we  have  a 
very  positive  indication  that  we  shall  be  safe  in  assuming  that 
by  using  a  pusher  of  equal  power  over  the  worst  grade,  we  shall 
in  effect  reduce  it  to  the  equivalent  for  a  single  engine  of  a 
pusher  grade  of  1.2  per  cent,  which  is  (Table  182,  page  593)  0.45 


CHAP.  XXIV.— OLD   LINES— VIRTUAL   PROFILE. 


8oi 


per  cent  (23.8  feet  per  mile).  This,  therefore,  is  what  we  should 
try  for  over  the  remainder  of  the  division.  If  we  find  it  easy  of 
accomplishment,  we  may  consider  reducing  it  still  lower  and 
using  a  heavier  pusher  engine,  but  such  course  is  to  be  adopted 
with  caution. 

The  actual  grade  at  stations  on  this  grade  should  not  be 
more  than  0.5  for  at  least  700  ft.,  and  i.o  for  1000  ft.  beyond,  but 
by  use  of  sand  may  be  somewhat  higher  for  short  distances. 


Over  the  remainder  of  the  division  we  are  liable,  at  various 
points,  to  have  cases  like  the  following: 

1085.  A  station   grade  at  A,  Fig.  257,  on  an  actual   grade  of 
0.6,  is  operated  very  easily  now,  the  train  quickly  getting  under 
way  even  without  the  use    ***«•. 
of  sand.     By  taking  more  "'*^*»->.^ 

time    for    starting    heavy 
trains   (say  attaining    full 

working  speed  at  j5*)    the  Fig.  258. 

virtual  grade  might  be  reduced,  perhaps,  to  75,  but  it  is  neces- 
sary to  reduce  it  to  0.5  at  least,  and  if  possible  to  0.4,  the  actual 
grade  needing  to  be  considerably  less. 

The  neatest  and  most  effectual  method  is  to  remove  the  sta- 
tion at  once  from  A  to  B,  this  alone  having  the  effect  to  favor- 
ably modify  the  virtual  profile  far  more  than  was  desired,  giving 
that  shown  in  Fig.  258.  If  this  be  impossible,  the  next  best 
method  is  to  take  out  the  bad  gradient  in  the  virtual  profile  by 
raising  the  grade  at  A  on  the  actual  profile  to  A' ^  giving  it  the 
form  shown  in  Fig.  259.  Changes  of  this  kind  are  apt  to  be 
expensive  because  of  their  locality;  but,  on  the  other  hand,  they 


802 


CHAP,  XXIV.— OLD  LINES— VIRTUAL  PROFILE. 


are  inexpensive  in  tliat  they  are  seldom  very  long.  The  effect  is 
to  substitute  (in  the  lower  half  of  the  diagram)  a  broken  actual 
but  good  virtual  profile,  in  place  of  a  good  actual  but  bad  virtual 
profile,  as  in  the  upper  half  of  Fig.  259. 

1086.   A  modification  of  the  same  case  may  be  as  follows:  A 
-_,^_  station  originally  well  situ- 

ated, as  S,  Fig.  260,  but 
which  has  been  complicated 
by  subsequent  additions  of 
grade-crossings  for  other 
lines  C  and  C,  at  which  all 
trains  have  to  stop  and 
^^^'  ^^^'  start  again  on  a  grade. 

The  first  and  best  remedy  for  this  evil  is  the  use  of  inter- 
locking signals,  saving  the  necessity  of  a  stop  except  to  let 
another  train  pass;  but  as  that  is  a  contingency  which  may  hap- 
pen not  infrequently,  it  can  never  be  a  perfect,  nor  in  some 
cases  sufficient,  remedy.     The  evil  may  also,  in  cases,  be  reme- 


FlG. 260. 


died  by  raising  the  grade  of  the  track  approaching  the  crossing 
as  outlined  at  Cand  C",  provided  the  virtual  grade  of  the  approach 
be  not  increased  thereby  to  an  inadmissible  rate.  The  only 
remaining  course  is  either  to  use  a  yard  engine  as  a  helper  over 
the  crossings  or  to  boldly  lower  the  grade  by  passing  under 
each  road,  and  grading  a  new  road-bed  or  lowering  the  existing 
one,  for  which  room  may  be  so  scant  as  to  require  retaining- 
walls.  This  will  make  the  improvement  a  costly  one,  and  yet 
the  cost  w^ill  probably  be  small  in  proportion  to  the  gain, 
unless  it  is  only  one  among  many  costly  improvements  required 
for  the  desired  end. 

1087.  At  large  towns  it  is  a  very  common  thing  to  find  the 
station  located  at  some  point,  like  S  or  S' ,  Fig.  261,  which  was 


Fig.  261. 


CHAP.  XXIV.— OLD   LINES— VIRTUAL   PROFILE.  803 

originally  fixed  more  with  reference  to  the  convenience  of  the 
town  than  to  the  grades.  This  is  of  course  the  proper  thing  to 
do,  and  a  decrease  of  station 
facilities,  or  a  change  causing 
inconvenience  to  the  patrons  of 
the  line,  will  in  general  be  inex- 
pedient. Such  large  stations, 
moreover,  are  generally  well  provided  with  side  tracks,  so  that 
the  result  is  that  they  are  largel}^  used  by  train-dispatchers  as 
passing  points. 

The  proper  remedy  in  such  cases  is  to  establish  sidings,  For 
y,  to  serve  as  passing  points  for  through  trains  only,  with  a 
separate  telegraph-office,  leaving  the  local  facilities  undisturbed. 
This  requires  the  services  of  two  operators  to  do  the  work  of  one, 
and  perhaps  one  or  two  other  otherwise  needless  employes,  but 
the  wages  of  one  train  crew  for  a  single  trip,  it  should  be  re- 
membered, will  pay  the  wages  of  a  good  operator  for  a  week. 

1088.  The  case  sketched  in  Fig.  261,  moreover,  is  one  of 
those  where  the  whole  difficulty  in  handling  heavier  trains  may 
be  made  to  vanish  by  a  modification  of  the  system  of  dispatch- 
ing, to  the  effect  that  only  trains  going  down  grade,  or  say  east, 
shall  be  held  at  this  station  and  compelled  to  take  side  track 
(except,  of  course,  in  emergencies),  especially  if  there  be  another 
regular  station  near  to  it,  as  For  Y' ,  which  may  be  used  as  a 
passing  point,  b}^  holding  one  or  the  other  train,  in  case  it  is  im- 
possible for  the  eastward  train  to  reach  S  or  S'  first.  It  is  not 
essential,  although  it  is  convenient,  that  a  dispatcher  should  feel 
at  liberty  to  hold  any  train,  bound  either  way,  at  any  station,  in 
the  regular  routine  of  business,  provided  that  to  do  so  interferes 
with  a  material  addition  to  the  train-load.  It  is  the  rule  and 
not  the  exception,  however,  that  he  can  and  does  do  so. 

1089.  The  decision  as  to  what  course  to  adopt  for  modifica- 
tions of  gradients  on  the  open  road  is  a  much  simpler  matter 
than  at  stations.  The  vital  point  to  be  determined  in  the  begin- 
ning, before  studying  the  details  of  the  various  difficult  points  at 
all,  is  what  rate  of  speed  is  practicable  and  allowable  at  the  foot 


804  CHAP.  XXIV.— OLD  LINES— VIRTUAL   PROFILE. 

of  the  grade,  which  largely  depends  on  the  alignment.  The 
modern  tendency  is  very  decidedly  to  permit  of  higher  speed  in 
handling  freight  trains,  and  it  is  essential  to  do  so  at  points  to 
handle  the  maximum  train  on  all  undulating  gradients.  The 
probable  introduction  in  the  near  future  of  freight-train  brakes 
and  more  mechanical  coupling  devices  than  are  now  in  use  will, 
when  accomplished,  greatly  increase  the  admissible  maximum 
of  speed  for  equal  safety;  but  even  as  freight  equipment  stands 
at  present  it  is  probable  that  30  or  35  or  even  40  miles  per  hour,, 
for  short  distances  at  special  points  (the  writer  must  not  be 
understood  to  recommend  the  latter  speed),  are  quite  as  safe  as 
50  to  65  miles  per  hourfor  passenger  trains.  It  has  been  tolerably 
well  determined  (par.  664  et  al^  that  higher  speeds  than  15  miles 
per  hour  are  more  economical  for  freight  trains;  and  the  not  un- 
common feeling  that  any  speed  of  over  15  or  20  miles  per  hour 
verges  on  the  dangerous  is  in  part  a  relic  of  the  old  days  of  iron 
rails,  poor  ballast  and  road-bed,  and  less  solidly  constructed  roll- 
ing-stock. 

1090.  Therefore,  when  required  for  reducing  virtual  gradients 
by  taking  a  "  run  at  them,"  as  part  of  a  general  system  of  im- 
provements, a  speed  of  30  miles  per  hour  (which  takes  31.95  ver- 
tical feet  out  of  the  depth  of  a  hollow;  Table  118)  should  be 
freely  permitted  and  counted  on,  with  fair  alignment;  and  with 
a  tangent  in  the  hollow  of  the  gradients  this  limit  may  in  gen- 
eral be  safely  increased  to  35  miles  (43.49  vertical  feet),  if  that 
speed  seems  essential.  These  speeds  and  even  higher  ones  are 
now  frequently  used  in  handling  freight  trains  on  many  lines. 
Whatever  the  limit  adopted,  however,  it  should  be  determined 
in  advance,  by  reference  to  the  records  obtained  as  already  de- 
scribed, and  especially  with  careful  consideration  as  to  whether 
the  assumed  speed  ca7i  with  certainty  be  counted'on  as  attainable  at 
the  given  point.  Unless  there  be  a  descending  gradient  in  the 
approach  so  as  to  give  the  required  speed  quickly,  the  high  speeds 
mentioned  cannot  be  counted  on  safely. 

1091.  This  preliminary  being  determined  and  the  present  and 
desired  gradients   being  the   same  as   already   assumed,  viz.,  1.2 


CHAP.  XXIV.  — OLD  LINES— VIRTUAL   PROFILE. 


805 


Fig.  262 


actual  and  0.45  desired,  Figs.  262  to  265  will  serve  as  types  of  all 
the  cases  which  can  arise  on  the  open  road.  In  Fig.  262  let  AB 
be  a  long  i.o  per  cent  grade  with 
curved  alignment  at  B  so  that 
more  than  30  miles  per  hour  is 
not  deemed  safe  at  that  point, 
but  that  or  even  higher  velocity- 
is  easily  attainable.  With  the 
short  trains  heretofore  in  use  the  grade  has  not  been  a  difficult' 
one,  so  that  the  virtual  profile  obtained  in  observations  on  trains 
as  now  run  has  been  nearly  parallel  with  the  grade,  the  speed 
being  lower  at  B  and  higher  at  A  than  was  necessary.  It  is  de- 
sired to  determine  to  what  extent  (i.e.,  for  what  length)  such  a 
grade  can  be  operated  as  a  virtual  0.5  gradient. 

1092,  A  certain  speed  at  A,  not  less  than  10  miles  per  hour 
(3.55  vertical  feet),  niust  be  assumed,  as  a  margin  for  error, 
whether  there  be  a  station  at  A  or  ?iot  (par.  1095).  Then  31.95  —  3.55 
=  28.4  vertical  feet,  as  the  maximum  through  which  momentum 
can  be  relied  on  to  lift  the  train.  Moreover,  the  actual  grade  i.o 
—  0.5  (assumed  virtual  grade)  =0.5  feet  per  station  as  the  defi- 
ciency in  power  of  the   locomotive  which  must  be   made  up  by 

o 

momentum.     We  have  then  — '—  =  56.8  stations,  or  over  a  mile, 


Fig.  263 


or  56.8  vertical  feet  of  rise,  as  the  length  of  this  grade  which  it 
is  possible  to  operate  in  this  manner.  If  the  grade  be  longer  or 
shorter  than  this,  the  overplus,  but  the  overplus  only,  must  be 
taken  out  by  new  construction,  either  by  raising  the  grade  at  B 
or  (what  is  better)  lowering  it  at  A.    If  the  grade  were  ten  stations 


8o6  CHAP.  XXIV.— OLD   LINES— VIRTUAL   PROFILE. 

longer,  those  ten  stations,  but  those  only,  must  be  reduced  to 
0.5  actual  grade  in  one  or  the  other  of  the  methods  outlined  in 
Fig.  263.  If  the  change  be  made  at  the  bottom  of  the  hill,  as  at 
B^  we  shall  have  the  disadvantage  that  on  the  whole  of  the  new 
0.5  gradient  a  speed  of  30  miles  per  hour  must  be  maintained  to 
have  the  desired  effect.  As  this  may  be  or  may  seem  objection- 
able, the  modification  may  need  to  be  more  extensive  to  effect 
the  desired  end,  and  should  be,  wherever  possible. 

1093.  The  same  is  true,  in  less  degree,  of  the  change  at  the 
top.  The  train,  under  the  assumptions,  will  not  be  able  to  move 
faster  than  10  miles  per  hour  until  it  has  passed  entirely  over  it. 
Therefore  the  maximum  figures  for  the  gain  by  momentum 
should  be  used  only  for  determining  whether  or  not  any  modification 
of  the  grade  will  be  required.  If  it  is  even  then  found  necessary,  a 
more  liberal  margin  should  at  once  be  adopted,  if  attainable  at 
moderate  increase  of  cost,  as  it  generally  will  be. 

In  fact,  when  some  construction  in  any  case  has  been  once 
found  necessary  it  may  often  be  best  and  almost  as  cheap  to  take 
the  whole  hill  out  at  once  by  a  detour;  perhaps  making  the  new 
and  old  lines  together  serve  as  in  effect  a  double  track. 

1094.  It  is  to  be  remembered  in  considering  what  allowance 
it  is  safe  to  make  for  assistance  by  momentum,  that  in  many 
cases  an  error  in  the  estimate  of  the  possible  gain  from  that 
source  will  have  no  disastrous  consequences,  since  if  it  be  found 
that  the  assumed  speed  was  too  great  to  be  relied  on  it  is  pos- 
sible at  any  time  to  raise  the  grade  three  to  five  feet  in  the  hol- 
low, as  outlined  in  Fig.  264,  and  thus  materially  reduce  the  speed 

required.      To   do  this  is  in 
most   cases   a  comparatively 
simple  matter,  since  the  fills 
^^^^..^-^"'^^  need    not    be    very   long    to 

Pj^  ^g  raise  the  hollow  between  two 

gradients  by  a  considerable  amount.  If  the  two  gradients  are  i 
per  cent,  the  total  length  of  the  fill  is  only  200  feet  per  foot  of 
lift ;  with  0.5  gradients,  400  feet  per  foot  of  lift;  and  with  1.5 
gradients,  133  feet  per  foot  of  lift,  etc.     To  make  fills  by  train  in 


CHAP.  XXIV.— OLD   LINES— VIRTUAL   PROFILE.  807 

such  locations,  even  if  of  considerable  magnitude,  is  rarely  ex- 
pensive, and  it  can  be  done  at  any  time  when  found  convenient 
and  essential.  Therefore,  when  it  is  seen  that  a  not  excessive 
fill  will,  if  made,  fulfil  all  necessities,  it  is  proper  to  rely  quite 
largely  on  momentum  for  the  time  being,  if  by  so  doing  the  fill 
can  be  dispensed  with  for  a  time  at  least,  and  perhaps  forever. 

1095.  On  the  other  hand,  there  is  a  danger  connected  with 
the  study  of  such  virtual  profiles,  which  has  been  alluded  to 
above,  but  which  should  be  still  more  explicitly  pointed  out. 
When  the  question  whether  or  not  we  can  keep  within  a  certain 
virtual  gradient  is  at  stake,  as  in  Fig.  265,  it  is  in  no  case  safe, 
even  when  there  is  a  station  at  r~~-^ 
the  top  of  the  hill  at  A,  to  assume 
that  we  can  arrive  there  with  no 
velocity,  and  can  consequently 
lay  the  virtual  gradient  directly 
on   the  actual.     It  seems  plausi-  ^^"  ^^^' 

ble  that  we  can  do  this,  as  we  are  certain  that  we  shall  need  no 
velocity  at  A\  but  what  we  are  not  sure  of  is  of  never  falling 
below  the  desired  velocity  at  B,  and  if  we  do,  our  virtual 
gradient  is  at  once  increased.  If  we  assume  a  certain  moderate 
velocity  at  A,  say  10  miles  per  hour  (3.55  vertical  feet),  and  any 
maximum  velocity  deemed  reasonable  at  B,  as  in  cases  where  no 
stop  is  contemplated,  we  are  safe,  because  our  velocity  at  ^  may 
then  fall  quite  a  little  below  that  assumed  without  endangering 
our  arriving  at  A  with  some  velocity,  so  as  to  float  the  train  over 
it;  but  if  we  assume  we  are  to  arrive  at  A  with  no  velocity,  sim- 
ply because  the  train  must  stop  there,  we  are  liable  not  to  reach 
there  at  all.  No  advantage  can  be  assumed,  therefore,  from  the 
fact  of  a  stop  at  the  top  of  the  gradient  more  than  would  exist  if 
there  were  to  be  no  stop  there  at  all.  In  either  case  we  must  be 
sure  of  reaching  the  top,  and  in  neither  case  is  it  important  to  be 
sure  of  more  than  that. 

1096.  The  temptation  may  be  great  to  fall  into  this  plausible 
error,  when  an  estimate,  perhaps,  must  be  kept  very  close  to  have 
the  work  go  through  at  all,  and  when  there  maybe  an  expensive 


8o8  CHAP.  XXIV.— OLD   LINES— VIRTUAL   PROFILE. 

bridge  at  B^  making  it  difficult  to  lift  up  the  grade  at  that  point; 
but  if  a  reasonable  velocity  at  B  and  some  velocity  at  A  will  not 
suffice,  there  is  nothing  for  it  but  either  to  raise  the  bridge, 
lower  the  station,  increase  the  distance  between  them,  or  give  up 
the  desired  virtual  maximum  as  unattainable. 

1097.  By  attacking  the  work  of  improving  old  lines  in  the 
method  here  outlined,  halving  the  more  formidable  and  inevi- 
table grades  at  once  by  using  a  pusher  on  them,  without  spend- 
ing a  dollar  on  them,  and  spending  all  our  money  on  what  were 
before  the  very  easy  grades,  and  hence  are  usuall}^  in  light  work, 
the  average  train-load  may  be  doubled  at  small  cost  on  thousands 
of  miles  in  this  country  ;  whereas  by  merely  attacking  the  heav- 
iest grades  which  show  on  the  profile  with  force  and  arms,  so  to 
speak,  a  great  deal  of  money  must  be  spent,  and  there  will  be 
comparatively  little  to  show  for  it. 


CHAP.  XXV.—GRADE-CROSSINGS  AND   INTERLOCKING.    809 
CHAPTER   XXV. 

GRADE-CROSSINGS    AND    INTERLOCKING. 

1098.  The  multiplication  of  grade-crossings  has  become  a 
great  and  serious  question,  especially  in  the  West.  The  topo- 
graphical conditions  in  the  East  greatly  restrict  the  danger  from 
such  crossings,  as  well  as  their  frequency;  but  throughout  vast 
regions  of  the  West  there  is  absolutely  nothing  to  prevent  a 
railvva}"  being  built  from  anywhere  to  anywhere  in  very  nearly 
an  air-line  by  accepting  "  moderate"  grades  of  40  to  80  ft.  per 
mile.  As  a  consequence,  many  important  lines  have  little  or  no 
assurance  that  crossings  may  not  be  demanded  of  them  sooner 
or  later  on  any  single  mile  of  their  track,  and  it  becomes  of  great 
importance  to  determine  how  strenuously  they  should  oppose 
such  crossings,  what  expense  they  may  and  should  incur  to 
avoid  them,  and  what  can  be  done  to  reduce  their  disadvantages 
to  a  minimum  when  unavoidable. 

The  problem  has  been  greatly  simplified  in  recent  years  by 
the  fact  that  the  disadvantages  of  grade-crossings  may  be  largely 
diminished,  and  sometimes  almost  destroyed,  by  the  use  of  inter- 
locking apparatus,  as  we  have  seen  in  par.  1086  and  elsewhere; 
but  while  there  were  in  1885  some  60  railways  in  the  United 
States  using  interlocking  more  or  less,  the  total  amount  in  use 
was  considerably  less  than  on  the  London  &  Northwestern 
alone. 

1099.  There  are  18  different  sizes  of  standard  signal-cabins  on  the  London 
&  Northwestern  Railway,  which  are  : 

A.  5    levers,     6    X    6  ft.  D.   20  levers,  16  ft.  2\  in.  X  12  ft. 

B.  10       "  9    X    9  ft.  (and  so  on  to — ) 

C.  15        "         I3|-Xi2ft.  T.    180  levers,  96  ft.  6  in.  X  12  ft. 

The  usual  rule  being  that  the  cabins  are  all  12  ft.  wide  and  are  6  in.  long  per 
lever,  plus  about  6^  ft.     There  are  1344  of  these  cabins  on  1753  miles  of  road, 


8lO     CHAP.  XXV.— GRADE-CROSSINGS  AND   INTERLOCKING. 

containing  26,500  levers.  The  annual  average  cost  for  maintenance  is  $187,000, 
which,  divided  by  the  number  of  levers  in  use  on  the  line,  comes  to  $7.07  per 
lever.  This  amount  includes  not  only  the  renewal  and  repairs  of  the  locking 
apparatus,  but  that  of  the  signal-cabins,  signals,  and  all  subsidiary  apparatus, 
and  also  the  cost  of  providing  any  new  and  additional  apparatus,  when  under 
$50.  The  amount  of  work  to  be  maintained  has  increased  80  per  cent  since 
the  year  1874,  while  the  cost  of  maintenance  has  only  increased  5^  per  cent. 

In  the  whole  United  States  there  are,  of  all  systems  (1885),  somewhat  less 
than  250  cabins  and  3000  levers,  or  but  about  one  fifth  as  many  cabins  and 
about  one  ninth  as  many  levers  as  are  in  use  on  the  London  &  Northwestern 
alone. 

1100.  In  England  there  are  practically  no  grade-crossings 
of  railways,  and  this  apparatus  is  used  chiefly  for  yards  and 
junctions.  In  America  there  are  a  great  many  grade-crossings^ 
even  on  important  lines;  but  the  clumsy  and  costly  precaution 
of  a  full  stop  of  every  train  at  every  crossing  is  still  the  rule,  al- 
though it  can  hardly  be  that  such  an  absurd  relic  of  barbarism 
will  linger  much  longer,  now  that  there  is  a  considerable  and 
increasing  number  of  grade-crossings  operated  without  a  stop 
by  the  aid  of  interlocking  apparatus,  and  always  with  perfect 
safety  and  success. 

1101.  In  part,  the  slow  progress  in  this  matter  is  easily  ex- 
plained. The  great  loss  and  delay  from  grade-crossing  stops 
goes  on  quietly  and  silently,  sapping  the  life-blood  of  the  com- 
pany, as  do  the  consequences  of  bad  location  (page  2),  without 
interfering  much  with  the  routine  of  operation,  and  at  points 
removed  from  the  managing  officers'  immediate  observation, 
whereas  the  difficulties  at  yards  obtrude  themselves  on  atten- 
tion, and  many  of  the  most  crowded  yards  have  passed  the  limit 
of  their  capacity  without  some  such  mechanical  aid. 

1102.  Nevertheless,  from  an  economical  point  of  view,  abol- 
ishing the  stop  at  grade-crossings  is  by  far  the  most  important, 
especially  when,  as  is  so  frequently  the  case,  they  reduce  the  num- 
ber of  cars  hauled  below  what  it  otherwise  would  be.  To  reach 
this  conclusion  we  need  not  adopt  any  of  the  wild  estimates 
which  give  the  cost  of  a  stop  at  anywhere  from  a  dollar  up. 
Without  going  elaborately  into  the  details  of  the  estimate,  to 
discuss  which  properly  by  items  w*ould   take  considerable  space, 


CHAP.  XXV.— GRADE-CROSSINGS  AND   INTERLOCKING.     8ll 

from  30  to  60  cents  may  fairly  be  taken  as  the  cost  of  a  stop, 
apart  from  all  effect  on  length  of  trains.  An  estimate  of  40  cts. 
per  stop  for  average  trains  on  lines  doing  considerable  through 
business  can  hardly  be  considered  excessive,  and  at  this  rate  the 
cost  per  year  of  each  train  per  day  stopping  at  the  crossings  is 
365  X  40  =  $146  per  year.  If  therefore  there  is  an  average  of 
ten  trains  per  day  each  way  for  each  of  the  roads  which  cross 
(and  the  average  at  grade-crossings  would  probably  be  more 
rather  than  less  than  this),  we  have  $146  X  10X2X2  =  $5840 
as  the  annual  loss  to  both  roads  from  the  fact  of  the  existence  of 
this  crossing. 

1103.  The  cost  of  saving  this  loss  by  constructing  a  new  line 
or  by  interlocking,  will  vary  more  or  less  with  the  locality  and 
in  less  degree  with  the  system  of  interlocking  adopted  ;  but  the 
variation  in  the  latter  respect  is  not  important,  and  the  outside 
limit  for  a  complete  system  of  interlocking;  switches  and  signals 
for  either  single  or  double  track  (it  makes  little  difference 
which),  by  one  system  of  approved  excellence  may  be  stated  to 
be  from  $2500  to  $4000,  averaging  $3000.  This  includes  eight 
signals  (four  "  home"  or  near  signals,  and  four  distant  signals, 
two  for  each  track),  four  derailing  switches,  one  for  each  track, 
which  throw  the  train  off  onto  a  graded  road-bed  (having  no 
rails  and  ties  for  only  a  short  way),  if  the  signal  be  carelessly  run 
by,  and  (for  a  separate  sum  of  $400),  electric  locking  apparatus 
which  renders  it  impossible  to  change  the  signals  after  a  train 
has  once  passed  the  first  distant  signal  until  it  is  over  the  cross- 
ing. The  cost  of  the  building  and  of  erection  is  included  in 
the  above. 

One  man  only  is  required  to  attend  to  the  signals,  as  is  re- 
quired without  interlocking,  and  his  wages  need  be  little  if  any 
higlier,  so  that  this  item  may  be  considered  unaffected. 

1104.  Even  with  the  lightest  ordinary  traffic,  therefore,  the 
lowest  reasonable  estimated  cost  of  stop,  and  the  highest  prob- 
able rate  of  interest,  the  sum  saved  annually  is  far  more  than 
enough  to  cover  the  additional  expe?ise  of  thoroughly  protecting  a  grade- 
crossing   so    that   no   stop   need   be    made,    without   considering    the 


Sl2     CHAP.  XXV  —GRADE-CROSSINGS  AND   INTERLOCKING. 

greater  safety  and  convenience.  At  more  important  crossings 
it  would  be  hard  to  find  a  clearer  case  of  an  expedient  improve- 
ment, even  if  the  stops  do  not  cut  down  the  length  of  train. 

1105.  If  the  length  of  train  is  cut  down,  so  as  to  take,  say, 
21  instead  of  20  trains  per  day  to  handle  the  traffic,  the  very 
lowest  cost  for  which  the  extra  train  can  be  run  is  (Table  176) 
35  to  40  cents  per  train-mile  (for  an  average  cost  of  70  to  80 
cents),  or  say  %2i'^  for  a  trip  of  100  miles,  amounting  to  $13,870  per 
annum,  or  $693.50  for  each  of  the  20  trains,  or  $1.90  per  stop  (if 
only  one  stop  causes  the  decrease  of  train-load)  in  addition  to 
THE  DIRECT  COST  of  the  stop.  In  such  cases,  of  which  there  are 
many,  it  is  culpable  folly  to  delay  availing  one's  self  of  so  cheap 
and  easy  a  remedy  for  such  losses  as  interlocking  affords,  if  the 
conditions  are  not  favorable  for  the  still  better  and  in  the  end 
often  cheaper  remedy,  an  over-  or  under-crossing. 

1106.  A  fact  which  explains  rather  than  excuses  the  prevail- 
ing negligence  in  this  matter  is  this, — that  the  protection  of 
grade-crossings  requires  the  joint  action  of  two  roads,  usually 
under  different  and  often  under  antagonistic  management,  and 
it  requires  no  little  negotiation,  and  a  conciliatory  spirit  on  both 
sides,  to  arrange  the  details  of  the  distribution  of  the  expense. 

It  can  hardly  be  doubted  that  this  difficulty  is  a  serious  one, 
and  it  is  largely  the  fault  of  the  laws  which  authorize  the  use  of 
interlocking  as  a  substitute  for  stops.  By  some  singular  over- 
sight, all  these  laws  as  yet  passed  (1886)  authorize  roads  to 
"agree"  on  putting  in  interlocking,  but  do  not  provide  a  way  by 
which  one  road,  anxious  to  act  under  the  law,  can  compel  an- 
other road  to  accept  a  reasonable  settlement  by  arbitration  or 
otherwise,  unless  it  chooses  to. 

1107.  The  provisions  of  the  State  laws  as  to  dispensing  with  crossing  stops 
may  be  briefly  summarized  as  follows  : 

The  Massachusetts  law  passed  in  1882,  after  somewhat  urgent  recommen- 
dations by  its  Commission,  which  were  at  the  time  regarded  by  many  as  some- 
what heretical  (because  the  public  knowledge  of  interlocking  was  much  less  then 
than  it  is  now,  even  among  railroad  men),  provides  that  "The  approval  of  the 
Board  shall  be  required  for  a  system  of  signals  to  be  established  and  main- 
tained in  concert"  by  railroads  which  cross  each  other,  but  that  a  full  stop  shall 


CHAP.  XXV.—GRADE-CROSSIiYGS  AND   INTERLOCKING.     813 

not  be  dispensed  with  "  unless  a  system  of  interlocking  or  of  automatic  signals, 
approved  in  writing  by  the  Board,  is  adopted  by  both  corporations." 

Ohio,  at  almost  the  same  time,  provided  by  law  that  "any  works  or  fix- 
tures" approved  by  the  Commissioner  of  Railroads  and  Telegraphs  as  render- 
ing it  safe  to  dispense  with  stops,  plans  having  been  filed  with  him,  shall 
.dispense  with  the  necessity  of  a  stop;  and  if  the  Commissioner  shall  fail  to 
approve  the  plan  within  twenty  days,  ''such  companies"  may  apply  to  the  Court 
of  Common  Pleas,  where  appropriate  action  will  be  held.  This  enactment 
seems  to  require  not  only  that  both  companies  shall  consent  passively,  but 
that  they  shall  unite  in  active  legal  proceedings  to  avert  a  decision  which  might 
be  not  unwelcome  to  one  of  them. 

Michigan  (1883)  passed  first  a  very  absurd  enactment  that  "authority  is 
hereby  given  to  said  Commissioner,  and  it  shall  be  his  duty,  if  he  shall  deem  it 
practicable,  to  prescribe  the  use  of  the  interlocking  switch  and  signal  system, 
provided  that  at  crossings  where  all  trains  come  to  a  full  stop  no  other  system 
than  that  requiring  such  stop  shall  be  prescribed." 

The  absurdity  of  thus  cutting  off  one  of  the  chief  advantages  of  interlocking 
signals  struck  the  Legislature  almost  immediately,  however,  and  another  act  of 
the  same  session  provided  that  "whenever  there  shall  be  adopted  and  used  at 
any  such  crossing  an  interlocking  switch  and  signal  system,  or  other  device," 
which  the  Commissioner  thinks  makes  it  safe  to  dispense  with  a  stop,  he  may 
authorize  it  in  writing,  with  any  regulations  as  to  speed  or  other  matters  which 
he  deems  necessary,  and  with  power  to  revoke  his  action. 

In  the  strict  letter  of  these  laws,  the  Commissioner  may  prescribe  automatic 
signals  without  dispensing  with  a  stop,  but  can  only  authorize  the  stop  after  the 
apparatus  is  adopted  and  in  use.  Neither  is  he — what  is  a  more  serious  matter 
—given  any  specific  power  to  say  what  part  of  the  expense  each  of  the  two 
companies  concerned  shall  bear.  These  provisions  come  the  nearest,  however, 
of  those  of  any  State  to  providing  means  by  which  one  railway  which  is  anxious 
to  escape  from  the  burden  of  stopping  at  a  crossing  can  compel  the  other  bene- 
ficiary to  bear  its  fair  share  of  the  cost. 

The  Indiana  law  (1883)  is  merely  permissive,  authorizing  the  Auditor  of 
State  to  approve  interlocking  or  automatic  signals  at  crossings,  from  plans 
submitted  by  '' tzvo  or  moi-e  railroads,"  which  have  erected  or  are  about  to  erect 
them,  and  thereafter  to  authorize  the  omission  of  stops.  It  is  specifically  pro- 
vided that  such  signals  shall  not  be  "used  or  put  in"  at  any  crossing  "  to  the 
detriment  of  any  other  railroad  company,"  unless  with  the  consent  of  that  com- 
pany in  writing.  Under  this  provision,  the  manager  who  wishes  to  dispense 
with  twenty  different  crossings  must  first  undertake  the  interesting  task  of 
persuading  twenty  different  companies  that  it  will  not  be  "to  their  detriment" 
to  do  so. 

The  New  York  law  (1884)  provides  that  the  requirement  of  a  full  stop  may 
be  dispensed  with  whenever  the   Board  of  Commissioners  "decide  it  to  be 


8 14     CHAP.  XXV.— GRADE-CROSSINGS  AND  INTERLOCKING. 

impracticable"  or  where  "  interlocking  switch  and  signal  apparatus  is  adopted 
and  put  in  use  by  the  railroads  there  crossing  each  other  at  a  level,"  of  a  form 
approved  by  the  Board. 

Illinois  passed  through  one  house  in  1886  an  act  essentially  similar  to  that 
of  New  York,  which  was  expected  to  become  a  law  at  the  following  session. 

1108,  It  is  easy  to  see  how,  under  any  of  these  laws,  a  manager  attempting 
in  good  faith  to  benefit  his  company  and  benefit  the  roads  crossing  and  the 
public  as  well,  by  perfectly  fair  and  equitable  arrangements  for  dispensing  with 
stops  at  crossings,  might  find  it  an  irritating  and  almost  hopeless  task,  and 
might  feel  compelled  to  give  it  all  up  in  disgust  before  he  had  fairly  begun. 

The  difficulty  of  agreement  is  precisely  the  same  as  would  exist  in  cities  as 
respects  party-walls,  without  the  law  which  authorizes  any  man  to  build  half  his 
wall  on  his  neighbors  land  and  compel  his  neighbor  to  pay  for  it  when  he  uses 
it.  The  equities,  and  the  great  advantage  to  both  sides,  are  here  exceedingly 
clear,  yet  how  often  would  it  be  impossible  to  arrange  the  matter  if  it  could 
only  be  done  by  mutual  consent  and  agreement  in  each  case? 

The  case  is  worse  with  crossings  because  they  are  very  frequently  so 
situated  that  the  joint  consent  of  three  or  four  lines  is  necessary  for  any  action, 
and  in  still  more  instances  a  great  part  of  the  advantage  to  be  realized  from 
dispensing  with  any  one  crossing  can  only  be  obtained  by  dispensing  with  a 
series  of  perhaps  a  dozen. 

1109.  To  require  that  grade-crossings  should  never  be  per- 
mitted would  unquestionably  be  going  too  far,  especially  now 
that  interlocking  apparatus  has  been  invented  and  perfected;  but 
the  unrestricted  freedom  with  which,  in  most  of  the  States,  grade- 
crossings  can  be  forced  over  any  line  at  almost  any  point,  regard- 
less of  the  injury  inflicted,  is  an  unfortunate  and  shameful  state 
of  things,  which  pressingly  requires  correction,  and  which  per- 
haps might  readily  be  corrected  if  the  older  and  more  important 
railways  would  make  a  united  effort  to  secure  reasonable  and 
proper  restrictions.  Unfortunately  they  overreach  themselves  by 
asking  far  too  much. 

1110.  The  theory  of  the  present  laws  is  a  very  simple  one  ; 
something  like  this  : 

1.  "  Railways  are  a  supreme  public  necessity,  and  no  private 
interest  or  ownership  shall  be  allowed  to  stand  in  the  way  of 
their  cheap  and  easy  construction. 

2.  "  When  two  railways  want  the  same  spot  of  ground  they 
shall  occupy  it  in  common." 


CHAP.   XXV.  — GRADE-CROSSINGS  AND  INTERLOCKING.     815 

Unfortunately,  like  most  short  and  easy  cuts  to  justice,  it  is 
unequal  and  unfair  in  practice. 

The  theory  of  the  great  existing  railways  is  equally  simple, 
and  would,  if  it  were  allowed  to  prevail  in  practice,  be  equally 
unfair  : 

1.  "Our  railway  is  a  much  greater  public  benefit  than  these 
other  new  projects,  and  we  have  bought  and  paid  for  our  prop- 
erty. 

2.  "If  they  want  to  pass  over  our  property  they  must  keep 
out  of  our  way." 

nil.  This  preposterous  attitude — from  corporations  whose 
very  existence  was  made  possible  only  by  the  exercise  of  the 
supreme  power  of  the  State,  and  whose  very  nature  is  to  per- 
form one  of  the  duties  of  the  State  to  the  public — is  all  but 
universally  assumed  by  established  corporations  in  discussions 
of  crossing  cases  ;  except  in  those  cases  when  they  wish  to  build 
branches  or  sidings  over  a  rival's  road.  They  are  ver}^  quick  to 
point  out  that  some  new  line  can  build  an  over-crossing  for  less 
money  than  they  lose  by  a  grade-crossing,  but  they  rarely  offer 
to  pay  a  reasonable  proportion  of  the  extra  cost  of  the  course 
they  desire.  Even  when  they  do^  so,  there  being  no  recognized 
tribunal  to  decide  the  matter,  they  will  higgle  and  chaffer  over 
the  amount  to  be  paid  till  the  whole  negotiation  goes  for  naught. 

1112.  The  solution  of  the  whole  matter  seems  comparatively 
simple.  The  law  very  properly  takes  the  position  that  mere 
priority  of  construction  shall  be  allowed  little  or  no  weight.  All 
railways  alike  are  supposed  to  be  of  pressing  necessity  to  a  cer- 
tain number  of  people — many  or  few,  as  the  case  may  be;  and 
the  necessities  of  even  a  very  few  are  given  greater  weight  than 
a  loss  and  inconvenience  which  is  comparatively  trifling  to  each 
individual  affected,  and  can  only  become  very  large  when  dis- 
tributed among  a  large  number  of  people.  This  is  right  and 
proper  as  far  as  it  goes,  but  the  law  should  also  take  this  further 
precaution  :  without  paying  any  attention  to  the  vested  interests 
concerned,  as  such,  it  should  endeavor  to  enforce  that  course 
which  is  for  the  best  i7iterest  of  the  community  as  a  whole,  and  which 


8l6     CHAP.  XXV— GRADE-CROSSINGS  AND  INTERLOCKING. 

involves  the  least  aggregate  waste  of  human  labor  and  property; 
and  it  should  endeavor  to  distribute  the  cost  of  so  doing  as 
nearly  as  may  be  in  proportion  to  benefits  derived,  and  in  such 
manner  that  each  party  shall  be  benefited,  by  taking  what  is 
abstractly  the  proper  course.  All  this  might  be  obtained  by 
something  like  the  following  simple  provisions  : 

1113.  I.  Every  railway  hereafter  attempting  to  cross  another 
at  grade  shall  be  obliged  to  erect  and  pay  for  a  system  of  inter- 
locking signals,  to  be  thereafter  maintained  at  the  joint  expense 
of  the  two  roads,  unless  it  shall  appear  that  less  than  twenty 
trains  per  day  pass  the  crossing. 

2.  Any  railway  may  at  any  time  erect  interlocking  apparatus 
at  any  grade-crossing,  and  half  the  cost  of  erection  and  subse- 
quent maintenance  shall  be  chargeable  to  the  other  party  con- 
cerned, with  certain  provisions  for  exceptional  cases  ;  and  also 
provided — 

3.  Either  party  wishing  to  avoid  a  grade  crossing  should  be 
at  liberty  to  locate  an  over-  or  under-crossing  on  unobjectionable 
gradients,  and  to  demand  the  appointment  of  arbitrators  in  the 
usual  manner.  It  should  be  the  duty  of  these  arbitrators,  ^rj-/,  to 
determine  that  the  grades  and  alignment  of  the  new  line  are  of  a 
suitable  and  appropriate  character,  or  to  make  them  such  ; 
secondly,  to  determine  the  excess  in  cost,  if  any,  of  the  over-cross- 
ing over  the  grade-crossing;  and,  thirdly,  to  assess  this  difference 
in  cost  upon  the  two  lines  in  proportion  to  the  benefit  to  each  of 
avoiding  a  grade-crossing. 

1114.  These  three  provisions  seem  calculated  to  accomplish 
what  every  good  law  ought  to  accomplish.  They  would  make 
it  for  the  interest  of  both  parties  to  take  that  course  which  would 
be  best  for  their  joint  interest,  if  they  were  one  corporation. 
Thus,  supposing  a  new  road  which  will  run  say  five  trains  a  day 
wishes  to  cross  a  trunk  line  running  50  trains  a  day.  The  actual 
loss  to  the  community  of  a  grade-crossing  at  such  a  place  is  the 
cost  of  stopping  55  trains  a  day,  and  no  one  has  a  right  to  en- 
force such  a  loss  upon  others  to  save  an  investment  of  a  few 
thousand  dollars.     On  the  other  hand,  if  the  new  project  wanted. 


CHAP.  XXV.—GRADE-CROSSINGS  AND   INTERLOCKING.     817 


to  cross  another  minor  line  like  itself,  running,  say,  five  trains  a 
day,  neither  road  would  be  likely  to  move  for  an  over-crossing, 
nor  perhaps  even  for  interlocking  signals;  nor  is  it  for  the  interest 
of  the  community,  considered  as  a  whole,  that  they  should  do  so. 
It  is  not  true  at  all  that  every  element  of  danger  must  be  wholly 
eliminated  before  any  saving  of  expense,  however  great,  is  per- 
missible, but  that  methods  which  are  at  once  more  dangerous 
and  more  costly  should  have  continued  in  such  wide  and  all  but 
universal  use  so  long  will  seem  in  later  years  a  strange  comment 
on  our  civilization. 
52 


8l8  CHAP.  XXVI.— TERMINALS. 


CHAPTER   XXVI. 


TERMINALS. 

1115.  Terminal  facilities,  or  the  lack  of  them,  have  so  many 
times  been  a  leading  factor  in  the  success  or  failure  of  railways, 
and  are  in  all  cases  so  important  a  factor,  that  it  seems  desirable 
to  show  more  fully  than  has  been  yet  done  how  great  a  part  they 
are  of  the  investment  in  and  the  expenses  of  prosperous  lines, 
and  hence  how  dangerous  it  is  for  a  new  line  to  neglect  ample 
provisions  for  them.  This  perhaps  can  be  best  accomplished  in 
a  small  space  by  presenting  some  details  as  to  the  terminal  facil- 
ities at  a  few  great  traffic  points. 

1116,  Table  202  gives  an  unofficial  approximate  estimate,  com- 
piled by  Gratz  Mordecai,  C.E.,  of  the  actual  capital  represented 
in  the  terminal  work  of  moving  and  handling  freight  by  the 
trunk-line  railroads  at  the  port  of  New  York.  It  includes  the 
work  of  handling  coal  on  the  Delaware,  Lackawanna  &  Western 
Railroad,  but  on  no  other,  and  only  includes  a  small  part  of  the 
expenses  of  handling  and  lighterage  of  grain,  oil,  and  live-stock 
and  none  of  the  expenses  of  clerical  work  and  management  on 
any  of  the  roads.     It  may  be  summarized  thus  : 

Estimated  Cost  of  New  York  Terminal  Facilities. 

Capital      Cost        P  C. 

sum,         per  of 

millions,      year.       total. 

200  miles  track @  $10,000       2.0       0.12         2.2 

378  acres  yards %    52,000     20.0 

2.2  millions  sq.  ft.  piers @         i.oo        2.2 

2.0  millions  sq.  ft.  floor  area @        0.80        t.6 

o.Sg  millions  sq.  ft.  N.  Y.  city  stations @        6.00        5.4 

69  yard  engines  (cost). , @.      8,700        0.6 

44  propellers  (cost) @    25,000        i.i 

230  lighters  (cost) @      9,000       2.  i 

Total  investment  charges 35.0        2.1         38.5 

4.700  employes @$2  per  day  47.0        2.82       51.6 

450  tons  coal  per  day .@$4,  90       0.54         9.9 

Total.. 91.0       5.46      lOO.O 


CHAP.  XXVI.— TERMINALS. 


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820  CHAP.  XXVI.— TERMINALS. 

The  only  direct  return  received  from  the  merchants  by  these 
railways  for  tliis  work,  the  plant  of  which  represents  an  aggre- 
gate capital  of  at  least  ^35, 000,000,  and  the  power  and  force  em- 
ployed an  annual  expenditure  of  at  least  $3,500,000,  are  the 
charges  collected  for  long-distance  lighterage.  There  is,  how- 
ever, a  considerable  fixed  terminal  charge  of  five  cents  per  ton, 
more  or  less,  which  is  credited  to  the  terminal  road  before  the 
division  of  rates  is  made  according  to  distance  (par.  210),  so  that 
the  roads  terminating  at  New  York  are,  perhaps,  less  burdened 
than  the  average  by  the  terminal  expenses.  Assuming  6  percent 
interest,  this  estimate  shows  a  total  annual  expense  of  $5,500,000, 
and  taking  into  account  clerk  hire,  management,  repairs,  taxes, 
light,  stationery,  insurance,  and  all  other  expenses,  the  total  is 
probably  not  far  from  $10,000,000,  or  an  average  burden  on  each 
road  of  $2,000,000  every  year. 

1117.  If  we  include  the  terminal  expenses  paid  by  the  indi- 
vidual shippers,  as  well  as  by  the  railways,  the  above  totals,  large 
as  they  are,  sink  into  insignificance.  It  was  estimated  in  1875 
by  a  committee  of  the  American  Society  of  Civil  Engineers  that 
on  some  4,632,000  tons  of  the  freight  delivered  at  New  York  the 
total  terminal  expenses  were  $3.07  per  ton,  or  about  three  fifths 
of  the  then  rate  (25  cts.  per  100  lbs.)  from  Chicago  to  New  York. 
The  total  receipts  at  New  York  in  that  year  were  about  15,000,000 
tons  of  all  kinds  of  freight,  and  on  half  of  this  the  cartage  charge 
alone  was  estimated  at  $1.60  per  ton. 

Inasmuch  as  so  much  more  for  cartage  means  so  much  less 
available  for  freight  rates,  and  vice  versa,  on  a  large  proportion 
of  the  freight,  and  more  or  less  so  on  all  of  it  (par.  47),  we  have 
in  these  figures  some  indication  of  how  serious  a  deduction  the 
total  terminal  expenses  must  make  from  the  amount  available 
for  railroad  transportation  proper,  and  how  important  it  is  to 
have  terminal  facilities  of  the  best.  New  York,  however,  is  a 
true  terminal,  in  the  strict  sense  of  the  word.  Some  of  the  ter- 
minal points,  which  are  really  only  yards  of  interchange,  are  of 
even  greater  magnitude,  if  not  cost.  Lest  the  great  error  be 
fallen  into  of  assuming  that  the  terminal  facilities  at  New  York 
are  as  much  greater  than  those  at  other  cities,  as  New  York  is 


CHA  P.   XX  PV.  —  TERM  IN  A  L  S. 


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822  CHAP.  XXVI.— TERMINALS. 

greater  in  population,  some  notes  may  be  added  as  to  what  is 
really  only  the  largest  of  many  examples  of  interior  yards — those 
at  Buffalo,  N.  Y.  So  far  from  there  being  anything  exceptional 
in  the  New  York  terminals,  they  are  probably  smaller  in  extent 
and  cost  per  head  of  population  than  at  most  important  termi- 
nals, and  vastly  smaller  than  at  a  number  of  them. 

1118,  The  statistics  presented  in  Table  203  of  the  yards  in  Buf- 
falo leave  no  reasonable  doubt  that,  of  its  kind,  it  is  the  greatest 
in  the  world.  How  much  of  this  abnormal  magnitude  is  the 
healthy  and  natural  result  of  peculiar  traffic  conditions,  and  how 
much  of  it  is  mere  fungous  growth  from  diseases  of  management 
whose  existence  is  universally  felt,  it  would  be  useless  to  inquire 
here,  because  as  things  are  it  is  all  necessary,  and  there  is  no  im- 
mediate evidence  of  any  probable  change.  The  headings  to  Ta- 
ble 203,  in  which  fourteen  different  kinds  of  side  tracks  are  spe- 
cified, will  at  once  explain  in  part  why  so  much  of  some  of  them 
is  necessary.  In  the  aggregate  there  is  a  total  of  some  300  miles 
of  side  track  within  an  area  of  some  eight  square  miles  (about  i-J 
b}^  5y  miles,  5.63  square  miles  being  actually  owned  by  the  rail- 
ways within  the  cit}^  limits),  which  it  is  expected  to  increase  in 
the  near  future  to  some  450  to  500  miles,  mostly  by  accessions  to 
the  trackage  of  the  newer  lines  entering  Buffalo,  and  required  by 
them — as  will  be  seen  by  the  detailed  table — to  afford  to  them  no 
greater  facilities  than  the  older  lines  already  enjoy.  The  lease 
of  the  West  Shore  to  the  New  York  Central  saved,  it  is  estimated 
(somewhat  liberally,  it  would  appear),  the  construction  of  as 
much  as  50  miles  of  track  which  would  otherwise  have  been  ne- 
cessary, but,  barring  that,  there  is — 

, Miles. ^ 

Single  track. 
Tracks  of  all  kinds  in  city  limits  of  Buffalo  or  immediately  ad- 
jacent thereto 436.  i 

And  to  be  laid  by  the  new  roads  (chiefly)  now  imperfectly  sup- 
plied    176.0       612. 1 

Of  this  there  is  7naiti  track,  including  three  double-track  lines 
swinging  around  the  city  to  a  connection  with  the  Interna- 
tional Bridge I55-I 

And  projected  (minor  extensions) 5.7        160.8 

Leaving  as  side  track. 45I-S 


CHAP.  XXVI.— TERMINALS.  823 

Of  the  main  track  a  considerable  portion  is  only  nominally  main 
track,  but  really  more  in  the  nature  of  track  for  yard  use 
only,  which  may  be  estimated  as  at  least 50.0  50.0 

(Main.)  (Side.) 
Leaving  as  the  true  proportions  of  main  track  and  side  track,  ac- 
tual and  projected 110.8  501.3 

Of  which  there  was  laid,  October,  1884 109.3  326.8 

An  d  projected,  a  considerable  fraction  of  which  has  since  been 

constructed 1.5  174-5 

1119.  If  we  compare  this  with  the  figures  for  the  yards  of  New 
York  City,  as  given  in  Table  202,  we  shall  have  a  better  idea 
of  the  magnitude  of  the  Buffalo  yards.  The  total  miles  of  track, 
main  line  and  sidings,  at  the  two  points  compare  as  follows  : 

New  York  Buffalo 

yards.  yards. 

New  York  Central 28  157 

Erie   49  116 

Lackawanna 50  63 

West  Shore  (and  Ont.  &  West.) 34  23 

Pennsylvania 39 

Other  roads 77 

Total 200  436 

It  will  be  seen  that,  with  all  the  immense  traffic  of  New  York, 
there  is  less  than  half  as  much  track  at  New  York  as  at  Buffalo. 
In  the  yards  of  Boston  there  are  150  miles  of  side  track,  on  568 
acres,  with  26  acres  of  buildings;  the  total  side  track  on  all  the 
nine  roads  centring  there  being  765  miles  for  a  total  of  814  miles 
of  main  line. 

1120.  The  New  York  tracks  are  also  different  from  those  at 
Buffalo  in  not  being  all  bunched  together,  so  as  to  be  in  fact,  if 
not  in  form,  one  vast  yard,  whose  different  parts  are  constantly 
interchanging  business  with  each  other.  The  New  York  yards 
are  miles  apart  from  each  other,  and  have  comparatively  the 
most  insignificant  interchange  relations.  Most  of  them,  in  fact, 
could  be  most  fairly  compared  with  the  thirteenth  class  of  Buffalo 
side  tracks,  those  for  "local  city  freight"  alone,  of  which  there 
are  in  Buffalo  2of  miles,  with  as  much  more  projected  ;  for,  al- 
though there  is  a  very  large — in  fact  immense — coal,  steamer, 
and  stock-yard  traffic  at  New  York,   as  well  as  the  usual   shop 


824  CHAP.  XXVI.— TERMINALS. 

and  coaling  tracks,  yet  the  business  of  New  York  is  carried  on 
under  such  different  conditions  from  that  at  Buffalo  that  the 
same  traffic  requires,  as  is  apparent  from  the  figures,  several 
times  less  track  room.  For  example,  there  are  39  miles  of  shop 
and  coaling  track  at  Buffalo,  and  35  miles  more  projected,  of 
which  the  New  York  Central  and  the  Erie  have  each  some  13 
miles,  which  (without  being  able  to  present  the  exact  figures)  is 
undoubtedly  several  times  greater  than  the  same  roads  have  for 
the  same  purposes  at  New  York,  the  reason  being  that  sick  and 
wounded  cars  from  all  over  the  continent  tend  to  accumulate  at 
Buffalo,  while  they  are  kept  away  from  New  York  so  far  as  pos- 
sible. The  same  contrast  is  visible  in  the  16  miles  of  transfer 
tracks  at  Buffalo,  which  it  is  proposed  to  double  ;  and  the  enor- 
mous aggregate  of  87  miles  for  the  direct  use  of  trains  from  the 
East  and  West  and  Canada,  and  for  distributing  West-bound 
freight  (columns  3,  4,  5,  6,  7,  Table  203),  to  which  it  is  proposed 
to  add  over  40  miles  more,  mostly  by  the  newer  roads,  is  in 
itself  something  for  which  there  is  no  very  exact  parallel  in  New 
York,  either  in  quantity  or  quality,  although,  of  course,  the 
mileage  devoted  to  similar  uses  is  very  great. 

1121.  The  same  contrast  exists  to  an  even  larger  extent  in  the 
areas  of  land  occupied  in  the  two  cities,  which  compare  as  fol- 
lows : 

In  New  York,  land 378  acres. 

piers 5     " 

383  acres. 
In  Buffalo,  land 3,600  acres. 

Land  in  Buffalo  is,  of  course,  a  very  different  and  much 
cheaper  thing  than  land  in  New  York,  and  this  area,  moreover, 
includes  several  hundred  acres  of  what  is  more  properly  main- 
line right  of  way,  not  properly  chargeable  to  yards.  But  after 
making  all  allowances  in  this  respect,  the  immense  proportion- 
ate magnitude  of  the  Buffalo  yard,  due  to  the  nature  rather  than 
to  the  absolute  volume  of  the  business  transacted,  which  makes 
Buffalo  a  point  where  innumerable  side  tracks  naturally  accumu- 
late, is  clearly  indicated. 


CHA  P.  XX  VI.  —  TERM  IN  A  L  S. 


1122.  While  Buffalo  seems  to  be  far  ahead  of  any  other  one 
point  in  its  yard  facilities  proper,  3^et  that  it  is  only  the  leading 
example  of  a  general  tendency  may  be  indicated  by  the  figures 
given  in  Table  204  of  the  total  side-track  mileage  of  the  roads 
entering  there,  which  well  illustrate  the  immense  aggregates  of 
sic  .^  track  which  even  ordinary  yard  demands  produce.  There 
seems  to  be  what  might  almost  be  called  a  rude  law,  that  trunk 
lines  proper,  as  distinguished  from  roads  of  the  next  grade 
below,  will  have  at  least  as  much  side  track  as  the  length  of 
their  main  line.  Thus,  the  Boston  &  Albany,  in  addition  to 
being  somewhat  more  than  double-tracked,  has  almost  exactly 
this  amount  of  sidings,  viz.,  203.2  miles  against  201.6  miles  of 
main  line.  Exceptions,  no  doubt,  exist;  but  Table  204  indicates 
that  the  assumed  "  law"  has  at  least  some  foundation  in  fact. 

Table  204. 

Mileage  of  Sidings  in  the  Aggregate  and  at  Buffalo  and  New  York, 
ON  THE  Leading  Lines  entering  Buffalo. 


Miles 
Main 
Line. 

Miles  of  Sidings. 

Per  Cent 
of  all 

Road. 

Buffalo. 

N.  Y. 

Else- 
where. 

Total. 

Sidings 

in 
Buffalo. 

New  York  Central. . . 
Lake  Shore 

442 
540 

94.1 
9-3 

28.0 

418.9 
539.7 

541.0 
549.0 

17.4 
16.9 

Total 

982 
460 
413 
430 
213 
426 

103.4 
77.2 
30.8* 
19.0* 

4.9* 
16.3; 

3-5* 

49.0 
50.0 

34.0 

958.6 

430.8 

442.2 

129.0 

48.1 

91.7 

85.5 

1,090.0 
557.0 
523.0 
148.0 

53.0 
142.0 

89.0 

9-5 
13.9 

Lackawanna 

B.,  N.  Y.  «&  P 

Rochester  &  Pittsb'g. 
West  Shore   

N.  Y.,  C.  &St.  L.... 

*  These  roads  have  completed  less  than  one  half  of  their  proposed  Buffalo  sidings. 


The  immense  aggregate  of  capital  expenditure  represented 
by  these  aggregates  of  side  track,  and  the  still  larger  capital 
sum  represented  by  the  annual  expenditure  to  "operate"  the 
side  tracks,  are  plainly  factors  in  the  future  of  new  and  old  lines 
which  can  never  be  safely  forgotten. 


S26  CHAP.  XXVI.— TERMINALS. 

1123.  It  is  estimated  that  fifteen  miles  alone  of  the  local 
tracks  at  Buffalo  have  cost,  or  would  cost  to  replace,  $350,000 
per  mile,  or  $5,250,000,  this  particular  fraction  of  the  local  track- 
age being,  as  is  often  necessary,  on  exceptionally  expensive  land, 
where  it  is  readily  salable  at  $300  to  $500  per  foot  front.  The 
railways  own  strips  varying  from  60  to  100  ft.  deep,  and  on  them 
are  laid  three  to  five  tracks,  giving  the  following  estimate  for  four 
miles  of  track  : 

5280  ft.  of  land  at  $250  per  front  foot $1,320,000 

Planking,  60x5280  ft.  x  3   in. =  1050  M.   ft.,  or  with  sab-sills 

1200  M.  ft.  at  18  cts 21,600 

Grading,  averaging  3  ft.  deep  at  25  cts.  per  cu.  yd         ii,75o 

4  miles  of  track  at  $6000 24,00a 

Total $1,377,350 

Per  mile  of  track 344,340 

Add   for  approaches   of   paved   streets,  paving  many  of  the 

tracks  themselves,  and  incidentals 5,660 

Total  per  mile ....    $350,000 

We  need  not  attempt  the  difficult  task  of  estimating  the  total 
exactly,  but  for  the  other  items  :  At  f  10,000  per  mile  the  300 
miles  of  side  track,  more  or  less,  in  the  Buffalo  yards  represent 
$3,000,000.  At  $5000  per  acre  for  the  3600  acres  of  land  owned 
and  used  for  railway  purposes,  the  capital  investment  would  be 
$18,000,000.  The  shop  facilities  alone,  with  the  tracks  for  their 
use,  represent  $3,000,000.  Vast  as  these  sums  appear  and  are,  the 
interest  on  them  represents  but  a  small  part  of  the  addition  to 
the  cost  of  haulage  which  the  terminal  facilities  cause,  and  still 
less  is  the  bare  trackage  required  any  fair  criterion.  This  will 
be  clearly  indicated  by  referring  back  to  Table  202,  where  it 
will  be  seen  that  at  New  York  the  bare  cost  of  the  track,  esti- 
mated at  a  very  liberal  figure,  and  exclusive  of  land,  amounts  to 
but  2.2  per  cent  of  the  total  cost  of  yard  work,  and  that  this 
total  is  as  great  a  tax  upon  the  five  lines  concerned  as  if  they 
had  $91,000,000  invested,  say  in  three  thousand  miles  of  idle,  un- 
operated,  and  tolerably  costly  railroad,  at  $30,333  per  mile,  on 
which  they  had  to  pay  interest,  but  which  contributed  nothing- 
to  revenue. 


CHAP.  XXVI.— TERMINALS.  82/ 


1124.  Nothing  equal  to  this  in  degree  exists  in  Buffalo,  but 
the  analogous  tax  at  that  point  is  very  great  indeed,  and  is  in  ad- 
dition  to  the  New  York  tax,  as  is  likewise  the  yard  tax  at  Chicago, 
and  all  other  intermediate  points.  Therefore,  vast  as  is  the  tax 
of  maintaining  within  the  city  limits  of  Buffalo  enough  track 
for  local  purposes  only  to  build  a  new  line  to  New  York,  that 
direct  expenditure  is  but  a  small  part  of  the  total  burden  repre- 
sented by  those  facilities,  even  if  a  many  times  larger  part  than 
at  New  York,  as  no  doubt  it  is. 

At  no  other  point  in  this  country,  not  even  at  Chicago,  do  so 
many  conditions  combine  to  bring  about  such  abnormal  growth, 
and  the  same  is  still  more  true  of  even  the  largest  cities  of  the 
old  world.  Buffalo,  therefore,  although  outdone  by  many  other 
cities  as  a  traffic  point,  will  doubtless  continue  to  be  the  greatest 
yard,  properly  so  called,  in  the  world,  even  after  that  consider- 
able fraction  of  its  trackage,  which  is  with  reason  felt  to  be  due 
to  profligate  and  discreditable  imperfections  of  management,  has 
been  done  away  with.  But  its  interest  for  our  immediate  pur- 
pose lies  in  the  fact  that,  large  as  it  is,  it  is  only  the  largest  out- 
growth of  universal  tendencies;  and  that  road  which  attempts  to 
compete  with  another  without  having  approximate  equality  in 
such  terminal  facilities,  competes  on  about  as  favorable  terms 
as  it  would  in  crossing  a  river  by  some  new  bridge  in  which 
every  span  but  the  last  had  been  built,  and  was  of  very  superior 
quality. 

Much  greater  sums  have  been  spent  in  Europe  than  here  in  building  stations 
in  the  trade  centres  of  cities  close  to  the  warehouses  and  wholesale  stores.  In 
Liverpool  (600,000  inhabitants),  the  London  &  Northwestern  Railway  up  to 
3881  had  expended  $9,300,000  in  providing  freight  stations  alone.  In  London 
it  had  expended  $11,200,000.  Interest  at  the  rate  of  4  per  cent  on  the  cost  of 
these  stations,  less  rents  received  for  warehouses,  etc.,  amounted  at  Liverpool 
to  14.6  cents,  and  at  London  to  32  cents  per  ton  of  freight  handled.  Thus  the 
mere  payment  of  interest  on  the  terminal  facilities,  excluding  any  charge  for 
handling  the  freight,  would,  on  a  haul  from  Liverpool  to  London,  amount  to 
46.6  cents  per  ton,  or  nearly  \  cent  per  ton-mile.  These  figures  do  not  include 
the  cost  of  collecting,  distributing,  and  sorting  sidings,  of  which  there  are  38 
miles  at  Edgehill  (Liverpool),  and  proportionate  lengths  at  other  places.     The 


828  CHAP.  XXVI.— TERMINALS. 

London  &  Northwestern  is  in  no  way  exceptional  in  this  respect  among  the 
great  English  railways. 

The  total  actual  average  cost  of  loading  and  unloading  freight  per  gross  ton, 
exclusive  of  interest,  was  given  as  under  for  the  year  1880,  at  the  following 
places  : 

London 70.1  cents. 

Manchester 4i-0     " 

Birmingham 34-0     " 

Liverpool 39-4 

This  total  cost  includes  everything  incidental  to  carrying  on  the  business  of 
the  station,  but  no  charge  for  risk,  breakage  and  pilferage,  or  for  cartage. 


PART  V. 


THE  CONDUCT  OF  LOCATION. 


*'  O,  what  a  precious  book  the  one  would  be 
That  taught  observers  what  they're  not  to  see! " 

— O.  W.  Holmes:  A  Rhymed  Lesson^ 
*'  Some  things  can  be  done  as  well  as  others." — Sam  Patch. 


\ 


r 


PART  V. 

THE  CONDUCT  OF   LOCATION 


CHAPTER   XXVII. 


THE    ART    OF    RECONNAISSANCE. 


1125.  An  art,  as  distinguished  from  a  science,  is  something  which, 
although  it  in  part  can  be  taught,  yet  cannot  be  written  down  in  definite 
fixed  rules  which  have  only  to  be  followed  with  exactness.  A  science, 
correctly  so  called,  however  difficult  or  intricate  it  may  be,  is  always  m 
its  nature  susceptible  of  rigorous  and  exact  analysis.  An  art  is  not. 
Thus  we  may  speak  with  strict  propriety  of  the  science  of  bridge-build- 
ing, but  only  of  the  art  of  reconnoitring. 

Nevertheless,  just  as  there  is  no  scientific  branch  of  the  practical  work 
of  life  so  purely  a  science  that  it  is  possible  to  dispense  with  a  certain  apti- 
tude and  tact  which  is  outside  of  and  beyond  written  rules,  so,  on  the 
other  hand,  even  in  what  is  so  purely  an  art  as  discerning  the  physical 
possibilities  of  a  given  region  by  the  aid  of  the  eye  alone,  certain  general 
rules  and  cautions  will  greatly  diminish  the  danger — which  often  rises  to 
certainty — that  without  such  aid  an  inexperienced  engineer  will  fail  to 
discern  the  possibilities  which  lie  right  before  him,  and  reach  wholly 
mistaken  conclusions  as  to  what  he  can  and  cannot  do  with  the  region 
before  his  eyes. 

112o.  For  there  is  nothing  against  which  a  locating  engineer  will  find 
it  necessary  to  be  more  constantly  on  his  guard  than  the  drawing  of  hasty 
and  unfounded  conclusions,  especially  of  an  unfavorable  character,  from 
apparent  evidence  wrongly  interpreted.  If  his  conclusions  on  reconnais- 
sance are  unduly  favorable,  there  is  no  great  harm  done — nothing  more 
at  the  worst  will  ensue  than  an  unnecessary  amount  of  surveying;  but 
a  hasty  conclusion  that  some  line  is  not  feasible,  or  that  further  improve- 


832         CHAP.  XXVII.— THE  ART   OF  RECONNAISSANCE. 

ments  in  it  cannot  be  made,  or  even  sometimes — often  very  absurdly — 
that  no  other  line  of  any  kind  exists  than  that  one  which  has  chanced  to 
be  discovered — these  are  errors  which  may  have  disastrous  consequences. 
On  this  account,  if  for  no  other,  the  locating  engineer  should  culti- 
vate and  habitually  preserve  what  may  be  called  an  optimistic  habit  of 
mind.  He  should  not  allow  himself  to  enter  upon  his  work  with  the 
feeling  that  any  country  is  seriously  difficult,  but  rather  that  the  problem 
before  him  is  simply  to  find  the  line,  which  undoubtedly  exists,  and  that 
he  can  only  fail  to  do  so  from  some  blindness  or  oversight  of  his  own, 
which  it  will  be  his  business  to  guard  against. 

1127.  The  chances  are  greatly  in  favor  of  his  ultimately  finding  this 
assumption  to  be  correct.  Occasionally  he  may  be  deceived,  but  the 
young  and  inexperienced  engineer  cannot  proceed  on  a  safer  hypothesis 
than  this  :  That  however  forbidding  the  region,  a  line  exists  which  is 
conspicuously  better  than  any  other,  and  which  will  in  all  cases  be  found 
to  be — in  comparison  with  what  was  expected — a  line  cheap  to  build  and 
economical  to  operate;  and  that,  on  the  other  hand,  the  line  which  he, 
as  an  inexperienced  man  and  acting  without  special  training  for  the 
work,  will  be  likely  to  first  select  as  the  best,  is  perhaps  twice  as  costly 
in  first  cost  and  considerably  less  favorable  in  gradients  and  operating 
value  than  that  which  he  can  secure  by  greater  care,  attention,  and 
study.  Although  this  may  seem  a  sweeping  generalization,  it  is  so  near 
a  general  average  of  probabilities  in  both  easy  and  difficult  country,  that 
in  a  rude  way  it  may  be  assumed  as  truth. 

1128.  For  the  reason  that  there  is  so  much  danger  of  radical  error  in 
the  selection  of  the  lines  to  be  surveyed  (or,  rather,  of  the  lines  not  to  be 
examined),  it  results  that  the  worst  errors  of  location  generally 
ORIGINATE  IN  THE  RECONNAISSANCE.  This  truth  once  grasped,  the 
greatest  of  all  dangers,  over-confidence  in  one's  own  infallibility,  is  re- 
moved. 

1129.  The  most  fundamentally  important  technical  qualification  for 
entering  upon  the  reconnaissance  is  an  understanding  of  the  economic 
questions  considered  in  the  first  parts  of  this  volume,  especially  as  to 
what  a  railway  should  be  from  a  business  point  of  view,  and  what  the 
relative  importance  is  of  engineering  (or  geometric)  and  commercial  ex- 
cellence ;  for  if  the  engineer  cannot  correctly  distinguish  between  the 
financially  important  and  unimportant,  as  well  as  between  the  practically 
feasible  and  the  practically  impossible,  he  will  be  almost  as  liable  to  go 
astray  as  if  he  were  physically  blind,  by  omitting  to  examine  as  worthless 
the  very  possibilities  which  he  should  look  into  most  carefully.     It  fol- 


CHAP.  XX VII.— THE  ART   OF  RECONNAISSANCE.         833 


lows  also  that  he  should  be  well  posted  as  to  the  relative  cost  and  diffi- 
culties of  construction. 

1130.  These  qualifications  being  presupposed,  before  beginning  the 
reconnaissance,  as  well  as  during  it  and  after  it,  the  nature,  extent,  and 
probable  sources  of  the  traffic,  and  especially  of  way  traffic,  should  be 
carefully  looked  into,  as  a  consideration  which  will  be  often — it  might 
almost  be  said  usually — so  important  as  to  fix  the  general  route  in  de- 
spite of  quite  important  engineering  disadvantages.  The  small  effect 
on  profit  and  loss  of  even  considerable  differences  of  distance,  and  the 
small  effect  on  distance  of  even  considerable  and  "ugly"  swerves  from  a 
straight  line,  may  well  be  especially  studied  up,  not  to  make  one  reck- 
less of  sacrificing  distance,  but  to  enable  one  to  sacrifice  it  and  save  it 
intelligently. 

1131.  On  the  other  hand,  the  engineer  should  with  especial  care  dis- 
abuse his  mind  of  the  very  natural  feeling  that  what  may  be  called  his 
own  particular  and  especial  department — getting  a  cheap  line  to  sub- 
grade — is  of  much  relative  importance  to  the  future  of  the  company.  He 
should  remember  that  it  requires  a  continuous  cut  or  file  of  about  7  feet, 
or  say  an  average  maximum  cut  or  fill  of  10  to  12  feet,  with  its  ordinar}?- 
accompaniments  of  masonry,  to  equal  the  cost  of  superstructure  ready 
for  operation ;  that  the  total  investment  for  rolling-stock,  machinery, 
buildings,  and  miscellaneous  purposes  will,  on  a  line  of  active  traffic, 
very  nearly  equal  that  for  road-bed  and  track  complete,  and  that,  finally, 
and  more  important  than  all,  the  interest  on  the  total  de-facto  invest- 
ment for  all  purposes  rarely  absorbs  more  than  from  one  sixth  to  one 
fourth  of  the  gross  revenue.  Broadly  speaking,  therefore,  we  may  say 
in  general  terms  that — 

To  increase  gross  revenue  \  we  may  double  the  whole  investment. 

iV  "  cost  of  road-bed  and  track. 

"  "  -^  "  "      grading  and  masonry. 

These  percentages,  of  course,  are  subject  to  important  fluctuations,  but 
the  fact  still  remains  in  all  cases  that,  for  obvious  reasons,  the  tendency 
of  an  engineer  is  to  concentrate  his  attention  unduly  on  the  work  below 
sub-grade. 

1132.  As  a  more  direct  qualification,  the  engineer  should  prepare  him- 
self as  carefully  as  possible  to  form  reasonably  accurate  estimates  of  the 
probable  cost  of  the  work  per  mile  on  various  lines  and  grades.  The 
faculty  of  making  tolerably  close  approximations  of  this  kind,  assisted 
by  the  eye  alone,  is  not  so  very  difficult  to  acquire,  but  can  only  be  gained 

53 


834         CHAP.  XXVII.— THE  ART  OF  RECONNAISSANCE. 

by  careful  observation.  The  best  manner  of  obtaining  it  is  by  noting 
the  general  appearance  of  as  many  lines  as  possible,  either  before  or 
after  their  completion,  and  then  comparing  a  guess  based  on  this  appear- 
ance with  the  actual  cost  or  quantities.  Experienced  contractors  can 
guess  in  this  way  within  a  very  small  percentage  of  how  many  yards  per 
mile  a  given  piece  of  work  w^ill  run.  The  engineer  should  by  previous 
practice  and  study  have  at  least  so  far  perfected  himself  in  this  art  as  to 
have  some  idea  as  to  his  "personal  equation"  or  probable  range  of  error. 

1133.  The  danger  with  most  young  and  inexperienced  engineers  in 
making  estimates  of  the  cost  of  work  is  decidedly  that  they  will  make 
too  small  estimates,  influenced  by  a  natural  hope  and  anxiety  to  show 
good  results.  But,  on  the  other  hand,  there  are  some  who,  especially  in 
preliminary  estimates,  go  to  the  other  extreme.  Just  as  it  is  the  mark 
of  an  untrained  engineer  to  make  estimates  too  low,  so  it  is  the  mark  of 
a  half-trained  man  to  persistently  make  estimates  too  high,  especially  on 
work  involving  difficult  or  doubtful  points,  which  it  may  be  in  question 
w^hether  to  attempt  at  all ;  a  practice  which  some  of  them  adhere  to 
through  life,  from  an  idea  that  they  are  being  thereby  more  prudent  and 
"practical."  Each  error  is  equally  discreditable.  An  estimate  should 
lean  in  the  direction  of  excess,  but  a  moderate  error  in  either  direction  is 
a  pardonable  fault  (par.  21). 

1134.  To  these  qualifications  is  to  be  added— not  by  any  means  as 
least  important,  but  as  last  in  order  of  importance,  if  the  intended  dis- 
tinction can  be  grasped — what  is  generally  known  as  an  "  eye  for  coun- 
try," the  nature  and  importance  of  which  has  already  been  considered  in 
par.  18.  Such  rules  and  cautions  for  acquiring  an  "eye  for  country"  as 
can  be  committed  to  paper  (which  are  not  a  few)  will  be  given  in  the  fol- 
lowing chapter.  The  fundamental  rule  is  to  have  an  abiding  conviction 
that  a  much  better  line  than  at  first  sight  appears  can  be  found  by  open- 
ing one's  eyes. 

1135.  Undertaking  a  reconnaissance  with  a  reasonable  measure  of 
these  qualifications,  it  will  require,  often,  nothing  more  than  careful  ob- 
servation and  one  or  two  trips  over  the  line  to  definitely  determine, 
once  for  all,  which  is  the  proper  general  route  to  adopt,  and  so  save  all 
necessity  for  running  any  duplicate  lines  whatever  except  for  short  alter- 
nate sections  of  2,  10,  20,  or  30  miles,  which  are  almost  always  necessary 
at  points,  and  which  may  be  called  matters  of  detail.  It  would  be  dan- 
gerous, perhaps,  to  state  that  it  is  a  general  rule  that  only  one  line  wnll 
need  actual  survey,  but  the  writer's  experience  is  that  this  is  far  more  often 
true  than  not,  and  that  it  is  true,  perhaps,  of  a  larger  proportion  of  heavy 


CHAP.  XXVII.— THE  ART  OF  RECONNAISSANCE.         835 

lines  than  of  light  lines.  When  all  the  traffic  and  business  considera- 
tions, as  well  as  engineering  differences,  have  been  duly  considered,  the 
writer  has  never  known  an  instance  where  there  seemed  the  slightest 
need  to  survey  more  than  two  general  routes,  although  such  instances 
may  well  occur.  In  any  case  the  reconnaissance  should  be  conducted 
always  with  as  much  care  as  if  it  was  expected  to  make  by  its  means  a 
final  selection  of  route. 

In  conducting  the  reconnaissance,  while  individual  habits  of  mind  no 
doubt  differ  greatly,  and  with  them  the  direction  in  which  error  is  most 
to  be  feared,  the  following  rules  and  cautions  are  believed  to  be  of  uni- 
versal application,  the  first  one  especially  being  fundamental : 

1136.  I.  The  reconnaissance  must  not  be  of  a  line,  but  of  an 
AREA,  including  at  all  times  in  the  mind  as  wide  a  belt  on  each  side  of 
an  air-line  between  the  two  fixed  termini  as  there  is  the  remotest  pos- 
sibility of  the  lines  reaching  to  ;  "remotest  possibility"  being  considered 
for  the  time  being  as  only  bounded  by  some  marked  and  decisive  topo- 
graphical feature  or  traffic  centre. 

Thus,  in  reconnoitring  a  proposed  line,  AB,  Fig.  266,  supposed  to  be  about 
100  miles  long,  we  may  reasonably  take  the  valley  Hne  V  to  the  right,  or  the 
town  C  to  the  left,  as  the  lateral  limits,  but  nothing  less  than  this,  and  the 
whole  area  between  them  should  be  studied  as  an  area,  and  a  topographical 
map  "  in  the  mind's  eye"  made  of  it  all  ;  exact  comparative  knowledge  of  all 
the  various  passes  and  other  governing  points  being  obtained  on  reconnais- 
sance, or  by  subsequent  survey  or  spur-lines. 

This  simple  rule  is  one  rarely  thought  of  or  acted  on  until  repeated  blunders 
have  enforced  it.  Error  is  particularly  liable  to  follow  from  neglecting  it,  as 
will  be  shown  later  by  a  few  examples  from  practice.  We  may  survey  lines, 
but  we  must  never  reconnoitre  them.     If  we  do,  it  is  not  a  reconnaissance. 

1137.  2.  All  prepossessions  in  favor  of  any  particular  line  must  be  aban- 
doned, especially  in  favor  of  that  line  which  seems  most  obvious.  The 
importance  of  this  is  too  obvious  to  need  dwelling  on,  yet  it  is  one 
thing  to  admit  it  in  theory  and  quite  another  to  do  it  in  practice.  Not 
to  do  so  is  a  dangerous  and  frequent  error. 

1138.  3.  A  tendency  to  see  with  undue  clearness  the  merits  of  lines 
LYING  close  to  HIGHWAYS  or  the  more  settled  and  open  districts  must 
be  carefully  guarded  against.  This  is  another  dangerous  and  frequent 
^rror,  which  is  always  imminent,  partly  because  it  seems  too  obvious  a 
danger  to  be  a  real  one.  The  writer  now  recalls  no  less  than  thirty  in- 
stances, some  of  them  of  the  first  importance,  in  which  the  deceptive 
•conveniences  of  highways  alone  were  responsible  for  serious  error,  as 


836         CHAP.  XXVII.— THE  ART  OF  RECONNAISSANCE. 

in  the  instances  of  Chapter  XXIX.  and  Appendix  C.     Allied  to  the 
above  are : 

4.  Lines  hard  to  get  over  on  foot,  or  overgrown  with  timber  or 
tangled  undergrowth,  seem  infinitely  worse  by  comparison  than  they 
really  are  ;  and, 

5.  Raggedness  of  detail,  sharp  rocky  points,  steep  bluffs,  and  the  like, 
exert  an  entirely  undue  influence  upon  the  mind  as  compared  with  long 
rolling  slopes  spread  out  over  a  longer  distance. 

These  two  dangers  are  so  imminent  where  the  conditions  specified  exist  at 
all,  as  in  comparing  many  valley  lines  with  ridge  lines,  that  they  will  be  sepa- 
rately discussed  (par.  1162).  The  disadvantages  of  a  route  for  a  railway  must 
not  be  measured  by  its  disadvantages  as  a  foot-path,  even  after  all  brush  and 
timber  have  been  removed,  yet  it  is  hard  not  to  do  so  to  some  extent. 

1139.  6.  A  complete  mental  map  of  the  watercourses  should  be  made 
as  the  reconnaissance  proceeds — sufficiently  exact,  at  least,  to  enable  the 
engineer  to  state  positively  where  the  water  of  every  stream  crossed 
joins  another,  and  what  streams  run  in  together,  until  they  have  passed 
off  the  limits  of  the  area  under  examination. 

It  is  not  always  convenient  to  do  this  for  each  stream  as  it  is  passed,  with- 
out undue  delay  ;  but  wherever  a  stream  is  passed  without  doing  it,  there,  if 
should  be  noted,  is  a  gap  in  the  necessary  knowledge  of  the  country,  which  may  be 
dangerous. 

A  skeleton  framework  for  this  information  can  generally  be  obtained  from 
maps.  It  is  in  respect  to  the  minor  streams  that  the  caution  is  particularly 
necessary,  and  it  is  even  more  important  to  adhere  to  it  in  the  smoother  than 
in  very  rough  country.     Neglect  of  it  often  carries  one  off  on  a  false  track. 

1140.  7.  False  summits,  or  those  which  appear  to  interpose  between 
two  water-sheds,  when  in  reality  they  are  only  between  different  parts  of 
the  same  water-shed,  are  very  liable  to  deceive  under  certain  circum- 
stances. The  latter,  fortunately,  do  not  often  occur ;  but  when  they  do 
occur  the  deception  is  often  very  perfect,  introducing  an  apparently  im- 
possible obstacle  to  the  progress  of  the  line  which  is  only  apparent.  One 
of  many  reasons  for  the  preceding  rule  is  to  avoid  this  danger. 

See  also  overlaps  (par.  1161),  which  are  a  kind  of  imaginary  false  summits. 

1141i  8.  As  a  very  necessary  safeguard  against  error,  the  engineer 
should  MAKE  IT  A  RULE  to  invariably  discredit  all  unfavorable  reports, 
from  whatever  source  derived,  which  do  not  accord  with  what  he  expects. 

This  merely  means  that  if  he  has,  or  thinks  he  has,  any  reasonable  shadow 
of  ground  for  hope  that  certain  things  are  possible  at  controlling  points,  he 
should  go  there  and  look  for  himself  before  he  finally  abondons  hope.     Not  un- 


I 


CHAP.  XXVII.— THE  ART  OF  RECONNAISSANCE.         837 

frequently  he  will  see  reasons  to  be  glad  he  did  go.  The  time  of  a  man  who 
may  have  been  previously  sent  to  the  point  is  not  therefore  lost.  Assurance  is 
at  least  made  doubly  sure,  and  he  might  have  brought  back  a  favorable  report ; 
but  the  most  trusted  assistants  are  liable,  with  the  best  of  intentions,  to  reach 
entirely  wrong  conclusions  by  looking  in  the  wrong  place  or  seeing  the  wrong 
things. 

1142.  The  reconnaissance,  it  should  be  understood,  although  spoken 
of  as  one  continuous  and  complete  examination  of  the  territory,  is  not 
necessarily  completed  all  at  once.  On  the  contrary,  it  should  in  a  sense 
be  always  in  progress  until  the  final  location  is  complete,  and  may  well 
be  made  in  part  while  a  party  is  running  some  first  experimental  line. 
It  may  also  continue  over  a  number  of  separate  and  complete  trips 
over  the  route,  which  in  a  literal  sense  are  examinations  of  so  many  dis- 
tinct lines;  but  it  should  never  be  felt  to  be  so  while  making  the  trips, 
but  as  broad  a  belt  should  be  taken  in,  in  imagination  at  least,  as  it  is 
possible  to  keep  in  mind.  The  feeling  should  always  be  present  in  the 
mind  of  the  engineer  that  he  ought  to  be  somewhere  over  the  edge  of 
the  horizon,  or  on  the  other  side  of  the  valley  or  ridge,  instead  of  fol- 
lowing his  nose  where  he  is. 

1143.  The  whole  reconnaissance  is  not  ordinarily  carried  on  in  the 
field,  but  a  part  of  it,  small  as  respects  time,  but  often  important  and 
even  decisive  as  respects  results,  is  obtained  from  the  study  of  such  maps 
of  the  region  as  may  exist.  The  same  arguments  apply  to  such  exami- 
nation as  to  examinations  in  the  fields,  and  the  same  methods  should  be 
used.  The  obvious  should  be  mistrusted  and  the  improbable  looked  for 
hopefully.  An  examination  of  maps  may  in  some  cases  be  the  only  recon- 
naissance, properly  so  called,  needed,  as  when  a  line  follows  for  its  entire 
length  a  deep  valley  of  known  character  between  points  both  situated  in 
the  same  valley.  On  the  other  hand,  the  reconnaissance  may  show  such 
nicely-balanced  possibilities  that  three  or  four  exploration  lines  will  be 
necessary,  merely  to  form  a  clear  idea  of  what  lines  to  examine  in  earnest. 

But,  as  a  general  rule,  neither  of  these  conditions  prevail.  A  careful 
reconnaissance  is  necessary,  but  it  is  also  decisive  ;  showing  beyond  doubt 
(at  least  any  doubt  which  a  survey  by  the  same  persons  could  remove) 
that  some  one  route  is  alone  worth  careful  survey,  or  at  most  two. 

1144.  The  method  of  making  a  reconnaissance  may  be  in  detail  some- 
what like  that  sketched  in  Fig.  266.  Such  ordinary  matters  as  that 
water  runs  down  hill  ;  that  streams  start  at  their  source  from  the  lowest 
point  in  their  immediate  vicinity  and  flow  toward  still  lower  ground; 
that  large  streams  usually  lie  lower  than  contiguous  smaller  streams,  and 


838 


CHAP.  XXVII.— THE  ART  OF  RECONNAISSANCE. 


mat  an  aneroid  barometer  will  be  of  assistance  to  fix  the  approximate 
elevation  of  points,  if  too  great  confidence  be  not  placed  in  it, — may  be 
supposed  to  be  understood. 

A  hand-level  is  a  more  important  tool,  which  should  always  be  at 
hand.  In  looking  through  it  do  not  close  one  eye,  but  while  one  eye 
looks  through  the  tube  of  the  hand-level  let  the  other  look  at  the  na- 
tural landscape.  The  bubble  will  then  be  seen  superimposed  on  the 
latter.     Hand-levels  are  very  often  out  of  adjustment,  and  still  more  often 

have  very  dull  bubbles,, 
which  read  quite  different- 
ly if  the  tube  has  been 
raised  or  lowered  to  posi- 
tion. A  guess  should  al- 
ways be  made  first,  before 
using  the  hand-level,  but 
no  man  ever  acquires  a 
very  trustworthy  faculty  of 
guessing  at  a  horizontal 
line.  In  ordinary  locali- 
ties a  practical  eye  will 
estimate  elevations  and  a 
horizontal  line  with  a  good 
deal  of  precision,  but  there 
are  peculiar  topographical 
conditions  which  make 
the  evidence  of  the  eye 
worse  than  worthless  (par. 
1160),  and  no  one  can  tell 
where  they  are  in  advance. 
An  odometer  may  be 
fastened  to  the  wheel  of 
the  carriage,  if  a  vehicle 
be  used;  but  distances  can 
usually  be  guessed  or  as- 
certained, by  time  esti- 
mates or  otherwise,  nearly 
enough  for  preliminary  purposes.  A  pocket  compass  is  a  necessity,  and 
a  succession  of  travelling  companions  with  a  local  knowledge  of  the 
country  are  very  desirable.  More  outfit  than  this  and  the  best  attainable 
maps  will  not  be  particularly  useful. 


CHAP.  XXVII.— THE  ART   OF  RECONNAISSANCE.         839 

1145.  As  a  preliminary  to  starting  out  to  explore,  say  from  B  to  A, 
Fig.  266,  one  should  strike  an  arc  mentally  across  the  country  with  B  as 
a  centre,  and  with  a  radius  of  2  to  20  miles,  according  as  some  definite 
topographical  feature  may  indicate.  In  country  at  all  rough  this  arc 
should  be  at  least  200°  long.  In  smoother  country  it  maybe  less.  A  pass 
through  a  range  of  hills  at  e  on  the  direct  line  to  A  may  determine  where 
to  strike  this  arc. 

Before  allowing  himself  to  pass  by  this  arc  at  any  point  the  engi- 
neer should  mentally  ask  himself  this  question,  and  either  answer  it  posi- 
tively and  definitely  on  the  spot,  or  note  that  he  must  find  an  answer: 
How  many  different  routes  are  there,  and  what  are  their  comparative 
merits,  for  passing  from  B  TO  BEYOND  THIS  ARC  at  any  point  in  its  whole 
extent  ?  If  there  be  some  point  like  e  or/"  which  is,  in  the  first  place,  out  of 
the  proper  direction  ;  secondly,  difficult  of  access  ;  and,  thirdly,  highly  un- 
promising in  appearance, — it  must  not  be  passed  until  it  is  known  that  it 
is  not  feasible,  or  else  noted  as  a  point  to  be  continually  remembered  as 
of  unknown  and  presumably  great  capabilities. 

Usually  there  will  be  three  or  four  routes  for  crossing  this  first  arc, 
which  will  appear  distinctly  better  than  any  others,  and  perhaps  be  the 
only  possible  ones.  Noting  every  one  of  those  which  have  not  been  ex- 
amined, and  assuming  'that  everything  is  possible  which  is  not  clearly 
seen  to  be  impossible,  the  imaginary  arc  may  be  crossed  to  the  next  belt. . 

1146.  Here,  at  some  fixed  topographical  feature  where  obstacles  occur, 
or  at  some  town,  a  second  mental  arc  may  be  struck,  likewise  with  B  as 
a  centre,  but  it  is  no  longer  necessary  to  make  it  200°  long,  but  merely 
long  enough  to  cover  a  route  to  A  from  every  possible  pass  of  the  first 
arc,  and  the  method  should  be  the  same.  The  question  should  be  :  In 
THIS  ANNULAR  BELT  what  is  the  bcst  way  to  pass  from  some  attainable 
point  in  the  first  arc  to  beyond  the  second,  and  which  will  give  the  best 
complete  route  from  B  ? 

By  this  time  we  shall  be  so  far  away  from  B  that  we  cannot  really  cover 
mentally,  even  in  the  rudest  way,  all  the  area  we  should  investigate,  and 
we  must  drop  the  furthest  half  of  it  entirely  from  mind  for  the  time 
being.  Remembering  that  it  is  dropped,  however,  the  method  is  the  same, 
so  far  as  it  goes.  By  assumption,  all  the  most  hopeful  chances  are  in  the 
region  beyond  the  horizon,  but  it  is  necessary  to  leave  them  for  the  time 
being. 

1147.  As  the  reconnaissance  approaches  A  it  will  be  more  natural  that 
our  work  should  be  carried  on  with  that  as  a  centre,  and  as  soon  as  pos- 
sible the  examination  of  the  whole  possible  area  at  once,  in  a  cursory 


840         CHAP.  XXVII.— THE  ART   OF  RECONNAISSANCE. 

way  at  least,  should  be  resumed.  On  reaching  A,  before  the  territor}^ 
passed. over  is  again  examined,  all  the  remaining  possible  area  should  be 
gone  over  in  the  same  way,  and  it  should  not  be  regarded  as  completed 
until  the  limits  of  the  water-shed  of  every  stream  in  the  whole  area  are  ' 
well  understood,  and  the  lowest  passes  through  the  ridges.  It  is  not  by 
any  means  the  roughest  regions  which  require  the  most  care  in  this  re- 
spect. Thus,  in  Fig.  266,  if  the  country  were  very  rough  the  chances 
would  be  very  strong  indeed  that  the  valley-line  B  VA  w^ould  be  the  best, 
and  a  very  cursory  examination  of  some  cross-line  VD  m.ight  suffice  to 
prove  it.  In  moderately  easy  country  the  line  BCD  A  would  be  far  more 
likely  to  be  the  best,  and  there  might  of  course  be  considerable  variations 
in  it ;  or  the  valley  at  be  might  be  so  low  and  the  town  C  so  small  that 
the  preference  clearly  lay  with  the  most  direct  line.  It  does  not  by  any 
means  follow  that  the  whole  area  should  be  examined  with  equal  care. 
If  one  part  is  positively  known  to  be  worse  than  another,  it  matters  little 
to  determine  how  much  worse  ;  only,  it  must  be  known,  and  not  guessed 
at. 

By  following  strictly  on  the  line  of  these  suggestions  serious  over- 
sights are  not  probable  ;  otherwise  they  are  exceedingly  probable.  Such 
assistance  as  it  seems  possible  to  give  for  training  the  eye  to  take  in  the 
meaning  of  what  it  sees  before  it,  is  given  in  the  following  chapter.  One 
general  caution  may  be  added  :  "  Rough  country  "  is  a  purely  relative 
term.  To  the  tyro,  the  rolling  hillocks  of  Ohio,  Michigan  and  New  Jer- 
se}'^  are  rough.  The  same  man,  with  a  little  experience  in  really  rough 
country,  will  take  the  worst  the  Rocky  Mountains  or  the  Andes  can  offer 
with  equanimity  ;  and  equanimity  is  in  every  calling  essential  for  success. 
No  country  in  which  most  of  the  surface  has  a  layer  of  soil  over  it  de- 
serves the  name  of  rough.  It  needs  but  little  study  and  care  to  get 
several  lines  of  reasonable  cost  through  it.  The  art  of  location  consists 
merely  in  making  a  judicious  choice, — not  in  getting  a  line,  which  is 
alwa3^s  easy  in  such  regions. 

1148.  An  accomplishment  which  is  not  very  difficult  to  acquire,  and  which 
is  constantly  useful  on  reconnaissance,  is  to  estimate  the  rate  of  fall  of  streams 
from  their  general  appearance.  No  general  rules  can  be  laid  down,  because  so 
much  depends  upon  the  volume  of  the  stream.  A  fall  of  4  to  8  feet  per  mile 
will  give  a  good-sized  stream  or  river  a  very  rapid  current,  with  many  stretches 
where  it  will  seem  to  the  careless  eye  as  if  there  were  iiearly  that  fall  at  a  single 
point,  succeeded  by  pools  above  and  below.  On  the  other  hand,  a  fall  of  30  or 
35  feet  per  mile  does  not  necessarily  give  to  a  small-sized  river  the  character  of 
a  torrent,  and  large  brooks  or  small  creeks  must  fall  100  feet  per  mile  or  more 
before  they  have  any  violent  current. 


CHAP.  XXVII.— THE  ART   OF  RECONNAISSANCE.         84 1 

1149i  A  special  report  on  the  Water-Power  of  the  United  States  in  the 
Tenth  United  States  Census  gives  a  tabular  statement  of  the  slopes  of  the 
principal  streams  flowing  into  the  Atlantic  and  the  Eastern  Gulf,  which  might 
perhaps  be  profitably  abstracted.  It  shows  that  the  slope  of  the  streams  is 
pretty  much  the  same  per  mile  from  the  Merrimack  to  the  Chattahoochee;  the 
average  slope  of  twenty-one  main  streams  being  5.4  feet  per  mile,  with  the  Sus- 
quehanna the  flattest,  at  2.8  per  mile,  and  the  Hudson  River  the  steepest,  at  10 
feet  per  mile. 

The  slope  of  some  of  the  southern  tributaries  of  the  Ohio  River  is  very  light, 
ranging  from  0.41  foot  per  mile  for  the  Green  River  to  2.84  feet  for  the  Alle- 
gheny as  a  maximum.  The  falls  in  these  streams  generally  take  the  form  of 
long  shoals.  As  an  example,  however,  of  the  rapidity  which  some  of  these 
rivers  descend  from  their  elevated  sources  to  the  gentle  slope  of  their  subsequent 
course,  Mr.  Dwight  Porter  mentions  that  the  Cheat  River,  in  West  Virginia,  falls 
2400  feet  in  the  last  eighty  miles  of  its  way  to  the  Monongahela,  while  the  latter 
river  descends  but  75  feet  in  the  ninety  miles  between  the  mouth  of  the  Cheat 
and  Pittsburg.  The  northern  tributaries  of  the  Ohio  have  usually  steeper  slopes, 
but  the  average  is  far  below  the  rivers  on  the  upper  Atlantic  coast.  The  Ohio 
River  itself,  from  Pittsburg  to  its  mouth,  a  distance  of  967  miles,  falls  430  feet, 
or  an  average  of  0.44  foot  per  mile.  At  Louisville  there  is  a  fall  of  26  feet  in 
two  miles. 

The  Upper  Mississippi,  from  its  extreme  sources  to  St.  Paul,  500  miles  by 
the  river,  falls  1000  feet.  The  Missouri  River  falls  2464  feet  in  the  2644  miles 
of  its  course  above  Fort  Benton,  being  navigable  to  that  point.  The  tributaries 
of  the  Mississippi  from  Eastern  Iowa  have  a  general  slope  of  about  3  feet  per 
mile,  ranging  from  1.84  to  3.83  feet  per  mile. 

The  Arkansas  River,  from  its  source  to  Pueblo,  Colorado,  averages  34.11 
feet  per  mile.  In  the  upper  120  miles  the  river  falls  40  feet  per  mile,  then 
flattens  out  to  8  feet  per  mile  for  500  or  600  miles,  and  at  150  miles  above  its 
mouth  its  slope  is  only  0.46  foot  per  mile. 

The  Niagara  River,  in  its  short  course  of  37  miles,  descends  333  feet  to  Lake 
Ontario  with  a  vertical  plunge  of  160  feet  at  the  Falls,  discharging  a  volume  of 
water  nearly  half  as  great  as  the  Mississippi  River,  or  166,600  cubic  feet  per 
second.  From  Buffalo  to  3  miles  above  the  Falls,  the  river  descends  20  feet,  or 
about  a  foot  per  mile,  yet  the  stream  is  readily  navigable;  from  this  point  to  the 
brink  of  the  Falls  it  descends  about  53  feet,  or  18  feet  per  mile. 


842  CHAP.  XXVIII.— OCULAR  ILLUSIONS. 


CHAPTER  XXVIII. 


OCULAR    ILLUSIONS. 


1150.  The  natural  eyesight  is  readily  deceived  even  where  the  ap- 
parent differences  are  so  great  as  to  seem  clear  and  positive.  Among 
the  more  serious  ways  in  which  this  danger  may  make  trouble  are  : 

I.  The  eye  foreshortens  the  distance  in  an  air-line  and  materially  ex- 
aggerates the  co7nparative  length  of  a  lateral  offset,  so  as  to  greatly  exag- 
gerate the  loss  of  distance  (and  hence  of  curvature)  from  any  deflection. 
A  deflection  which  will  not  in  reality  add  more  than  10  to  15  per  cent  to 
the  length  of  a  line  will  seem  to  the  eye  to  double  it.  This  marked  ten- 
dency to  great  exaggeration  results  from  the  effect  of  two  concurrent 
causes  :  (i)  the  foreshortening  alluded  to,  and  (2)  the  tendency  of  the  mind 
to  exaggerate  the  distance  lost  by  lateral  deflections  even  when  looking 
down  upon  a  map — as  Fig.  13,  page  237,  where  the  loss  of  distance  in  C 
might  be  easily  estimated  at  four  or  five  times  what  it  is. 

These  two  causes  combined,  both  of  them  having  much  effect  in  the 
same  direction,  make  the  judgment  of  inexperienced  men  on  this  subject 
almost  absurdly  deceptive. 

1151.  2.  The  eye  exaggerates  the  sharpness  of  projecting  points  andsptirs, 
and  the  degree  of  curvature  necessary  to  pass  aroimd  them :  an  exceed- 
ingly common  difficulty,  leading  to  serious  consequences.  It  results  from 
a  combination  of  natural  causes,  viz.:  (i;  The  eye,  in  looking  at  all  nat- 
ural slopes,  from  any  point  of  view  whatever,  greatly  exaggerates  their 
steepness.  A  60°  slope  seems  almost  vertical ;  a  45°,  fully  75°;  a  i-|-  to  i 
slope  (the  rate  of  the  very  steepest  mountain  sides),  at  least  i  to  i  ;  etc., 
etc.  This  tendency  is  especially  strong  in  looking  at  slopes  from  above. 
(2)  Such  points  are  generally  looked  at  from  above ;  but  whether  looked 
at  from  above  or  below,  the  eye  instinctively  searches  for  something  fixed 
and  definite  to  start  from,  which  is  usually  found  in  the  crest  or  ridge  li7te, 
especially  if  the  latter  runs  nearly  to  a  knife-edge.  Likewise  the  eye  al- 
most invariably  tends  to  exaggerate  angles,  from  whatever  point  the  view 
is  taken  on  which  the  judgment  is  formed.  If  formed  from  the  side 
(Fig.  267),  it  exaggerates  the  distance  C  in  comparison  with  AB\  making 


CHAP.  XXVIII.— OCULAR  ILLUSIONS.  843, 

it  seem  half  as  long,  for  example,  when  it  is  only  one  fourth  as  long,  thus 
making  the  point  seem  to  require  a  curve  of  180°  where  perhaps  no" 
only  will  suffice.  If  formed  from  in  front  of  very  sharp  points,  Fig.  268, 
the  tendency  is  to  look  upon  the  two  range-sights,  B,  C,  as  at  a  much 
sharper  angle  U  to  each  other  than  they  really  are,  because  tJte  eye  ranges 

along  both  slopes  at   07ice — an    unusual         :^ ^ ^^^_ 

circumstance,  the  more   common   case      \'^>  ^ -"-^  ^*/ 

being  that   of  Fig.    269,  in  which  the        ^/^   ^'^'•-.V.- •''    ^    ^/ 
tendency  is  in  the  opposite  direction,  ^^^  -i>'^7'' 

In  Fig.  268  one  tends  to  approximate  v%fe  •^)\^^^~/^ 

-- — ^^ — r  -  -^       '^/iiy/m  y 

^^  ^/^    V       t  \.uJ 

^^^^^ 

*  E 

Fig.  267.  Fig.  268. 

the  angle  V  to  180°;  or,  in  other  words,  to  think  of  B  and  C  as  nearly  par- 
allel to  each  other,  as  if  we  were  looking  from  E  at  an  infinite  distance. 

1153.  From  these  causes  combined,  the  eye  at  E  first  fixes  on  the 
crest-line  and  then  exaggerates,  say,  a  i-|-  to  i  slope  into  a  i  to  i  slope ;  in 
other  words,  makes  the  chord-line  A,  Fig.  268,  one  third  shorter  than  it 
is.  This  alone  gives  a  15°  curve  where  10°  will  suffice.  But  having  first 
got  our  chord-line  too  short,  we  then  proceed  to  mentally  exaggerate  the 
angle  to  which  it  is  a  chord,  and  thus  still  further  shorten  the  supposed 
radius,  so  that  we  may  easily  picture  a  20°  curve  where  10°  would  prove 
on  survey  all-sufficient. 

Whether  this  explanation  of  the  philosophy  of  the  tendency  to  error 
be  correct  or  not,  the  fact  of  its  existence  in  about  the  degree  stated  is 
beyond  question,  especially  with  those  who  are  for  the  first  time  con- 
fronted with  "rough  country."  They  are  almost  sure  to  exaggerate 
greatly  the  difficulties  of  such  localities. 

1154.  3.  An  opposite  tendency — to  decrease  the  probable  angles  re- 
quired— exists  in  looking  at  smooth  gentle  slopes,  especially  from  a 
distant  point  of  view,  for  reasons  hinted  at  in  part  in  Fig.  269.  Smooth- 
ness and  gentleness  of  slope  mean  that  we  must  either  go  out  a  long  way 
to  gain  a  little  difference  of  elevation,  or  must  put  up  with  very  long,  if 
not  very  deep,  cuts  or  fills.     In  order  to  bring  down  the  work  to  reason- 


844  CHAP.  XXVIII.— OCULAR  ILLUSIONS. 

able  lightness,  therefore,  we  must  often  adopt  a  quite  crooked  alignment 
on  the  smooth  and  (for  foot  travel)  very  tractable  slopes,  and  even  then 
have  pretty  heavy  work. 

This  error  is  especially  liable  to  occur  on  the  long  gentle  rolling  slopes 

which  are  met  over  vast  areas  of  the  far- 

y^f//j'  \v  "^N        western   United    States,    Mexico,   South 

y^' ^''•;  Vy/////;.'ji(V\  nV'   s  N^'*,'      America,  and  (the  writer  believes)  much 

-wV//'^ '/' '  1.^  ^  ^^\^  X.         of    Asia,   Africa,    and    Australia,    in    all 

'''•  v/    I  '  '\m\\^v'^     "*       of  which  regions  Nature  seems  to  have 

rU  /,  1 1  *  '  \  A  V  .\\V  planned  all  her  works  on  a  vast  scale  and 


\m- 


taken  plenty  of  room  to  spread  out  in. 

y^         /  In   the    Eastern   United   States    and    in 

\    /  Europe  west  of  Russia  it  is  less  immi- 

'^  nent. 

^'°-  2^9-  When  we  happen  to  be  comparing  two 

lines,  one  of  which  lies,  say,  in  a  valley,  where  the  tendency  is  to  exaggerate 

the  sharpness  of  curves  and  angles,  while  another  lies  on  a  smoother  and 

higher  region,  where  the  tendency  is  in  the  other  direction,  these  two 

opposite  tendencies  may  combine  to  cause  most  calamitously  mistaken 

conclusions,  one  line  being  made  up  in   large   part   of  points  like  Fig. 

268  and  the  other  like  Fig.  269. 

1155.  The  unassisted  eye  is  also  liable  to  be  deceived  in  many  ways 
as  to  gradients  and  elevations,  as  noticeably  in  the  following: 

4.  A  slope  looked  at  from  a  distance  always  appears  steeper  and 
higher  than  it  really  is,  especially  if  we  are  standing  on  ground  descend- 
ing towards  it,  when  the  eye  tends  to  look  on  the  slope  where  we  stand 
as  more  nearly  level  than  it  is,  and  to  exaggerate,  often  to  an  absurd  ex- 
tent, the  steepness  of  the  rising  ground  in  front.  This  is  a  familiar  ex- 
perience, which  most  men  have  learned  to  allow  for,  more  or  less.  The 
best  training  for  the  eye,  to  check  the  danger,  is  to  study  the  phenomenon 
on  highways  or  constructed  railways,  where  the  effect  of  a  given  vertical 
angle  is  far  more  marked  than  on  a  natural  unbroken  surface,  for  the 
reason,  probably,  that  where  the  mind  looks  for  uniformity,  as  on  a  rail- 
way or  road,  it  is  forcibly  impressed  by  a  deviation  from  it,  but  where,  on 
the  other  hand,  irregularities  are  looked  for  and,  as  it  were,  "discounted" 
in  advance,  the  very  same  surface  angle  produces  less  impression. 

1156.  Another  and  perhaps  truer  explanation  of  this  and  many  other 
ocular  illusions  is  that  it  is  simply  lack  of  practice  and  training  of  the 
eye  under  those  particular  conditions.  The  child  had  absolutely  no  per- 
ception of  distance  or  perspective,  and  hence  of  size,  but  puts  out  his 


CHAP.  XXVIII.— OCULAR  ILLUSIONS. 


845 


hand  to  touch  everything  he  sees  within  his  field  of  view,  even  on  the 
distant  horizon.  To  measure  distances  and  sizes  as  accurately  as  we  do 
by  the  aid  (i)  of  the  short  base-line  of  2\  inches  between  the  two  eyes, 
and  (2)  of  our  gradually  acquired  knowledge  of  the  probable  sizes  of  ob- 
jects, is  really  a  mental  process  of  extraordinary  difficulty  and  delicacy, 
which  is  only  acquired  by  the  incessant,  unconscious  practice  of  years. 
Under  the  conditions  in  which  we  have  been  most  trained  we  do  toler- 
ably well ;  but  whenever  we  strike  the  unfamiliar  and  unusual,  then  the 
eye  reverts  to  its  original  untrained  tendency  to  bring  everything  in  the 
distance  up  into  its  own  vicinity,  with  an  inevitable  distorting  effect  on 
what  the  mind  makes  out  of  the  picture  seen.  Thus  it  is  that  the  sun 
and  moon  appear  to  the  eye  a  great  deal  larger  when  they  are  rising  or 
setting,  the  mind  never  admitting  that  they  can  be  very  far  off,  except  when 
forced  to  do  so  by  seeing  them  beyond  the  immediate  horizon.  Thus, 
rather  than  by  the  common  explanation  that  there  are  no  intermediate 
objects  to  fix  on,  distances  across  water  are  always  under-estimated  by 
those  unaccustomed  to  it.  For  the  same  reason,  possibly,  the  eye  brings 
forward  the  farther  end  of  a  long  line  of  rails  beyond  a  hollow  until — 
aided  somewhat  by  the  further  assumption  that  we  are  standing  on  a 
level — they  seem  almost  to  stand  up  and  down.  For  the  same  reason, 
the  steepness  of  the  slopes  of  mountains  are  exaggerated  ;  and  possibly 
for  the  same  reason,  in  part  at  least,  the  immense  scale  on  which  the 
topographical  features  of  the  great  West,  Mexico,  South  America,  and 


Fig.  270. 

similar  regions  are  laid  out,  deceives  as  to  distances  the  Eastern  man  or 
European,  accustomed  to  a  pettier  topography. 

1157.  A  comparison  of  the  different  effect  upon  the  eye  of  railway 
gradients  and  natural  slopes  of  the  same  rate,  wherever  two  descending 


846 


CHAP.  XXVIII.— OCULAR  ILLUSIONS. 


gradients  can  be  found  nearly  following  the  natural  surface,  is  an  in- 
structive training  of  the  eye.  By  standing  first  on  the  track  and  then  a 
few  hundred  feet  to  one  side,  the  difference  in  the  degree  of  the  decep- 
tion is  marked ;  but  trial  from  various  points  of  view  will  show  that  it 
always  exists,  even  on  the  natural  surface. 


Fig.  271. 

1158.  5.  Allied  to  the  above,  but  operating  more  obscurely  and  on  a 
larger  scale,  is  the  deception  which  comes  from  THE  propinquity  OF 
LARGE  MASSES  OF  HILLS  OR  MOUNTAINS  when  looked  at  from  a  dis- 
tance, or  even  from  a  mere  general  slope  in  one  direction  of  the  whole 
foreground  within  view,  especially  if  it  be  much  broken  up  in  detail  by 
minor  hillocks  and  ridges,  so  that  the  general  trend  of  the  surface  is  not 
readily  detected.  The  best -trained  eye  is  quite  incapable,  under  these 
circumstances,  of  estimating  horizontality  so  as  to  detect  the  lowest  points 
with  the  same  success  as  under  ordinary  circumstances.     Fig.  212,  page 


Fig.  272.— a  Distant  View  of  an  Overlap. 

680,  reproduces  admirably  an  ocular  illusion  of  this  kind.  The  grades 
against  the  stream  seem  enormously  steep,  and  those  with  it  nearly  level. 
The  reverse  is  the  case  at  the  viaduct  in  the  background,  and  elsewhere 
the  rate  is  the  same.  In  Fig.  270  the  pass  A,  which  seems  to  the  eye  of 
a  distant  observer  to  be  slightly  lower  than  B,  may  be  counted  on  with 
great  certainty  to  be  considerably  higher.  To  be  in  fact  on  a  level  with 
it,  it  must  appear  to  the  eye  very  much  lower.     Fig.  270  was  sketched 


CHAP.  XXVIIL— OCULAR  ILLUSIONS.  847 

from  an  instance  where  half  a  dozen  skilled  men  under-estimated  the 
height  of  A,  and  over-estimated  B,  by  nearly  200  feet,  from  a  point 
of  view  less  than  3  miles  off,  over  an  apparently  level  plain,  on  a  line  of 
sight  nearly  parallel  with  the  slopes  of  the  mountain,  and  with  A  and  B 
hardly  more  than  half  a  mile  apart ;  the  pass  having  been  looked  at, 
likewise,  from  both  sides. 

1159.  Another,  the  most  extraordinary  ocular  deception  which  the 
writer  has  ever  encountered,  and  for  which  he  could  not  then  or  later 
imagine  an  explanation,  is  badly  sketched  from  memory  in  Fig.  271.  In  a 
gently  rolling  but  much  "  accidented  "  country,  through  a  little  pass  with 
(seemingly)  long  gentle  slopes  on  each  side,  the  little  hut  appeared  only 
10  feet  above  the  bottom  of  the  notch  less  than  400  ft.  off,  when  in  fact 
it  was  80  ft.,  there  being  in  this  case  no  preponderance  of  large  masses 
on  either  side  of  the  field  of  view  to  unbalance  the  eyesight.  This  decep- 
tion, likewise,  was  common  to  every  man  of  a  large  and  experienced 
corps,  and  perhaps  came  from  an  obscure  train  of  association  with  a  sharp 
and  tremendous  descent  a  short  distance  back  (1500  feet  in  a  six-mile 
view),  which  might  have  been  seen  in  part  by  eyes  in  the  back  of  one's 
head  while  looking  at  the  hut,  but  which  neither  existed  in  fact  nor  ap- 
peared to  exist  in  the  view  taken  in  by  the  natural  eyesight,  as  rudely 
and  very  inadequately  sketched  in  Fig.  271.  The  hut  looks  far  too  high 
in  the  cut,  and  the  very  bottom  of  the  valley  was  in  sight. 

1160.  Similar  ocular  illusions,  and  perhaps  more  remarkable  ones, 
may  be  seen  wherever  there  are  irrigating  or  other  nearly  level  ditches 
winding  around  the  slopes  of  mountains  above  rapidly  descending  val- 


FiG.  273. — The  same  Overlap — Near  View. 

leys.  They  invariably  appear  to  run  up  hill,  and  often  in  a  very  marked 
and  extraordinary  way,  as  with  man}^  of  the  irrigating  ditches  of  Colorado. 
These  examples  are  but  pronounced  types  of  frequent  topographical 
irregularities,  which  make  the  eyesight  utterly  worthless  for  measuring 
important  elevations  and  slopes  in  certain  localities;  and  where  those 
localities  are,  unfortunately,  cannot  be  determined  in  advance.  The 
aneroid  barometer,  altazimuth,  or  hand-level,  consequently,  should  be 


S4B 


CHAP.  XXVIII.— OCULAR  ILLUSIONS. 


constantly  used  on  reconnaissance,  and,  in  general,  all  such  points,  if 
important,  should  be  actually  visited,  for  another  reason: 

1161.  6.  Overlaps  of  hills  or  elevated  ground  at  a  distance  are  a 
frequent  source  of  deception  and  error.  Views  which  from  a  distance 
appear  like  Fig.  272  are  found  on  nearer  acquaintance  to  be  more  like 
Fig.  273,  with  an  easy,  open  valley,  and  perhaps  a  running  stream  pass- 
ing through  what  seemed  to  be,  "beyond  question,"  a  solid  ridge.     Illu- 


FiG.  274. — Better  Country  than  it  Looks. 

sions  of  this  kind  are  often  very  perfect,  even  in  the  near  vicinity  of  the 
observer.  An  example  on  a  small  scale  (small,  because  the  mind  realizes 
that  it  must  be  a  deception)  may  be  seen  in  ascending  the  Hudson  River 
when  approaching  Peekskill,  especially  in  the  early  summer  evenings, 
when  the  lights  and  shades  are  such  as  to  produce  a  very  vivid  feeling 
that  it  is  a  closed  basin  without  further  outlet  to  the  north.  It  is  said 
to  be  on  record  that  it  deceived  Hendrick  Hudson  himself,  and  almost 
induced  him  to  turn  back. 


CHAP.  XXVIII.— OCULAR  ILLUSIONS. 


849 


The  great  safeguard  against  errors  of  this  kind  is:  Form  a  complete 
picture  of  the  water-shed  over  the  area  to  be  reconnoitred,  so  that  it  is 
known  where  water  falling  on  it  anywhere  will  flow  to. 

1162.  7.  The  eye  often  deceives  itself  in  estimating  quantities,  for 
reasons  which  in  part  result  from  what  has  preceded.  Most  serious  con- 
sequences flow  from  this,  leading  to  the  abandonment  without  survey  of 
lines — especially  valley-lines — which  should  have  been  regarded  as  the 


Fig.  275. — Worse  Country  than  it  Looks. 

most  promising  of  all.  The  root  of  the  difficulty,  in  addiuion  tu  t'ne 
various  causes  of  deception  which  have  been  noted,  lies  in  the  inability 
of  the  mind  to  distinguish  (i)  between  what  seems  rough  and  what  is, 
and  (2)  between  what  is  rough  for  foot  or  horse  travel  and  what  is  rough 
for  railway  construction. 

The  extent  of  the  first  cause  for  deception  will  be  better  appreciated, 
by  those  who  have   had  any  considerable  experience  in  construction,  if 
they  will  but  recall  what  a  tremendous  reduction  in  the  apparent  diffi- 
54 


850  CHAP.  XXVIII.— OCULAR  ILLUSIONS. 

culty  of  work  follows  from  the  mere  act  of  thoroughly  clearing  the 
ground,  even  if  there  were  nothing  on  it  before  but  light  undergrowth 
and  brush.  To  a  thoroughly  trained  eye  this  should  make  no  appreci- 
able difference,  yet  the  unconscious  feeling  of  every  one  is  "well  begun, 
half  done." 

1163.  When  to  ordinary  timber  we  add  tangled  vines  and  under- 
growth, making  progress  on  foot  exceedingly  slow  and  difficult,  this 
effect  IS  increased.  We  are  apt  to  measure  distances  by  time  under  such 
circumstances,  so  that,  if  we  went  over  an  aggregate  of  10  miles  at  one  mile 
per  hour,  and  of  90  miles  at  five  or  six  miles  per  hour,  in  exploring  100 
miles,  we  shall  finish  with  a  feeling  that  fully  a  third  of  the  line  has  been 
very  rough.  On  the  other  hand,  when  we  strike  a  highway  and  go  along 
rapidly  over  the  ground,  we  at  least  never  exaggerate  the  difficulties 
which  we  walk  over  the  hill  to  take  a  glance  at,  and  the  long  stretches 
of  easy  country  are  what  we  have  been  most  conscious  of  and  remember 
most  vividly. 

In  Fig.  274  we  have  a  sketch  of  a  jagged  rocky  point  in  a  river  valley; 
in  Fig.  275  a  sketch  of  a  line  on  a  gently  rolling  side-hill.  Nine  men  in 
ten  will  be  rather  appalled  by  the  rocky  bluffs  and  take  the  side-hill  line 
very  calmly;  yet  the  chances  are  very  strong  that,  mile  for  mile,  the  val- 
ley-bluff line  will  be  the  cheapest,  in  addition  to  having  the  best  grades. 

1164.  This  results  from  the  fact  that  in  following  a  valley-line  it  is 
exceedingly  difficult  to  make  due  allowance  for  the  fact  that  Nature 
HAS  MADE  OUR  FILLS.  It  may  be  necessary  to  hit  such  a  rocky  point 
as  that  in  Fig.  274  pretty  hard,  but  never  very  hard,  because  before  we 
have  done  very  much  work  on  it  we  have  excavated  enough  material 
to  carry  the  line  past  it  on  a  fill,  even  in  a  raging  torrent;  and  hence  we 
are  not  obliged  to  hug  into  the  point,  as  on  ordinary  ground,  to  avoid 
running  our  line  above  all  supporting  ground  in  the  hollow  beyond. 
There  are  no  hollows  beyond.  As  soon  as  we  have  passed  this  point  we 
come,  probably,  to  a  narrow  but  sufficient  stretch  of  bottom-land,  already 
rip-rapped  with  vegetation,  and  already  standing,  as  all  bottoms  do  (when 
there  are  any)  in  such  valleys  as  that  pictured,  just  above  the  ordinary 
level  of  high-water,  so  that  they  are  not  often  overflowed  deeply  (usually 
once  in  10  to  30  years),  or  else,  when  they  are  overflowed,  are  not  sub- 
mitted to  a  destructive  current.  The  more  violent  and  rapid  the  ordi- 
nary current  the  less  likelihood  there  is  that  the  bottoms  are  often  de- 
structively overflowed.  If  overflowed,  the  current  cannot  be  rapid,  or  the 
bottoms  would  wash  away. 

Therefore,  when  we  have  passed  the  rocky  bluff  in  Fig.  274  we  have 


CHAP.  XXVIII.— OCULAR  ILLUSIONS.  85 1 

comfortable  running,  and  can  get  a  good  alignment  until  we  come  to  the 
next  similar  point.  At  every  one  of  them,  although  we  are  thrown  out  to 
and  into  the  water.  Nature  has  provided  the  material  to  resist  the  water  on 
the  spot.  The  profile  of  such  a  line  is  very  apt  to  be  quite  light ;  rather 
deceptively  so  in  fact,  since  there  will  be  a  great  deal  of  work  in  protect- 
ing banks  and  working  very  steep  slopes,  which  will  not  show  on  the 
profile  at  all. 

1165.  On  the  other  hand,  in  Fig.  275,  gentle  as  is  its  general  effect,  we 
must  cut  into  our  hills  far  more  than  the  eye  will  appreciate  in  order  to 
avoid  enormous  fills.  If  the  slopes  be  at  all  steep  (they  might  well  be 
steeper  in  the  view  to  bring  out  the  effect  desired),  the  eye  when  reconnoit- 
ring will  underrate  the  depth  of  these  fills,  especially  from  a  distance,  by 
taking  a  mental  section  of  them  oji  a  plajie  normal  to  the  slope  instead  of ' 
on  a  vertical  plane.  The  loss  from  the  side-hill  slope  of  the  ground, 
likewise,  will  be  very  likely  to  be  under-estimated :  not  that  the  eye  will 
not  exaggerate  the  slope  of  the  ground  relatively  to  the  horizontal,  for  it 
will,  but,  by  a  seeming  paradox,  the  angle  of  the  ground  with  the  side- 
slopes  of  a  cut  or  fill  will  be  rather  underrated,  because  the  mind  men- 
tally exaggerates  the  latter  also,  and  still  more. 

It  is  almost  an  invariable  rule  that  fills  turn  out  deeper  than  they  are 
expected,  and  on  a  side-hill  line  most  of  the  water-ways  are  in  fills  of 
considerable  depth.  The  water  channels  are  also  more  ramified,  and 
hence  more  numerous,  on  high  slopes  than  lower  down  in  the  valleys, 
where  the  total  discharge  is  more,  but  the  water  has  collected  in  larger 
streams. 

Much  expense  can  be  saved  on  side-hill  lines,  and  danger  of  washouts  as 
well,  by  catching  the  water  in  a  ditch  at  or  a  little  below  grade  and  carrying  it 
under  the  road-bed  in  a  small  structure,  with  the  foundations  of  the  discharging 
end  of  the  structure  properly  secured,  instead  of  putting  the  structure  in  the 
very  bottom  of  the  gulch. 

1166.  CuL-DE-SACS  are  another  incessant  source  of  deception  and  error,  al- 
though rather  due  to  negligence  or  inexperience  than  to  ocular  illusion  proper. 
It  constantly  happens  that  men  walk  into  them  as  a  mouse  into  a  mouse-trap, 
and  for  the  same  reason — blindly  following  one's  nose;  or  rather,  from  recon- 
noitring a  LINE,  foot  by  foot  and  mile  by  mile,  instead  of  an  area  as  a  whole.  A 
man  sees  a  beautiful  open  area  ahead  of  him  as  far  as  the  eye  can  reach,  prob- 
ably with  a  highway  through  it.  He  is  satisfied,  and  looks  no  farther,  until  he 
comes  to  the  end  of  it.  Then  it  is  too  late.  He  has  accepted  his  line  so  far 
as  a  finality,  and  knows  no  other.  He  assumes  that  he  can  do  nothing  better 
behind,  and  "therefore"  must  get  out  of  his  trap  ahead  as  best  he  can.  Unless 
he  is  confronted  with  very  great  difficulties,  he  is  likely  to  do  so.     To  read  in 


852  CHAP.  XXVIII.— OCULAR  ILLUSIONS. 

cold  print,  this  seems  an  improbable  bit  of  stupidity.     It  is  one  of  the  common- 
est of  faults. 

1167.  A  single  instance  on  an  important  survey,  affecting  40  miles  of  line, 
will  illustrate  how  it  happens.  In  a  very  broad  flat  valley  which  extended  for  six 
or  eight  miles  farther  a  dry  run  was  encountered.  It  was  assumed  to  drain  to 
the  west,  and  passed  as  of  no  moment.  It  really  drained  to  the  east,  through 
a  small  rocky  overlap  about  two  miles  off,  which  opened  out  half  a  mile  be- 
yond into  a  broad  open  valley  leading  directly  to  the  desired  terminus.  The 
cul-de-sac  gave  a  fine  line  as  long  as  it  lasted,  and  then  over  20  miles  of  rather 
heavy  work,  with  bad  grades  and  bad  curves,  yet  it  was  run  by  an  engineer  of 
large  experience,  and  came  very  near  being  built. 

1168.  Of  all  these  types  of  ocular  deceptions  there  are  many  varia- 
tions. To  thoroughly  guard  against  them  comes  with  experience  alone, 
and  rarely  with  that.  Until  they  have  been  learned  by  experience,  and 
the  engineer's  "  personal  equation '  determined,  very  wide  limits  of 
error  alone  can  be  safely  assumed.  Nevertheless,  provided  the  danger 
of  error  be  realized,  it  is  not  a  particularly  serious  one,  because  errors 
of  the  eye  will  be  checked  by  surveys.  The  greater  danger  is  that 
the  untrained  eye  will  tell  such  wholly  delusive  tales  as  to  make  the 
worse  appear  the  better  course,  and  cause  that  line  or  part  of  a  line  to 
be  rejected  without  survey  which  was  really  the  best.  To  guard  against 
this  danger,  and  not  to  advise  substituting  the  eye  for  the  precision  of 
surveys  except  within  known  limits  of  safety,  this  chapter  has  been 
written. 


1169.  A  single  example  of  the  way  in  which  ocular  illusions  and  some 
of  the  causes  mentioned  in  the  previous  chapter  may  combine  to  lead  to 
wrong  conclusions  by  errors  of  reconnaissance,  pure  and  simple,  may  be 
of  value  to  save  the  student  from  underrating  the  magnitude  and  im- 
minence of  the  dangers  against  which  he  has  been  cautioned.  It  sum- 
marizes the  facts  of  a  very  important  piece  of  line  on  which  a  number 
of  causes  combined  to  bring  about  calamitously  wrong  conclusions. 
Those  particular  causes  for  wrong  conclusions  against  which  cautions 
have  been  given  are  printed  in  italics.  The  map  is  modified  somewhat, 
but  the  other  conditions  are  in  no  way  exaggerated.  Appendix  C  con- 
tains another  example,  and  the  writer  had  made  a  list  of  nearly  a  dozen 
others  which  he  had  intended  to  annotate  similarly,  but  space  forbids. 

The  line  was  about  100  miles  long  from  A  to  G,  Figs.  276-7,  through 
a  region  of  much  difficulty  after  reaching  the  crucial  point  B  or  B' , 
where   an  exit  was  to  be  found  from  an  easy  open  basin  surrounding 


CHAP.  XXVIII.— OCULAR  ILLUSIONS. 


853 


A.  An  established  and  much-travelled  highway  followed  the  general 
route  selected,  ABCFG.  The  pass  B  was  a  little  easier  than  B',  and 
seemed  for  special  reasons  much  easier  than  it  was.  The  difficulties  of 
co?tstruction  were  distributed  over  almost  the  entire  line  ACG,  so  that, 


Fig.  276. 


£     -.- 


^^t- 


J    \ 


Fig.  277. 


B  M 


C 
I    t 


--  >     /J 


although  a  costly  line  in  the  aggregate,  the  work  was  at  no  point  of  a 
specially  forbidding  character. 

Another  route,  AB'DEG,  for  these  and  other  more  pardonable  rea- 
sons, was  not  even  examined  until  too  late.     The  pass  B'  was  slightly 


854  CHAP.  XXVIII.— OCULAR  ILLUSIONS. 

higher  and  more  difficult  of  approach.  Upon  reaching  it  the  outlook  for 
the  next  few  miles,  to  the  pass  D, — which  was  indeed  visible  from  B,  but 
could  not  be  recognized  as  a  pass  from  that  distance  owing  to  an  overlaps 
so  that  the  mountain  range  appeared  unbroken, — was  over  a  deep  and 
ugly  basin,  and  so  was  exceedingly  forbidding,  admitting  of  easy  grades 
but  plainly  requiring  heavier  work  and  worse  alignment  to  get  them  than 
any  stretch  of  equal  length  on  the  other  line.  On  the  other  hand,  the  en- 
tire difficulties  of  construction  were  concentrated  on  this  short  stretch  of  6 
to  8  miles.  Once  through  the  pass  D  {which  could  be  reached  from  B' 
only  with  much  difficulty  and  a  long  detour),  an  open  and  unobstructed 
valley  admitted  of  a  light  and  straight  surface-line  for  some  6o  miles  to 
the  point  E, — a  traffic  of  special  value  to  the  line  being  distributed  from 
Elo  H.  At  jS"  a  valley  was  struck  leading  by  a  comparatively  easy  de- 
scent directly  to  the  terminus  G,  whereas  the  other  line  at //'was  so  high 
above  the  valley  that  a  costly  side-hill  descent  on  a  heavier  grade  was  the 
only  resource.  The  comparative  profiles  of  the  t.vo  lines  are  shown, 
without  exaggerating  the  contrast,  in  Fig.  292. 

The  dotted  line  was  in  this  case  superior  in  every  detail,  unless  pos- 
sibly in  cost,  for  the  stretch  B'D,  although  not  over  8  miles  long,  was 
more  costly  than  any  40  miles  on  the  other  line.  But  the  grades  were 
materially  better,  the  line  shorter  and  with  less  curvature,  and  the  local 
traffic  it  offered  was  many  times  more  valuable  than  all  on  the  other  line 
put  together. 

1170.  The  error  on  reconnaissance  lay  in  passing  the  point  B  with- 
out completely  investigating  all  the  possibilities  of  the  line  B'D  before 
leaving  it,  and  so  determining  for  a  certainty  that  the  possible  line  turn- 
ing oflf  through  the  gap  to  the  left  not  only  began  bad,  but  continued 
bad.  Once  having  passed  through  B,  and  accepted  that  pass  as  a 
finality,  the  case  was  hopeless.  The  two  lines  then  speedily  diverged 
from  each  other  completely,  till  they  were  40  miles  apart  and  1500  feet 
different  in  elevation.  C  then  became  another  fixed  point,  from  which 
there  was  no  possible  escape.  F  and  H'  in  their  turn  followed ;  and 
when  at  last  the  long  and  open  valley  E  came  within  sight,  the  false 
premise  that  B  must  be  the  pass,  now  70  miles  behind,  made  it  a  legiti- 
mate and  logical  conclusion  that  it  offered  no  possibilities  for  considera- 
tion. 

1171,  Had  the  reconnaissance  happened  to  begin  from  G,  the  error 
would,  in  this  particular  instance,  have  been  avoided,  for  the  natural 
line  GEHD  would  almost  certainly  have  been  followed  in  the  first  in- 
stance, no  natural  line  whatever  existing  in  the  direction  G//'/'^,  so  that  a. 


I 


CHAP.  XXVIII.— OCULAR  ILLUSIONS.  855 

large  portion  of  the  whole  cost  of  the  line  was  concentrated  on  the  initial 
stretch  GH', 

This  very  circumstance,  however,  with  the  conditions  of  relative  ad- 
vantage reversed  (especially  with  the  pass  B  a  little  less  tempting  and 
no  highway  along  GFCA),  would  have  been  almost  certain  to  result  in  an 
error  precisely  similar  in  principle,  with  a  reverse  result.  Starting  at  G, 
the  fine  open  line  GEH  would  have  been  followed  with  increasing  cer- 
tainty that  it  was  the  only  line  to  take,  the  possibility  6^i^^  having  been 
turned  from  as  out  of  the  question  or  perhaps  impossible  (almost  cer- 
tainly the  latter  with  an  inexperienced  man,  for  it  took  much  skill  to 
obtain  it).  Arriving  at  D,  the  reconnoiterer  would  find  himself  in  a  ctd- 
de-sac,  caught  in  the  mazes  of  his  own  negligence  and  hasty  preposses- 
sions. A  beautiful  line  was  behind  him,  but  8  miles  of  tunnels  and  via- 
ducts were  before  him,  from  which  there  was  absolutely  no  escape  with- 
out going  back  again  to  G,  mentally  as  well  as  physically,  and  picking 
out  the  line  GHFC,  every  foot  of  which,  while  nowhere  excessively  diffi- 
cult, was  a  forced  line,  resulting  from  having  got  into  the  hole  C  and 
having  to  get  out  of  it  somehow  in  the  direction  G.  Under  these  cir- 
cumstances, there  being  but  the  two  lines,  so  widely  separated,  it  would 
have  been  well-nigh  a  certainty  that,  had  the  reconnaissance  began  at 
G  instead  of  .4,  the  tempting  plains  GD  would  have  proved  an  even  more 
irresistible  bait  than  the  pass  B  to  bias  the  mind  against  fair  and  com- 
plete examination  of  even  the  possibilities  of  the  other  line. 

1172.  The  writer  is  able  to  give  no  more  apt  illustration  than  this  of 
the  importance  of  following  the  seemingly  over-minute  instructions  of 
this  and  the  preceding  chapter,  whether  because  of  the  importance  of  the 
instance,  or  because  of  the  salient  and  marked  topographical  features, 
which  do  not  confuse  the  min^d  with  a  multitude  of  detail.  There  was 
just  one  point  on  the  line  of  reconnaissance,  and  that  point  one  affording 
a  most  forbidding  and  helpless  outlook,  where  there  was  reasonable 
chance  to  discover  the  error.  Guessing  that  an  overlapped  mountain 
eight  miles  off  had  no  pass  through  it,  and  that,  even  if  it  had,  the  ragged 
eight  miles  which  could  be  seen  meant  a  ragged  eighty  miles  beyond  it 
which  could  not  be  seen,  and  which  was  smooth  as  a  prairie,  caused  the 
error.  Examples  might  easily  be  multiplied  of  similar  errors,  and  some 
of  them,  as  in  the  instance  mentioned  in  Appendix  C,  of  much  greater 
magnitude.  Valley  lines  are  particularly  apt  to  be  rejected  in  this  way, 
without  thorough  examination,  because  of  supposed  obstacles  which  are 
largely  imaginary. 


856  CHAP.    XXIX.— WHEN   TO  MAKE   SURVEYS, 


CHAPTER  XXIX. 


WHEN    TO    MAKE    SURVEYS. 


1173.  The  reconnaissance  having  been  thoroughly  and  carefully  made, 
the  most  important  part  of  the  location  is,  in  general,  concluded.  For, 
assuming  all  business  as  well  as  topographical  questions  to  have  been  as 
carefully  weighed  as  is  possible  in  advance  of  surveys,  a  difference  be- 
tween any  two  lines  which  cannot  be  detected  by  such  an  examination 
can  hardly  be  a  vital  one,  seriously  affecting  the  future  of  the  property. 

Nevertheless,  although  really  ruinous  errors  can  rarely  come  from  an 
inadequate  amount  of  surveying  or  from  imperfect  balancing  of  their 
nice  results,  good  or  bad  judgment  in  the  conduct  of  surveys  may  well 
make  a  large  difference  in  the  earning  capacity  of  the  line,  and  a  still 
larger  difference  in  first  cost, — that  so  often  vital  consideration  for  the 
original  projectors. 

1174.  Drawing  an  analogy  from  the  construction  of  a  building,  the 
reconnaissance  is  like  the  selection  of  the  site  for  a  building,  the  deter- 
mination of  its  size  and  general  plan,  and  the  rough  but  (in  skilled  hands) 
close  guessing  at  the  cost  of  comparative  plans.  The  survey  is  like  the 
preparation  of  the  detail  plans  and  exact  estimation  of  cost.  The  con- 
struction of  a  railway  is  like  the  construction  of  a  building  after  all  these 
details  have  been  determined.  * 

1175.  The  seeming  paradox  is  yet  true,  that  both  too  much  and  too 
little  time  and  money  is  generally  devoted  to  surveys.  Too  many  miles 
of  line  are  surveyed,  but  that  which  is  surveyed  is  not  surveyed  as  well 
and  thoroughly  as  it  should  be.  The  perhaps  dangerous  assertion  (dan- 
gerous because  it  may  give  an  excuse  for  hasty  and  over-confident  con- 
clusions) has  already  been  made  (par.  1 128),  that  more  often  than  not  there 
is  only  one  general  route  between  two  points  to  be  connected  by  railway 
of  sufficient  comparative  promise  to  justify  even  a  flying  line  over  it;  but 
good  and  certain  reasons  should  appear  for  failing  to  run  at  least  two 
lines.  Doubtless  sometimes  there  may  be  real  necessity  to  survey  three 
or  more  lines,  but  the  writer  has  never  happened  to  meet  such  a  case. 
Considerations  of  policy,  however,  often  require  the  running  of  numerous 


CHAP.   XXIX.— WHEN   TO  MAKE   SURVEYS.  .  857 

lines  for  which  no  engineering  necessity  exists;  and  in  the  study  of  the 
details  of  location,  over  distances  of  one  to  twenty  miles,  there  are  often 
a  dozen  or  more  different  lines  or  modifications  of  lines,  which  will  re- 
quire to  be  attentively  studied. 

1176.  The  true  method  of  determining  whether  or  not  there  is  need 
to  survey  more  than  one  general  route  is  this  : 

Having  carefully  examined,  m  the  manner  detailed  at  length  in  the 
preceding  chapter,  every  possible  line,  and  having  gathered  as  full  details 
as  possible  of  the  actual  cost  and  gradients  and  resulting  traffic  and 
earnings  of  other  lines  from  previous  experience  and  study  of  recorded 
results,  a  maximum  and  minimum  estimate  should  be  made  of  each  ; 
that  is  to  say,  it  should  be  said  of  each,  "  This  line  will  apparently  af- 
for  dgradients  of  —  per  cent,  which  estimate  cannot  (guarding  well 
the  'cannot')  be  in  error  more  than  —  per  cent  either  way,  giving 
a  range  for  possible  error  of  judgment  of  from  —  to —  per  cent.     Its 

cost  will  apparently  be  about  % ,  and  cannot  range  above  or  below 

this  estimate  more  than  —  per  cent  either  way.  It  will  reach  (such  and 
such)  sources  of  traffic  more  (or  less)  than  the  other  lines,  which  cannot 

add  less  than  % per  annum  to  the  net  revenues  of  the  company, 

and  might  add  as  much  as  % .     In  the  minor  details  of  distance, 

curvature,  and  rise  and  fall  it  has  advantages  (or  disadvantages)  which 
may  be  considered  as  liable  to  affect  the  future  revenues  per  annum  of 
the  company  by  from,$ to  $ ." 

If,  then,  after  making,  with  more  or  less  elaboration,  an  estimate  of 
this  kind  for  each  of  the  various  possible  lines,  it  be  found  that,  taking 
the  most  unfavorable  view  deemed  possible  of  that  line  which  seems  the 
best,  it  is  still  a  better  line  than  the  most  favorable  possible  result  from 
any  of  the  others,  it  is  a  waste  of  time  and  money  to  survey  more  than 
one  line. 

1177.  In  the  application  of  this  rule  there  is  real  danger  of  error,  but 
ithe  danger  lies,  not  in  the  rule  itself,  but  in  careless  or  over-confident 
application  of  it;  not  in  taking  mere  guesses  at  maxima  and  minima  as 
decisive,  but  in  failing  to  make  the  limits  wide  enough.  Even  with  the 
most  elaborate  precautions  all  human  judgment  is  fallible.  No  amount 
of  surveys  will  do  much  to  prevent  an  incompetent  man  from  selecting 
and  building  one  of  the  many  possible  wrong  lines  instead  of  the  one 
right  line  which  he  should  have  chosen.  On  the  other  hand,  no  amount 
of  skill  and  experience  will  make  a  man's  unassisted  judgment  as  to  the 
absolute  results  of  a  possible  future  survey  anything  more  than  the  rudest 
of  rude  approximations.     Nevertheless,  the  most  inexperienced  engineer 


8s 8  CHAP.    XXIX  — WHEN   TO  MAKE   SURVEYS. 

knows  that  a  line  in  average  country  cannot  cost  more  than  the  St. 
Gothard  Railway  nor  less  than  the  cheapest  line  he  can  find  record  of 
over  the  Illinois  prairies,  and  that  the  grade  which  he  can  certainly  attain 
lies  somewhere,  say,  between  a  level  and  2  percent.  A  moderate  amount 
of  experience  and  skill  enables  these  limits  to  be  much  contracted,  while 
still  leaving  margin  enough  to  afford  as  nearly  absolute  safety  as  is  pos- 
sible in  human  affairs.  It  is  in  the  rash  and  over-confident  fixing  of  the 
limits  that  the  danger  lies, — and  it  is  a  great  one, — and  not  in  the  delib- 
erate and  conscious  acting  upon  them  after  once  fixing  them  ;  for  it 
must  be  done  consciously  or  unconsciously  in  any  case,  sooner  or  later. 

1178.  Acting  upon  the  rule  given  will  generally  lead  the  quite  inex- 
perienced man,  moreover,  to  survey  two  lines  at  least,  as  it  is  but  right 
that  it  should,  because  his  limits  of  error  are  so  very  wide.  The  unduly 
great  importance  attached  to  the  minor  details  of  alignment,  distance, 
curvature,  and  rise  and  fall  is  responsible  for  much  unnecessary  survey- 
ing. In  these  details  large  differences  very  often  exist,  and  how  large 
they  are  can  only  be  determined  with  any  degree  of  precision  by  actual 
survey.  But  this  is  not  so  of  traffic  advantages,  nor  even  of  grades,  nor 
do  surveys  help  to  develop  the  former. 

1179.  Even  in  the  case  of  lines  through  difficult  country,  passing  over 
one  or  more  high  summits  and  with  no  local  traffic  to  consider,  connect- 
ing terminals  only,  it  will  in  general — although  with  not  infrequent  ex- 
ceptions— be  found  that  thorough  and  faithful  reconnaissance  will  remove 
all  doubt  as  to  which  is  the  proper  route ;  many  details,  of  course,  requir- 
ing extensive  examination.  The  lowest  pass  or  passes  are  so  commonly 
the  only  proper  place  for  the  line,  that  it  may  almost  be  said  to  be  a  law 
of  nature,  and  the  lowest  pass  can  be  determined  with  close  approxima- 
tion by  the  barometer  and  study  of  the  drainage  lines  alone.  The  natural 
advantages  of  routes  by  the  lowest  pass  result,  not  alone  from  its  lowness, 
but  from  the  fact  that  at  such  points  natural  causes  have  produced  more 
manageable  slopes,  a  greater  proportion  of  good  material,  and  a  shorter* 
distance  to  pass  over  before  reaching  the  easier  and  more  practicable 
country,  affording  favorable  grades  and  cheap  construction.  The  lines 
from  Vera  Cruz  to  the  city  of  Mexico,  described  m  Appendix  C,  are  an 
example  on  an  immense  scale  of  the  certainty  with  which  a  single  gen- 
eral route  can  be  picked  out  as  alone  worthy  of  instrumental  examination, 
even  in  regions  of  the  most  extreme  difficulty.  Too  much  is  trusted 
to  surveys,  because  only  the  facts  determined  on  survey  are  taken  mto 
consideration.  As  a  rule,  the  general  route  may  safely  be  selected  in 
advance  by  reconnaissance  merely.     If  the  engineer  be  not  able  to  select 


CHAP,   XXIX.— WHEN   TO  MAKE   SURVEYS. 


859 


Fi 


wisely  without  surveys,  he  will  be  no  better  able  after  the  surveys  are 
completed.     But  to  this  rule  there  are  exceptions. 

1180.  In  such  cases  as  Fig.  278,  where  there  is  a  certain 
natural  line  which  manages  to  miss  three  or  four  consider- 
able towns,  CDEF,  lines  running  to  and  into  those  towns 
should  always  be  run,  as  shown  by  the  dotted  lines,  whether 
■  the  other  line  is  run  or  not.  This  is  a  very  common  case, 
because  towns  are  apt  to  be  in  hollows  or  otherwise  incon- 
venient of  access,  and  a  better  grade,  as  well  as  cheaper 
right  of  way,  can  often  be  had  by  keeping  away  from 
them. 

The  dotted  line  in  Fig.  278  is  a  very  awkward  looking 
line  by  comparison  with  the  solid  one,  but  if  its  comparative 
length  be  carefully  measured,  it  will  be  found  to  differ  but  a 


>C 


-?-. 


•.  "'■'.S' 


•■-.,4 


Fig,  279. 


'R 


— ,e 


Fig.  280. 


trifle  in  length  while  its  operating  advantages  are  materially  greater, 
unless  its  grades  should  be  decidely  against  it. 

1181.  In  such  cases  as  Figs.  279,  280,  the  line  running  through  BC 
should  likewise  be  always  run.  This  is  more  likely  to  be  done  with 
Fig.  279  than  with  Fig.  280.  In  each  the  distances  AB,  BC,  and  CD  are 
precisely  the  same;  but  the  angular  deviation  from  the  desired  direction 
is  greater  in  Fig.  280,  making  it  correspondingly  repellent.  By  varying 
the  intermediate  distances,  leaving  the  aggregate  the  same,  much  greater 
contrasts  can  be  obtained,  as  the  reader  can  find  out  in  a  rather  in- 
structive way  with  a  piece  of  black  thread  and  a  few  pins. 


86o  CHAP.    XXX.— THE  FIELD-WORK  OF  SURVEYS. 


CHAPTER  XXX. 

THE    FIELD-WORK    OF    SURVEYS. 

1182,  In  general,  the  economical  manner  of  making  surveys  of  a  route 
which  it  has  once  been  decided  to  survey,  and  which  offers  any  appreci- 
able'difficulties,  is  as  follows : 

The  surveys  should  be  planned  from  the  beginning  with  the  idea  that 
not  less  than  three,  generally  four,  and  frequently  five,  successive  lines 
will  be  run  over  the  route  for  the  purpose  of  fully  completing  the  final 
location,   viz.:    An    exploration  line,   first    preliminary,    second 

PRELIMINARY,   FIRST    LOCATION,    FINAL    LOCATION.       The  attempt  tO  do 

with  less  than  this  on  lines  of  any  considerable  difficulty  is  false  economy; 
or  rather,  it  is  an  attempt  at  economy  which  does  not  usually  result  in 
any  real  saving  of  either  time  or  money,  even  in  the  mere  direct  cost  of 
the  survey,  while  it  does  seriously  endanger  the  excellence  of  the  com- 
pleted work.  Running  what  may  appear  to  be  so  many  lines  does  not 
necessarily  involve  devoting  much  more  time  to  surveys,  but  only  dis- 
tributing the  work  somewhat  differently. 

1183.  First,  the  exploration  line,  or  what  is  popularly  called  a 
"  shoo-fly"  line,  should  be  run  as  rapidly  as  possible  over  the  entire  route 
which  it  is  contemplated  will  ultimately  constitute  the  road.  In  the 
case  of  very  long  lines,  circumstances  may  make  it  necessary  to  carry  on 
and  complete  the  surveys  by  sections,  but  this  is  to  be  regretted  and 
avoided. 

The  purpose  of  this  first  line  should  be  merely  to  get  a  general  idea 
of  the  topography  of  the  country,  and  especially  of  the  gradients,  and  it 
should  be  passed  over  all  alternate  routes  which  it  is  proposed  to  survey 
later  as  they  are  encountered.  No  attempt  to  study  the  location  in  de- 
tail should  be  made,  except  to  make  sure  that  the  line  being  passed  over 
is  certainly  feasible,  and  probably  on  the  most  favorable  ground  in  the 
vicinity,  especially  in  respect  to  gradients. 

For  this  line  a  mere  compass  line  will  not  only  answer  as  well,  but  is 
in  general  decidedly  preferable  to  a  transit  line,  except  in  easy  open  coun- 


CHAP.    XXX.— THE  FIELD-WORK  OF  SURVEYS.  86 1 

try,  for  reasons  discussed  in  par.  1185.  It  gives  a  mere  string  of  distances 
and  elevations  from  which  to  construct  a  scheme  of  grades  and  lay  out 
the  line  as  a  whole.  The  following  line  is  not  guided  by  it  in  any  ac- 
curate way,  nor  is  even  a  map  of  it  to  a  large  working  grade  generally 
worth  the  making. 

The  limit  of  speed  will  lie  in  the  levelling,  and  accordingly  two  rodmen 
should  be  used  if  there  be  only  one  leveller,  or  better,  two  complete  level 
parties  (especially  if  the  country  is  at  all  rough),  to  be  jumped  over  each 
other's  heads.  This  extra  force  does  not  expedite  the  work  enough  to 
pay  if  the  levelling  only  were  to  be  considered,  but  as  the  time  of  the 
whole  party  is  to  be  considered,  it  does  pay,  and  it  is  to  some  extent  a 
safeguard  against  errors,  as  the  levellers  are  not  so  hurried.  Sometimes 
an  extra  man  to  keep  notes,  with  two  rodmen,  may  be  preferable  to  two 
level  parties. 

A  full-scale  profile  of  the  ordinary  form  mayor  may  not  be  made; 
it  will  probably  be  a  waste  of  time  to  make  it  for  the  entire  distance ; 
but  a  small  scale  profile,  to  about  one  tenth  the  usual  horizontal  scale 
and  one  fifth  the  usual  vertical  scale  (par.  905),  should  by  all  means  in  all 
cases  be  made.  Fig.  281  shows  one  form  of  such  profile  for  a  completed 
road,  to  a  scale  of  about  one  inch  per  mile,  as  engraved,  which  was  origi- 
nally 4000  feet  per  inch,  or  ten  times  the  usual  profile  scale.  It  is  un- 
necessary to  encumber  a  similar  profile  for  location  purposes  with  details 
of  the  minor  structures. 

Following  this  line  comes — 

1184-  Secondly,  THE  PRELIMINARY  LINE  proper  (which  may  be  two 
successive  lines),  which  is  to  serve  as  the  basis  for  the  final  location.  On 
this  line,  in  all  but  very  easy  country,  careful  topography  should  be  taken, 
and  taken  in  the  field,  in  the  manner  considered  in  Chap.  XXXI.  The 
purpose  of  the  preliminary  is  to  serve  as  a  framework  for  this  topog- 
raphy and  the  located  line,  and  it  is  run  to  follow  closely  the  ground 
where  the  location  is  likely  to  lie,  as  nearly  as  the  eye  can  estimate  it, 
using  any  angles  which  come  handy  for  this  purpose.  Fig.  282  shows 
how  a  very  ivell  located  preliminary  is  apt  to  lie  with  relation  to  the  lo- 
cated line,  being  very  close  to  it,  and  yet  entirely  independent  of  it.  The 
average  preliminary  will  diverge  from  the  location  more  than  that  shown. 

This  line  also  may,  without  any  serious  disadvantage,  and  with  cer- 
tain considerable  advantages,  be  a  compass  line,  if  any  time  is  thereby 
saved  to  be  devoted  to  more  important  matters.  The  only  advantage  of 
a  transit  line  (and  it  is  a  slight  one)  is  that  it  enables  the  map  to  be  some- 
what more  accurately  made.     The  located  line  does  not  coincide  with 


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CHAP.  XXX.— TRANSIT  vs.   COMPASS  LINES.  863 

the  preliminary  at  any  point,  unless  by  accident,  nor  is  there  any  inten- 
tion that  it  should,  nor  is  the  location  checked  by  the  preliminary,  to  any 
great  extent,  but  by  the  profile  and  topography. 


Fig.  282. — Preliminary  and  Located  Line. 


TRANSIT   VS.  COMPASS   LINES. 


1185.  An  unreasonable  prejudice  exists  in  the  minds  of  some  engi- 
neers against  compass  lines,  because  of  a  false  assumption  that,  because 
there  is  a  certain  lack  of  precision  in  it,  the  work  is  therefore  inaccurate. 
On  the  contrary,  the  chances  of  substantial  accuracy  in  the  final  result, 
considered  as  a  whole,  are  better  with  the  compass  than  with  a  hasty 
transit  line  (it  being  assumed  that  no  local  attraction  exists),  since  large 
cumulative  errors  cannot  occur  in  the  one  case,  while  they  can  in  the 
other.     This  is  evident  if  we  consider  how  the  two  lines  are  run. 

A  compass  line,  strictly  so  called,  is  run  entirely  by  foresight,  guided 
by  the  needle  alone.  The  chief  of  party  goes  first,  accompanied  by  the 
"  back  flag,"  who  is  now  a  front  flag,  and  picks  out  the  points  to  which 
to  run  (unless  a  straight  line  is  being  run,  where  the  line  is  given  from 
the  instrument  as  soon  as  the  compass  has  come  to  rest).  The  chain- 
men  follow,  the  head  chainman  behind,  chaining  in  a  straight  line  as 
nearly  as  the  eye  can  determine  from  the  point  where  the  instrument  is 
standing  toward  the  flag.  As  the  line  is  sighted  in  by  foresight  this  is 
near  enough  for  all  practical  purposes,  since  more  than  two  or  three 
inches  deviation  is  not  probable. 

The  transitman,  or  rather  compassman,  is  at  the  rear  of  the  whole 
party,  and  simply  takes  the  bearing  of  each  line  by  the  needle,  or,  if  a 
given  line  is  to  be  continued,  gives  the  proper  line  to  the  flagman  in  ad- 
vance as  nearly  as  it  can  be  determined  from  the  needle.  If  a  tree  or 
other  obstruction  is  met,  the  instrument  is  simply  moved  to  the  other 
side  of  it,  placed  on  the  same  line  prolonged  as  nearly  as  may  be  (it  may 
be  a  foot  or  even  two  or  three  feet  off),  and  reset  to  the  same  bearing.  If 
accurately  reset,  it  will  give  a  line,  not  the  same  as  the  original,  but  par- 
allel  thereto.     Usually  there  is  a  few  minutes'  error  in  each  bearing  to 


864  CHAP.  XXX  — TRANSIT  vs.   COMPASS  LINES. 

one  side  or  the  other.  On  the  other  hand,  when  the  line  behind  is 
visible,  it  is  very  common,  even  in  running  compass  lines  to  run  by  back 
sight  for  considerable  distances,  as  on  a  transit  line,  or  at  least  to  check 
the  bearings  thereby.  This  practice  does  not  especially  conduce  to  real 
accuracy,  however,  but  rather  the  contrary. 

1186.  A  transit  line,  on  the  other  hand,  is  run  entirely  by  back  sight, 
from  an  accurate  sight  on  a  plug,  and  all  angles  are  measured  exactl)^  by 
the  vernier.  It  is  very  much  more  precise  than  a  com.pass  line,  and  is 
the  only  suitable  method  for  running  in  location  lines,  and  the  only 
method  now  practised,  although  it  was  not  used  in  the  earlier  days  of 
railways.     It  has  these  disadvantages  : 

1.  It  requires  the  cutting  away  of  all  obstructions,  or  tedious  offsets 
around  them,  thus  causing  great  loss  of  time  and  needless  destruction  of 
vegetation. 

2.  Any  error  in  measuring  or  laying  off  an  angle  is  cumulative,  or 
continued  indefinitely  in  plotting  the  notes.  To  guard  against  this,  the 
angles  in  well-conducted  transit-work  are  always  checked  by  the  needle, 
but  nevertheless  this  danger  causes  frequent  annoyance  in  practice. 

3.  The  angles  measured  are  never  used  as  such  in  properly  conducted 
mapping,  but  have  to  be  reconverted  into  bearings.  This,  however,  is  a 
small  matter,  and  may  and  should  be  avoided  in  the  manner  described  in 
par. 

1187.  On  the  other  hand,  there  is  this  to  be  said  for  the  transit  line — 
that  it  is  not  unfrequently  the  case  that  no  time  is  saved  by  using  the 
compass  instead  of  the  transit,  since  the  level  limits  the  rate  of  progress 
in  any  case.  When  this  is  so,  it  is  undoubtedly  as  well  to  run  the  more 
accurate  line,  and  wherever  there  is  danger  of  local  attraction  it  is  the 
only  proper  one  to  run.  But  it  should  be  clearly  recognized  that  the 
transit  line  is  to  be  preferred  only  for  these  reasons,  and  that  wherever 
they  do  not  obtain,  the  true  engineer  will  immediately  adopt  the  compass 
instead.  The  not  infrequent  notion  that  the  use  of  the  compass  is  de- 
rogatory to  his  skill  and  unworthy  of  him,  simply  because  it  is  less  pre- 
cise, is  absurd.  Under  the  doctrine  of  chances,  which  is  as  well  estab- 
lished as  the  law  of  gravitation,  the  probable  average  error  in  a  series 
of  observations  decreases  as  the  square  root  of  their  number.  If  in  a 
single  observation  it  be  10  ft.,  in  100  observations  it  will  be  only  i  ft. 
each,  and  in  10,000  observations  only  o.i  ft.  For  all  the  legimate  uses 
of  preliminary  lines  (they  are  sometimes  used  illegitimately)  such  errors 
in  no  way  detract  from  its  value  and  utility. 


CHAP.  XXX.— TRANSIT  vs.   COMPASS  LINES.  865 

1188.  The  writer  has  not  found  that,  even  when  the  imperfections  of 
mapping  are  reduced  as  they  should  be  by  the  use  of  large  scales,  the 
superior  precision  of  the  transit  is  of  much  practical  moment,  and  he 
feels  a  preference  for  the  use  of  the  compass  on  preliminaries,  other 
things  being  equal,  believing  that  it  is  easier  for  all  concerned,  and  that 
there  is  less  danger  of  giving  thought  to  splitting  tacks  with  the  cross- 
hairs which  might  better  be  given  matters  of  importance.  It  is  well  for 
the  locating  engineer  to  be  frequently  reminded,  especially  in  acquiring 
his  training,  that  instrumental  accuracy  is  not  an  end  in  location,  as  in 
ordinary  surveying,  but  simply  a  means  to  an  end;  that  a  thoroughly 
excellent  location  may  be  made  with  the  level  and  chain  alone  with- 
out other  instruments,  and  that  a  bad  line  is  not  a  whit  better  for  beins; 
instrumentallj'-  precise.  No  angular  or  lineal  error  which  is  not  great 
enough  to  affect  the  riding  of  the  locomotive  over  the  track  is  of  ulti- 
mate importance,  while  on  the  other  hand  errors  of  judgment,  or  unwill- 
ingness to  disturb  an  accurately  run  line  with  a  "  good  "  profile,  are  evils 
of  great  importance.  As  it  always  easier  and  in  the  end  less  costly 
to  be  accurate  than  inaccurate,  the  good  engineer  always  will  be  accu- 
rate in  all  essentials,  but  he  will  not  waste  time  in  attempting  unneces- 
sary precision  which  does  not  add  appreciably  to  the  final  value  of  his 
work. 

1189.  The  levels  should,  on  the  preliminary  lines,  be  kept  correct  by 
checking  on  the  exploration-line  benches  and  re-running  all  doubtful 
sections,  at  any  seeming  cost  to  the  progress  of  the  survey.  No  time  is 
saved  in  the  end  by  doing  otherwise.  No  time  should  be  wasted  in  try- 
ing to  keep  the  stationing  continuous. 

1190.  Whenever  the  country  becomes  quite  rough,  and  especially 
where  a  grade-line  is  to  be  fitted  to  the  ground,  the  preliminary  line 
should  from  the  beginning  be  divided  up  into  two  by  running  a  first  and 
second  preliminary.  It  might  seem  a  better  way  of  expressing  the  same 
truth  to  say  that  whenever  it  is  found  that  any  section  of  the  preliminary 
does  not  come  sufficiently  near  to  where  the  final  line  will  be,  it  should 
be  run  over ;  but  that  is  not  true,  and  that  plan  of  conducting  sur\^eys  is 
more  likely  to  result  in  loss  of  time  and  bad  work.  The  true  way  of 
conducting  surveys,  from  beginning  to  end,  is  to  recognize  in  the  begin- 
ning where  there  is  likely  to  be  difficulty  and  to  run  additional  preliminary 
lines  COMPLETE  over  those  sections,  thus  gaining  opportunity  for  more 
careful  study  and  more  thorough  knowledge.  Even  then,  there  will  be 
occasions  enough  when  it  will  be  necessary  to  "back  up"  and  correct 
false  steps  from  time  to  time  on  all  the  lines,  to  doing  which  occasionally, 

55 


S66  CHAP.  XXX.— TRANSIT  vs.   COMPASS  LINES. 

of  course,  it  is  not  intended  to  object ;  but  in  cases  where  there  seems 
more  than  an  even  chance  that  the  "backing  up"  will  be  a  large  fraction 
of  the  advance,  it  is  always  good  practice  to  give  up  from  the  first  all 
idea  of  completing  the  preliminary  work  with  one  line. 

1191.  When  two  preliminaries  are  thus  run  in  succession,  they  should 
in  general  be  frequently  tied  together  and  plotted  on  the  same  sheets  so 
as  to  give  continuous  topography,  all  errors  in  the  plotting  (which  with 
good  work  should  be  small)  being  left  in  the  tie-lines,  and  the  angles, 
and  distances  of  the  second  preliminary  not  distorted  to  make  a  fit. 

1192.  In  extreme  cases,  as  in  that  shown  in  Fig.  216  and  others,  the 
difficulties  of  location  are  so  great,  for  short  distances,  that  all  idea  of 
determining  the  final  location  from  lines  must  be  abandoned,  and  a  com- 
plete topographical  study  of  the  difficult  section  made,  after  the  fashion  of 
what  was  formerly  customary  on  surveys  for  English  railways.  But  such 
cases  are  very  rare,  and,  in  general,  working  from  single  lines  is  all- 
sufficient. 

1193.  Thirdly.  The  location  line. — This  line  also  should  in  general 
be  divided  into  two  and  done  twice  over,  complete. 

It  will  save  time  often  and  money  always,  and  is  the  only  safe  way  to 
insure  good  work,  especially  where  it  is  necessary  to  entrust  a  part  of  the 
work  to  men  of  little  experience.  The  first  location  should  be  made  ap- 
proximately correct  as  it  goes  along,  by  backing  up  to  correct  the  more 
serious  and  evident  defects,  but  it  is  far  better  that  all  minor  changes 
and  modifications  should  be  merely  studied  and  thought  over  as  the  first 
location  advances,  and  that,  after  completing  the  first  line  and  taking 
adequate  cross-sections  of  it  or  of  a  considerable  part  of  it,  the  party 
should  be  recalled  to  run  the  whole  of  it  over  again,  aided  by  its  plotted 
cross-sections. 

1194.  This  results  not  only  from  the  direct  advantage  of  having  the 
details  of  the  whole  line  at  once  to  study,  but  from  the  fact  that  the 
problem  is  studied  more  coolly  and  dispassionately,  with  the  aid  of  more 
extended  knowledge  and  experience  (the  whole  party  being  now  skilled 
in  their  work),  and  without  that  strong  inducement  to  tolerate  bad  work 
and  "  let  well  enough  alone"  which  is  derived  from  the  tedious  and  fret- 
ting process  of  "  backing  up."  A  little  consideration  of  the  weaknesses 
of  human  nature  will  make  it  clear  why,  for  many  reasons,  this  should  be 
so  ;  and  the  writer  cannot  urge  too  strongly  that  really  good  work  can- 
not be  otherwise  secured,  under  the  conditions  which  usually  prevail. 
Unnecessarily  sharp  and  frequent  curvature  will  be  left  in  the  line ;  side- 
hill  work  on  steep  slopes  will  have  its  centre  line  a  foot  or  two  out  of  its 


CHAP.  XXX.— RUNNING  IN    THE  LOCATION.  86/ 

proper  place,  and  be  unnecessarily  heavy ;  rock  cuts  will  be  run  into  to 
save  fills,  and  many  similar  imperfections  be  left  in  the  line,  which  are 
not,  indeed,  of  great  comparative  moment  to  the  line  itself,  since  they  do 
not  injure  its  earning  capacity,  but  which  are  often  of  serious  moment  to 
the  temporary  owners  of  the  line,  by  increasing  its  first  cost  beyond  the 
limits  of  their  means,  so  that  it  finally  passes  out  of  their  hands. 


ORGANIZATION    OF   PARTY. 

1195.  A  locating  party  should  be  full-handed,  especially  in  the  lower 
ranks.  To  do  otherwise  is  false  economy.  The  organization  should  in 
general  be  as  follows  : 

1.  Chief  of  party,  with  nothing  to  do  except  to  keep  his  eyes  open. 
Even  in  the  easiest  country  it  is  mistaken  economy  to  attempt  to  have 
him  run  the  transit,  and  it  is  now  rarely  attempted. 

2.  The  transit  party,  consisting  of  transitman,  head  and  rear  chain- 
man,  back-flag,  stakeman,  and,  in  wooded  country,  a  superabundance  of 
axemen.  From  four  to  eight  can  be  advantageously  used  where  there  is 
much  wood.  At  least  one  besides  the  stakeman  is  generally  economy, 
even  where  there  is  no  clearing. 

3.  The  level  party,  consisting  of  leveller,  rodman,  and,  in  wooded 
country,  one  axeman  and  peg-maker.  In  open  country  this  axeman  is 
unnecessary ;  but,  on  the  other  hand,  in  such  country,  since  the  level 
limits  the  speed  of  the  whole  survey,  two  rodmen  can  generally  be  em- 
ployed to  advantage,  since  they  expedite  the  work  somewhat. 

4.  The  topographical  party,  varying  from  one  to  three  or  four  men, 
according  to  the  country.  This  party  is  usually  not  full  enough  for  true 
economy. 

5.  The  trajtsportation  and  camp  outfit,  in  a  full  party  usually  consist- 
ing of  a  cook,  and  one  or  more  teamsters,  with  a  commissary,  who  looks 
after  all  camp  movements  and  expenses. 

Thus  a  fully-organized  locating  party  in  difficult  country  will  often 
consist  of  as  many  as  20  or  24  men ;  but,  on  the  other  hand,  in  thickly- 
settled  regions  and  easy  country  often  not  more  than  8  or  10  are  neces- 
sary. 

RUNNING   IN   THE   LOCATION. 

1196.  In  smooth  and  nearly  level  regions  the  notes  for  the  location 
line  may  be  made  up  from  the  notes  of  the  preliminary  surveys,  almost 
without  mapping  them  at  all,  and  certainly  with  very  little  topography. 


868  CHAP.  XXX.— RUNNING  IN   THE  LOCATION. 

Ordinarily,  however,  a  narrow  belt  of  topography  is  both  expedient  and 
necessary.  If  the  preliminary  work  has  been  skilfully  conducted,  it  will 
need  to  be  but  narrow.  On  this  topography  a  "  paper  location"  is 
made,  in  the  manner  we  shall  consider  later;  full  notes  of  the  projected 
alignment,  and  of  the  points  of  curve  and  tangency  taken  off,  and  a  pro- 
file of  the  paper  location  made. 

The  purpose  of  the  location  field-work  \^,  first,  to  put  this  paper  loca- 
tion on  the  ground  so  as  to  afford  at  least  as  good  a  profile  as  the 
"  paper"  profile,  and,  secondly,  to  study  the  line  thus  put  upon  the  ground 
in  more  detail  than  was  possible  before  the  precise  position  of  the  line 
had  been  so  accurately  fixed. 

In  running  in  the  notes  of  such  a  paper  location,  the  most  experienced 
chief  of  party  never  expects  that  the  notes  can  be  followed  in  the  field 
without  some  slight  correction  at  almost  every  curve.  The  profile  will 
be  found  to  be  running  too  high  or  too  low ;  errors  in  the  field-work  and 
the  topography  will  be  discovered  ;  new  changes  of  alignment  will  sug- 
gest themselves,  and  in  other  ways  changes  will  be  made.  Nevertheless,. 
the  correspondence  in  general  will  be  very  close  ;  so  much  so  that  it  will, 
be  difficult  to  distinguish  the  paper  and  actual  location  profile.  They 
may  both  be  wrong  and  bad,  but  they  are  apt  to  agree  with  each  other 
quite  closely. 

1197.  No  new  topography  should  be  taken  with  this  line,  but  instead 
of  it  cross-sections  only,  extending  from  30  to  100  feet  on  each  side, 
according  to  locality.  These  cross-sections  should  be  plotted  as  closely 
together  as  clearness  permits,  with  the  even  stations  at  uniform 
DISTANCES  apart,  even  at  the  expense  of  crowding  the  sections  so  that 
they  overlap  each  other  greatly,  which  does  no  particular  harm.  The 
character  of  the  material,  and  especially  the  precise  limits  of  the  rock,, 
should  be  carefully  determined.  Boring  tools  of  many  different  forms 
(the  simplest  of  which  is  the  common  post-augur)  are  readily  obtained, 
by  which  it  may  be  positively  determined  where  the  rock  lies,  at  no  great 
cost,  and  much  perhaps  needless  expense  saved.  It  is  a  very  common 
thing  to  have  shallow  rock-cuts  turn  up  in  the  bottom  of  excavations, 
which  are  always  disproportionately  expensive,  and  often  might  as  well 
as  not  have  been  avoided  altogether. 

Aided  by  these  cross-sections,  the  location  should  be  carefully  re- 
studied,  not  by  the  construction  parties,  who  have  other  things  to  think 
of  and  are  often  incompetent  for  the  work,  but  by  a  location  party  who 
re-run  the  entire  line  complete.  There  will  still  be  chances  enough  for 
the  construction  engineer  to  improve  on  it.  • 


CHAP.  XXX.— RUNNING  IN   THE  LOCATION. 


869 


1198.  This  last  work  especially,  and  in  fact  all  running  of  curves  and 
tangents,  is  greatly  facilitated  by  the  use  of  a  proper  system  of  transition 
curves.  What  transition  curves  are,  and  why  they  can  never  be  omitted 
if  an  easy-riding  road  is  to  be  obtained,  have  been  already  stated  (pars. 
279-81),  and  the  proper  method  of  running  them  in  is  given  in  the  field- 
book  which  follows  this  volume.  It  would  lead  us  too  far  to  attempt  it 
in  this.  The  nature  of  the  advantage  which  they  give  in  making  a  good 
location  is  this  : 

All  transition  curves,  by  whatever  method  they  are  run,  must,  from 
their  very  nature,  have  the  form  shown  in  Fig.  283.     The  actual  tangent 

must  lie  parallel  with 
and  outside  of  (at  a 
given  offset  from)  what 
would  be  the  tangent  if 
the  main  curve  were 
prolonged  to  include 
the  whole  angle  turned. 
In  all  the  systems  of 
transition  curves  which 
have  been  put  before  the 
public  by  others  than 
the  writer,  so  far  as  he 
knows,  these  offsets  are 

Fig.  283.-TYPICAL  Transition  Curve.  fixed,  which  makes  run- 

ning them  in  a  considerable  addition  to  the  field-work,  but  even  then 
they  are  likely  to  have  a  certain  beneficial  effect  on  the  construction,  for 
the  reason  that  the  curves  of  natural  slopes  generally  ease  themselves  off 
in  this  manner. 

1199.  But  in  any  entirely  satisfactory  system  of  transition  curves  any 
offset,  great  or  small,  within  wide  limits,  should  be  capable  of  use  with 
any  curve,  because  it  will  very  materially  add  to  the  flexibility  of  the  line 
and  facilitate  its  adaptation  to  the  topography.  If  we  consider  the  tran- 
sition curve  as  a  cubic  parabola,  the  only  difference  which  the  offset 
makes  in  the  curve  is  to  increase  its  length  in  proportion  to  the  square 
ROOT  of  the  offset,  so  that  if  the  latter  be  four  times  as  great  the  curve 
will  be  twice  as  long.  In  any  case,  the  curve  remains  a  cubic  parabola, 
and  is  readily  put  in,  either  directly  with  the  transit,  as  the  line  reaches 
it,  by  methods  similar  in  their  nature  to,  and  quite  as  simple  and  easily 
remembered  as,  those  for  running  circular  arcs,  or  by  offsets,  after  run- 


870 


CHAP.  XXX.— RUNNING  IN    THE   LOCATION. 


Fig.  284. 


ning  in  the  full  circular  arc  from  an  offsetted  tangent,  as  indicated  in 
Fig.  283. 

The  former  of  these  methods  is  generally  preferable  for  large  offsets, 
and  the  latter  for  small.  The  immense  advantage  which  the  method 
gives  for  making  the  finer  adjust- 
ments of  the  line  may  be  made 
evident  by  one  or  two  illustrations, 
but  it  should  be  remembered  that 
the  chief  object  of  the  curves  is 
not  to  facilitate  location,  but  to 
obtain  a  line  which  trains  will  run 
over  smoothly. 

1200.  Example  i.  It  is  found 
to  be  desirable  to  swing  a  located 
tangent.  Fig.  284,  in  2  ft.  at  a  and 
out  3  ft.  at  b. 

The  angle  between  the  old  and 
new  tangent  can  be  at  once  calculated.  Then  the  two  adjacent  curves 
must  be  extended  (in  'Fig.  284 — or  cut  off,  had  the  change  of  tangent 
been  in  the  other  direction)  by  the  same  angle.  This  can  be  done  at 
once;  the  offset  determined  by  measure,  whatever  it  may  be,  and  the 
corresponding  transition  curve  put  in  by  offsets  from  the  curve  and  the 
new  tangent ;  or  the  tangent  points  t  and  t  of  the  new  curve  may  be 
determined  and  the  transition  curve  run  in  by  the  transit. 

1201.  Example  2.  It  is  desired  to  take  out  a  "broken-back"  curve. 
Fig.  285.  Governing  points  which  it  seems  desirable  the  curve  should 
pass  through  are  a  and  b,  at  any  off-  ^^ 

set  from  any  point  on  the  tangent. 

The  angle  between  the  new  and 
old  tangent  can  be  calculated  as  be- 
fore ;  the  curves  extended  or  retraced 
by  an  equal  angle,  the  actual  offsets 
measured,  and  the  proper  transition 
curves  put  in.  If  the  change  has  been 
well  planned  and  the  conditions  are 
at  all  favorable,  the  two  curves  will  come  very  near  to  meeting  at  some 
point  near  the  middle  of  the  tangent. 

If  it  leaves  a  little  tangent  between  the  two  curves  it  will  not 
greatly  matter.     The  two   desired  ends  will  have  been   accomplished. 


^ 


Fig.  a85. 


CHAP.  XXX.— RUNNING  IN   THE  LOCATION. 


871 


The  two  shocks  to  the  train  in  entering  and  leaving  the  tangent 
will  have  been  avoided. 

2.  The  ugly  appearance  of  a  broken-back 
curve,  which,  owing  to  the  abrupt  transition 
from  curve  to  tangent,  always  has  the  appear- 
ance of  being  out  of  line  and  somewhat  re- 
versed, will  have  been  corrected. 

If  the  two  transition  curves  of  the  required 
lengths  for  the  offset  chance  to  overlap  each 
other  even  by  a  considerable  distance  it  will 
not  much  matter.  It  simply  introduces  (for 
reasons  which  cannot  be  given  here  without 
discussing  the  whole  theory  of  the  curve)  a 
short  CIRCULAR  ARC  of  very  long  radius  be- 
tween the  two  transition  curves. 


Fig.  286. 

Example  3.  A  curve  is  found  not  to  lie  on  precisely  the  right 
It  is  desired  to  throw  it  out  two  feet  at  a,  and  in  3  feet  at  b, 


1202, 

ground. 
Fig.  286. 

This  implies  that  there  will  be  a  certain  point  c,  at  which  the  new  and 
old  curves  will  coincide.  The  whole  curve,  radii,  centres  and  all,  will  be 
practically  rotated  around  c.  The  distances  ca  and  cb  can  be  deter- 
mined by  the  proportion 

ca  '.  cb  \\  offset  a  :  offset  b. 


The  angle  of  rotation  is  readily  calculated  by  computing  the  change 
in  position  of  the  chord  ab,  and  from  these  notes  we  may  either  start  at 
c,  and  run  in  the  new  curve,  or  start  at  a  or  b,  or  compute  the  new  posi- 
tions of  the  original  P.  C.  and  F.  T. 

If  the  new  curve  is  found  to  crowd  too  closely  upon  or  to  overlap  the 
tangents  we  must  change  the  latter  also.  This  we  do,  however,  entirely 
independent  of  the  curve,  if  it  appears  desirable  to  do  so  ;  putting  the 
tangent  upon  the  ground  which  will  suit  it  best,  measuring  the  actual 
offset  which  the  locations  chosen  give,  and  then  putting  in  the  corre- 
sponding transition  curves. 

1203.  These  examples  will  illustrate,  as  well  as  more,  the  peculiar  ad- 
vantage of  transition  curves,  thus  used  ;  that  they  enable  each  part  of  the 
line  to  be  studied  and  modified  in  detail,  independently  of  the  rest ;  and 
the  new  and  old  lindfe  to  be  then  connected  together  in  what  is  at  once 
the  very  best  possible  and  the  simplest  possible  way,  without  any  of 
the  puzzling  geometrical  problems  and  the  confusing  field-work  which 


%T2  CHAP.  XXX.— RUNNING  IN    THE  LOCATION. 

are  as  apt  to  result  from  slight  changes  as  great,  if  certain  geometrically 
exact  connections  at  all  points  of  circular  arcs  are  taken  as  essential. 

Differences  of  offsets  of  20  ft.  or  more  are  readily  admissible  under 
this  plan,  and  in  projecting  location  it  is  unnecessary  to  consider  what 
the  actual  offsets  will  be.  Figs.  208,  216,  and  others  illustrate  how  this 
is  done.  The  advantages  of  the  method  in  such  rough  localities  are  evi- 
dent from  those  engravings,  and  these  advantages  become  even  greater 
if  one  knows  how  to  save    unnecessary 

trouble   in   field-work,   which   will  not    -f 

tell  beneficially  in  the  final  result.  •&V'l<'~'"'~f  7"~*       ~~ 

1204.  As  a    single  example,    if  one  y'^ 
has    a   curve    formerly  terminating    at       /'       \^' 
T,   Fig.    287,  which  is  to  be  extended  \ 
to  Z'  in  order  to  connect  with  the  tan-  N 
gent  00  ;— to  determine  the  offset  O  it 
is  quite  unnecessary  to  run  in  T'  with  Fig.  287. 

a  transit.  The  offset  Oo  to  the  old  point  T  may  be  measured  instead. 
Then  will 

0=Oo  —  o,        and  [^^o  --^  ^n'D, 

in  which  D  =  the  degree  of  the  curve,  n  =  the  distance  in  stations  from 
the  tangent  point  T'  to  the  point  where  the  offset  to  the  curve  is  de- 
sired, and  O  =  the  desired  offset. 

1205.  This  latter  formula  is  one  of  the  most  useful  of  all  location 
formulae,  being  almost  indispensable  for  the  correct  and  expeditious 
conduct  of  field-work.  It  is  closely  approximate  (in  all  cases  sufficiently 
so  for  what  is  required)  within  the  widest  possible  range  of  values  of  D 
and  n,  and  it  is  one  of  the  few  formulae  which  should  be  indelibly  en- 
graven in  the  memory  of  every  locating  engineer,  ready  for  instant  use. 
It  applies  equally  well  for  offsets  from  one  curve  to  another  having  a 
common  tangent  point,  letting  D  =  the  difference  in  the  degree  of  cur- 
vature. 


CHAP.  XXXL— TOPOGRAPHY :  ITS  USES  AND  ABUSE,     873 


CHAPTER  XXXI. 

topography:  its  uses  and  abuse. 

1206.  Topography,  in  the  limited  technical  sense  of  the  word  which 
is  given  to  it  in  railway  location,  is  the  representation  upon  a  map  by 
*'  contour  lines"  of  the  comparative  or  absolute  elevations  on  the  area 
covered  by  the  map.  In  a  broader  and  more  literally  correct  sense,  it  in- 
cludes the  representation  of  all  the  details  of  the  surface  by  any  method 
whatever,  including  its  form,  character,  and  artificial  structures. 

Topography,  in  the  broader  sense,  may  be  represented  approximately 
either  by  hatchings  or  "hachures,"  or  by  washes  of  color.  Very  beauti- 
ful effects  may  be  produced  in  this  way  by  skilled  and  patient  work,  but 
the  results  are  only  of  pictorial  value,  to  give  a  general  idea  of  the 
region,  and  are  of  no  assistance  for  the  details  of  location.  Topography, 
when  spoken  of  in  connection  with  the  latter,  means  an  exact  repre- 
sentation of  the  form  of  the  surface,  so  that  the  elevation  of  any  point 
can  be  determined  from  the  map,  and  hence  a  line  be  drawn  on  the  map 
and  a  profile  of  it  called  off,  as  well  (barring  a  margin  of  error)  as  if  the 
line  had  been  run  in,  and  levels  run  over  it,  in  the  field.  Figs.  208,  216, 
and  others  are  representations  from  actual  practice  of  such  maps,  re- 
duced photographically  from  the  working  scales. 

1207.  The  nature  of  contour  lines  may  be  thus  explained  :  Conceive 
a  certain  area,  the  topography  of  which  is  to  be  taken,  to  be  entirely 
flooded  with  water.  Conceive  the  level  of  the  surface  of  this  water  to 
be  lowered  by  a  certain  fixed  distance,  say  ten  feet  at  a  time.  At  each 
lowering  of  the  water  a  new  shore-line  would  be  developed  :  The  con- 
tour lines  are  these  imaginary  shore-lines.  If  the  slopes  be  very  steep 
these  successive  shore-lines  will  be  at  small  distances  from  each  other 
horizontally.  If  the  slopes  be  flat  they  will  be  at  greater  horizontal  dis- 
tances, and  if  the  slopes  are  very  flat  they  will  be  at  very  great  distances 
apart,  and  only  a  few  will  appear  on  a  moderate  area.  Thus  the  lower 
part  of  Fig.  288  shows  a  contour  map  of  a  slightly  oblique  cone,  and  the 
lower  part  of  Fig.  289  a  similar  contour  map  of  a  hemisphere.  In  each 
case,  if  the  nature  of  contour  lines  has  been  grasped,  they  enable  the 
mind  to  form  a  very  correct  picture  of  the  form  of  the  surface. 


874     CHAP.  XXXI.— TOPOGRAPHY :   ITS  USES  AND  ABUSE. 

1208.  It  will  be  obvious  that  working  with  such  topographical  maps 
has  both  advantages  and  disadvantages.     The  advantages  are  : 

I.  The  eye  is  able  to  take  in  a  large  surface  at  once,  with  exact  in- 
formation as  to  the  form  of  every  part  of  it,  and  without  those  confusing 
optical  illusions  which  result  from  looking  at  a  natural  surface  horizon- 
tally instead  of  from  above,  and  in  successive  bits  instead  of  all  at  once. 


Fig.  288. 


Fig.  289. 


2.  Various  projects  can  be  studied  with  great  ease,  and  the  effect  of 
different  changes  considered  at  once.  A  curve  can  be  struck  in  with  a 
compass  in  a  moment,  and  three  or  four  different  ones  in  as  many  differ- 
ent positions  almost  as  quickly,  each  one  of  which  would  take  perhaps  a 
day's  hard  work  to  run  in  on  the  ground,  with  the  chance  after  they 
were  run  that  they  would  lie  considerably  out  of  the  position  intended. 

3.  By  dotting  on  the  grade-contour  (pars.  1246-8)  or  line  where  the 
plane  of  the  road-bed  cuts  the  natural  surface,  it  can  be  seen  almost  at 
once  whether  the  alignment  is  as  favorable  as  the  topography  permits, 
or  not. 

1209.  Each  one  of  these  advantages  is  a  great  one.  On  the  other 
hand  the  disadvantages  of  working  from  contours  are  : 

1.  The  making  of  good  contour  maps  is  expensive — which  is  a  very 
weak  objection,  even  if  their  cost  were  much  greater  than  it  is. 

2.  It  is  difficult  to  insure  accuracy. 


CHAP.  XXXI.— TOPOGRAPHY :  ITS  USES  AND  ABUSE.     875 

3.  They  afford  no  evidence  of  material. 

4.  They  do  not  impress  upon  the  mind  the  magnitude  of  the  works 
projected,  as  it  does  to  study  the  actual  surface. 

5.  They  are  of  assistance  only  for  doing  the  least  important  part  of 
the  work,  making  the  first  approximation  to  the  detailed  location  of  the 
line. 

These  and  other  difficulties  which  we  shall  shortly  consider  are  like- 
wise great  and  valid  ones.  They  indicate  what  is  the  fact,  that  topog- 
raphy has  both  its  uses  and  abuses,  and  which  predominates  is  often 
the  subject  of  heated  discussion. 

1210.  In  such  discussions  one  is  reminded  of  the  old  fable  of  the  two 
knights  who  fell  to  fighting  over  the  shield  which  seemed  gold  or  silver 
according  to  the  "  point  of  view  ;"  for  the  disputed  question  is  emphati- 
cally one  of  the  same  kind.  It  is  only  by  losing  sight  of  one  side  or  the 
other  that  one  becomes  a  strong  partisan  of  either  view. 

The  difference  between  the  two  views,  in  fact,  is  more  imaginary  than 
real.  On  the  one  hand,  there  are  no  engineers  of  any  standing  or  ex- 
perience who  believe  that  location  offering  any  difficulties  can  be  made 
to  advantage  in  any  other  way  than  from  topographical  notes  embodied 
in  a  more  or  less  elaborate  topographical  map ;  while,  on  the  other  hand, 
there  are  no  engineers  of  experience  who  would  think  of  claiming  that 
more  topography  than  is  really  necessary  for  intelligently  completing  the 
location,  and  making  sure  that  it  is  correct,  should  be  taken. 

The  true  question  to  be  decided,  therefore,  is  simply  how  much 
topography  should  be  taken,  and  where  the  line  should  be  drawn.  There 
is  no  such  difference  of  opinion  as  would  appear  from  an  error  into  which 
many  have  fallen — an  error  which  well  shows  how  completely  the  views 
of  those  who  take  one  side  of  this  question  are  misapprehended  by  those 
who  think  they  disagree  with  them  ; — that  is  to  say,  there  is  no  class  of 
engineers  who  attempt  to  make  a  final  location  assisted  by  the  natural 
eyesight  alone,  or  in  any  other  way  than  by  working  from  a  preliminary 
line  as  a  basis,  which  is  intended  to  lie,  and  if  skilfully  run  does  lie,  very 
close  to  the  line  on  which  the  final  location  is  placed,  as  in  Fig.  282. 

1211.  To  mark  the  limits  of  the  debatable  ground  still  more  closely, 
it  cannot  be  reasonably  questioned  (i)  that  in  proportion  to  the  skill  of 
the  engineer  the  preliminary  line  (often  at  difficult  points,  necessarily,  the 
result  of  two  or  three  trials)  will  approximate  more  and  more  closely  to 
where  the  final  location  will  ultimately  lie ;  (2)  that  it  should,  and  in 
general  will,  lie  nearer  than  300  or  400  feet  as  an  outside  limit ;  (3)  that 
the  placing  of  this  preliminary  line  upon  the  ground  is  and  must  be 


Sy6     CHAP.  XXXI —  TOPOGRAPHY :   ITS  USES  AND  ABUSE. 

purely  a  matter  of  individual  "  eye  for  country"  and  good  judgment;  and 
(4)  that  the  really  vital  and  dangerous  errors  of  location,  the  selection  of 
the  general  route,  the  system  of  gradients,  the  going  to  or  passing  by  the 
local  towns,  etc.,  etc.,  are  committed,  if  committed  at  all,  before  any  to- 
pography whatever  has  been  taken,  in  locating  this  preliminary  line ;  the 
usefulness  of  the  topography  beginning  only  after  the  more  momentous 
question  of  where  to  put  the  preliminary  has  been  decided,  and 
serving  only  for  the  more  ready  and  perfect  adjustment  of  details — de- 
tails which  have  an  important  effect  upon  the  cost  of  construction,  in- 
deed, but  do  not  otherwise  seriously  modify  the  earning  capacity  of  the 
line. 

1212.  The  remaining  ground  for  difference  between  extreme  advo- 
cates of  either  view  is  this  :  The  extreme  believer  in  topography  is  indif- 
ferent to  getting  his  preliminary  very  near  to  its  ultimate  location,  look- 
ing upon  400  or  500  feet  average  distance  apart  as  near  enough,  and 
takes  or  causes  to  be  taken  a  wide  belt  of  accurate  topography  to  save 
the  need  of  a  new  or  a  better  preliminary.  But  the  advocates  of  the  other 
view  say,  "No;  the  engineer  who  can  be  trusted  to  put  a  preliminary 
line  within  even  500  feet  of  the  true  location  can  and  ought  to,  in  gen- 
eral, put  it  much  nearer ;  or  if  not,  it  is  cheaper  to  put  a  new  line  through 
still  closer  to  the  ultimate  location  than  to  take  so  wide  a  belt  of  topog- 
raphy. By  one  method  or  the  other,  the  good  engineer  can  and  will 
bring  the  line  so  near  to  where  his  location  should  lie,  that  the  topog- 
raphy which  he  will  really  need  will  be  only  a  very  narrow  belt — usually 
no  more  than  a  few  series  of  cross-sections,  and  hardly  amounting  to  a 
topographical  map  at  all." 

1213.  The  truth  lies  between  these  two  limits.  Since  the  amount  of 
topography  ultimately  needed  and  used  (when  its  use  is  not  abused  by 
making  it  serve  as  a  substitute  for  the  careful  placing  of  the  preliminary) 
can  be  seen  on  any  location  map  to  be  very  little,  covering  a  map  all 
over  with  accurate  topography  is  a  sign  of  weakness  and  not  of  strength. 
On  the  other  hand,  accurate  topographical  contour  lines  for  a  reasona- 
ble and  moderate  distance  on  each  side  of  the  line  are  an  immense  as- 
sistance for  the  ready  projection  of  lines,  and  at  points  can  hardly  be 
dispensed  with.  It  is  also  an  important  truth  that  the  usefulness  of 
topography  is  not  confined  simply  to  that  portion  of  it  which  is  used  to 
project  the  line  adopted,  but  extends  also  to  the  portion  which  enables 
one  to  make  sure  that  no  other  and  better  alignment  might  have  been 
adopted.  However  confident  an  engineer  may  feel  that  he  has  in  fact 
studied  his  work  to  the  best  of  his  ability,  he  owes  it  to  himself  and  to 


CHAP.    XXXI.  — TOPOGRAPHY :   ITS  USES  AND  ABUSE.    8// 

his  employers  to  have  the  ocular  evidence  of  that  fact  before  him,  to  be 
placed  before  others  if  need  be;  and  it  is  but  reasonable  that  no  study  of 
the  ground  alone,  unassisted  by  accurate  maps,  can  be  as  complete  as 
one  which  has  been  so  assisted.  Yet,  on  the  other  hand,  it  is  even  more 
emphatically  true  that  no  study  of  maps  alone,  unassisted  by  study  of  the 
ground  in  detail,  both  before  and  after  the  making  of  the  maps,  can  be 
as  complete  as  it  should  be. 

1214.  No  skilled  engineer,  even  among  those  who  are  strong  believers 
in  the  proper  use  of  contour  maps  will  approve  of  such  elaborate  reli- 
ance upon  maps  alone,  as  is  sometimes  taught  and  advocated  ;  such  as 
taking  the  nicest  precautions  for  computing  notes  for  8  or  lo  miles  of 
location  at  once,  so  that  it  shall  fit  geometrically  onto  the  preliminary, 
and  so  dispense  with  renewed  and  more  detailed  study  of  the  ground. 
Not  but  that  the  field-work  and  mapping  might  be  dofie  so  accurately 
that  this  would  be  all  that  would  be  necessary,  and  not  but  that  much  of 
a  location  so  made  may  prove  on  examination  to  be  beyond  improve- 
ment, at  least  by  the  same  engineer  ;  but  that  for  practical  reasons  it  is 
inexpedient  to  rely  so  largely  upon  paper  location.  Among  these  rea- 
sons are — 

1215.  I.  As  above  suggested,  the  length  and  depth  of  cuttings,  and 
especially  the  classification,  do  not  impress  themselves  upon  the  mind  so 
forcibly  in  studing  a  topographical  map  as  in  studying  the  ground,  and 
hence  as  great  efforts  will  not  be  made,  practically,  to  avoid  this  danger 
when  the  principal  study  of  the  details  of  the  line  is  made  upon  the  maps 
as  when  the  paper  location  is  looked  upon  as  at  best  nothing  more  than 
a  close  approximation,  and  the  last  study  of  the  ground  is  made  with 
the  rock-cut  staring  one  in  the  face,  or  on  large  scale  cross-sections. 

1216.  2.  A  very  dangerous  error,  which  the  best  engineers  find  it  hard 
to  avoid  altogether,  is  especially  hard  to  avoid  in  making  paper  loca- 
tions, which  is,  to  regard  a  certain  HORIZONTAL  APPROXIMATION  TO  the 
GRADE-POINTS  as  about  the  proper  thing,  thus  leading  to  altogether  too 
much  curvature  and  respect  for  the  contours  in  easy  country,  and  alto- 
gether too  little  of  both  at  the  more  difficult  points.  The  watchful  en- 
gineer finds  himself  drifting  into  this  error  continually,  guard  against  it 
as  he  will.  It  results  in  part  from  a  natural,  but  evidently  erroneous, 
tendency  to  look  on  a  certain  percentage  of  decrease  of  curvature,  for 
example,  as  worth  a  certain  percentage  of  increase  in  the  work  (pars.  14, 
15^,  instead  of  being  merely  worth  a  certain  absolute  sum,  which  on  easy 
work  justifies  great  disregard  of  contours,  and  on  heavy  work  requires 
close  accordance  with  them. 


8/8     CHAP.  XXXI.— TOPOGRAPHY:   ITS  USES  AND  ABUSE. 

1217.  3.  The  best  topographical  maps  which  it  is  either  expedient  or, 
in  general,  possible  to  make,  with  the  time,  money,  and  men  at  command, 
cannot  by  any  means,  as  is  sometimes  foolishly  claimed,  be  relied  on 
within  a  foot,  nor  even  5  or  10  feet,  at  critical  points,  especially  if  extend- 
ing to  any  great  width  on  each  side.  Over  most  of  their  area,  if  well 
made,  they  will  be  trustworthy,  but  minor  irregularities  of  considerable 
importance,  if  nothing  more  than  a  few  big  boulders,  get  smoothed  out  of 
the  map  or  misplaced  or  exaggerated,  so  that  the  only  safe  rule  is  to  look 
on  the  first  location,  however  carefully  studied,  as  still  open  to  much 
improvement — an  expectation  which  will  rarely  be  disappointed.  But 
if  frequent  minor  changes  are  to  be  made,  much  of  the  advantage  of 
computing  field-notes  from  a  paper  location  so  precisely  as  is  often  at- 
tempted is  lost.     It  is  not  in  fact  good  practice  to  do  so. 

1218.  4.  To  run  in  long  stretches  of  location  successfully  without 
further  topographical  tests,  but  only  the  geometrical  test  of  a  "tie"  to  a 
preliminary,  requires  the  nicest  field  and  office  work  from  the  beginning 
to  the  end  of  the  survey.  It  is,  of  course,  only  a  question  of  degree.  No 
one  would  advocate  anything  but  good  work  of  the  kind,  but  it  is  obvious 
that  less  precision  is  required,  if  it  is  fully  understood  and  expected  that 
the  paper  location  will  be  topographically  tested  throughout,  than  if  it  is 
expected  to  be,  in  the  main,  afinalit3^  This  saving  of  needed  precision 
means  some  corresponding  saving  of  time  and  money,  which,  as  Mark 
Twain  said  of  his  profanity,  "can  then  all  be  saved  and  devoted  to  some 
other  end,  where  it  will  do  more  real  and  lasting  good." 

1219.  Another  objection,  which  is  perhaps  the  strongest  of  all,  against 
too  great  reliance  on  contour  maps,  is  founded  rather  on  the  foibles  of 
human  nature  than  on  any  purely  technical  reason  :  It  encourages  a  dis- 
position in  the  higher  engineering  officers  to  throw  the  field-work  of 
location  into  incompetent  hands,  and  to  assume  to  themselves  the  func- 
tion of  fixing  the  petty  details  of  location,  and  hence  (since  the  whole  is 
only  equal  to  the  sum  of  all  its  parts)  to  control  the  whole  location  from 
their  office  chair,  without  giving  to  it  that  careful,  thorough,  and  con- 
tinued study  on  the  ground  which  alone  will  qualify  the  ordinary  man  to 
wisely  exercise  such  control.  This  practice  works  injuriously  in  several 
ways : 

I.  It  deadens  the  perceptive  faculties  of  the  engineer  in  charge  of  the 
party  and  transforms  him  into  a  mere  machine.  He  may,  if  an  unusually 
skilful  and  faithful  man,  go  over  the  paper  line  with  a  microscope  and 
improve  its  details,  but  he  will  not  be  watching  out  for  and  thinking  of 
the  larger  details,  especially  as — 


CHAP.    XXXI.— TOPOGRAPHY :   ITS  USES  AND  ABUSE.    8/9 

2.  The  practice  leads  to  the  engagement  of  poorer  men  for  the  field- 
work  ;  and 

3.  The  engineer  who  puts  in  the  paper  location,  and  coni/ols  the 
work,  never  qualifies  himself  by  familiarity  with  the  ground  to  do  well 
even  that  minor  duty,  and  is  so  little  in  the  field  that  the  far  more  im- 
portant end  of  avoiding  the  larger  errors  is  not  duly  insured. 

1220.  The  "conclusion  of  the  whole  matter"  therefore  is,  that  accu- 
rate topography  for  a  certain  narrow  strip  is  a  highly  useful  adjunct  to 
practical  location,  which  should  never  be  omitted  altogether  and  should 
generally  be  very  carefully  taken  and  studied  ;  but  that  it  is  in  no  way  a 
safeguard  against  anything  but  minor  errors  of  location,  and  is  not  a  safe 
nor  expedient  reliance  for  giving  the  last  degree  of  perfection  even  to  the 
details  of  alignment. 

Great  differences  in  natural  aptitude  for  location  exist,  and  among 
the  strongest  believers  in  the  absolute  necessity  of  elaborate  topography 
may  well  be  some  who  have  less  of  this  natural  aptitude,  and  hence  will 
not  make  very  good  use  of  the  best  of  maps.  In  fact,  although  we  should 
not  allow  this  to  prejudice  us  against  topography,  it  is  beyond  doubt  that 
those  of  least  natural  aptitude  for  location  rely  most  on  topography,  and 
are  the  most  helpless  without  it.  On  the  other  hand,  those  who  have  or 
think  they  have  such  aptitude  may  be  led  thereby  to  be  over-confident, 
and  commit  errors  which  good  topography  would  reveal  to  them.  It  is 
certain  that  the  better  natural  qualifications  a  man  has  for  the  work  the 
less  topography  he  will  take,  because  he  will  see  in  advance  where  it  is 
and  is  not  important.  He  will  always  take  some,  however,  and  what  he 
does  take  will  be  correct. 

1221.  Another  truth  may  appropriately  be  added  here.  It  is  easier  to 
put  A  line,  of  some  kind  or  other,  on  a  topographical  map  than  on  the 
ground ;  but  to  do  the  best  that  the  ground  admits  is  almost  as  hard,  and 
takes  almost  as  much  study  and  skill,  on  the  contour  map  as  on  the 
ground.  This  the  inexperienced  projector,  of  good  natural  parts,  will 
soon  find  out  if,  after  having  put  in  a  paper  location,  which  he  thinks  is 
very  good,  he  will  start  in  over  again  on  the  assumption  that  it  is  all  very 
bad,  and  give  two  or  three  times  more  thought  and  care  than  before  to 
finding  out  wherein  it  is  bad.  He  will  probably  soon  be  satisfied  that 
his  assumption  was  correct,  by  finding  his  curvature  and  quantities 
simultaneously  diminishing. 

1222.  There  is  a  tendency  in  discussing  this  question,  as  in  many  others,  to 
fall  back  upon  the  singular,  yet  in  a  sense  natural,  argument  which  seeks  to 
defend  some  one  way  of  doing  things  by  showing  that  some  of  those  who  take 


88o   CHAP.   XXXI.— TOPOGRAPHY :  ITS  USES  AND  ABUSE. 

another  way  do  work  badly.  On  the  one  hand,  we  have  pictured  the  "born 
engineer"  spending  days  in  fitting  a  bad  line  to  the  side  of  a  hill  with  his 
"  practised  eye,"  when  hours  would  have  sufficed  with  the  assistance  of  a  little 
well-taken  topography;  and,  on  the  other  hand,  a  man  studying  over  topographi- 
cal maps  of  a  line  in  the  wrong  place,  missing  the  salient  features,  and  perpet- 
uating on  the  ground  errors  of  the  maps.  Either  picture  may  well  be  drawn 
from  life,  for  out  of  a  hundred  men  doing  anything  which  requires  skill,  more 
than  half  will  do  it  but  indifferently  well,  a  considerable  fraction  wretchedly  ill, 
and  only  a  small  proportion  thoroughly  well.  This  fact  insures  a  supply  of 
ready  weapons  for  supporting  either  side  of  any  argument,  yet  it  is  strange  that 
they  should  be  so  often  chosen,  since  it  is  clear  that  they  prove  nothing.  But 
as  evidence  of  this  inconclusive  character  seems  sometimes  to  carry  undue 
weight,  we  may  add  a  few  words  further  as  to  certain  details. 

1223.  The  fact  that  the  actual  profile  of  a  line  run  from  a  "paper  location" 
agrees  so  precisely  with  the  latter  that  the  two  cannot  be  told  apart,  is  no  proof 
of  the  excellence  of  the  system,  for  both  profiles  may  be  bad.  It  proves  the 
geometrical  excellence  of  the  work,  but  it  also  proves,  or  tends  to.  that  the 
whole  process  is  too  mechanical,  unless  the  "  paper  location"  has  been  at 
least  so  improved  or  modified  in  detail  as  to  be  distinguishable  from  the  other. 

1224.  On  the  other  hand,  fixing  the  details  of  the  alignment  in  the  office, 
to  be  put  on  the  ground  by  other  men  of  less  skill,  while  never  a  desirable,  is 
not  necessarily  a  wrong,  way  of  doing  things.  We  are  often  compelled  to  do, 
not  what  we  would,  but  what  we  can.  If  there  be  but  one  skilled  man  to  look 
after  half  a  dozen  parties,  and  perhaps  look  after  other  work  as  well,  it  is  im- 
possible that  he  should  do  much  more  than  put  the  line  on  paper,  and  he  is  far 
more  likely  to  project  a  good  line  in  that  way  than  an  inexperienced  man  is  to 
reach  the  same  end,  either  on  paper  or  on  the  ground,  or  both.  When,  how- 
ever, one  ceases  to  look  on  this  practice  as  merely  a  necessary  evil,  and  begins 
to  look  on  it  as  an  ideal  state  of  things,  so  that  on  a  difficult  line  it  is  "  re- 
quire^" that  the  projected  location  should  be  "  strictly  followed"  and  "no  cut- 
and-try  permitted, "  as  is  sometimes  done,  then  the  abuse  of  topography — and  a 
dangerous  abuse,  sure  to  waste  more  or  less  money — has  begun.  The  better 
course  in  such  cases  is  to  require  the  engineers  in  the  field  to  make  the  first 
projection,  which  is  simply  sent  in  for  examination  and  revision  if  necessary, 
so  as  to  compel  them  to  rely  on  their  own  intelligence  and  not  on  another's,  and 
especially  to  give  an  indication  of  the  extent  to  which  their  own  skill  can  be 
relied  on.  For  if  unequal  to  making  a  tolerably  correct  projection  in  the  first 
instance,  they  will  probably  be  still  more  unequal  to  the  more  responsible  duty 
of  putting  in  the  final  line. 

1225.  To  mention  one  instance  among  many,  of  the  evils  of  too  great  re- 
liance on  maps:  an  unusually  accurate  paper  location,  on  a  very  steep  side-hill, 
gave  a  beautiful  profile,  which  no  one  could  detect  in  the  office  to  have  any  fault. 
The  cut  averaged  about  a  foot,  which  was  what  prudence  seemed  to  require, 


CHAP.    XXXI.— TOPOGRAPHY :  ITS  USES  AND  ABUSE.    88 1 

and  what  no  one,  certainly,  in  the  office  would  have  thought  of  objecting  to. 
But  just  below  the  earth  was  rock,  as  a  "practised  eye"  might  have  detected  in 
the  field,  and  the  earth  itself  was  such  as  to  make  an  unusually  solid  bank,  so 
that  when  the  line  came  to  be  constructed  there  was  an  ugly  shallow  rock-cut 
on  the  inner  edge  and  a  broad  solid  platform  for  the  road-bed  nearly  twice  too 
wide,  due  to  the  unnecessary  amount  of  excavation,  which  involved  a  loss  of 
some  $8000  in  much  less  than  a  mile,  all  of  which  might  have  been  saved  by 
.throwing  the  line  out  three  or  four  feet  beyond  the  paper  location. 

Such  cases  occur  so  frequently  that  the  engineer  who  does  not  feel  the  limi- 
tations  of  the  map  and  wish  that  he  had  the  ground  before  him  in  making  a 
paper  location,  and  who  does  not  feel  that  it  may  be,  and  probably  is,  suscepti- 
ble of  further  improvement  by  further  study  in  the  field,  will  probably  be  wise 
to  leave  "  topography"  alone,  both  in   the  field  and  in  the  office. 

1226.  In  some  cases  the  larger  errors  of  location,  such  as  putting  a  line  on 
the  hill-side  with  a  short  tunnel,  instead  of  in  the  bottom  of  the  valley  with  a 
long  tunnel,  are  very  unreasonably  advanced  as  an  effect  of  neglecting  topog- 
raphy; whereas  it  is  precisely  such  errors  which  over-reliance  on  topography  is 
apt  to  lead  to.  The  result  depends  chiefly  on  the  man.  A  good  man  will  use 
every  tool  that  will  serve  his  end,  and  one  of  these  tools  is  topography.  Another 
one,  at  least  equally  essential,  is  shoe-leather. 

1227.  If  topography  is  to  be  taken  at  all  it  should  be  taken  accurately, 
and  to  combine  this  end  with  reasonable  rapidity  the  limits  within  which 
accurate  topography  is  taken  should  be  restricted  as  closely  as  possible. 
Beyond  these  limits  a  skilful  topographer  will  sketch  in  by  the  eye  the 
general  form  of  the  ground,  with  sufficient  accuracy  to  give  a  better 
general  idea  of  the  form  of  the  country,  and  occasionally  to  serve  a  use- 
ful purpose  in  a  rough  study  of  some  considerable  change  of  line. 

1228.  Topography  is  taken  from  the  preliminary  line  as  a  base-line, 
with  the  elevations  on  it  given,  by  determining  the  slopes  on  each  side  as 
far  out  as  seems  necessary.  Four  methods  for  taking  slopes  are  more  or 
less  practised : 

1.  By  a  slope-level  and  board  straight-edge,  with  or  without  a  tape- 
line. 

2.  By  a  hand-level  and  tape-line. 

3.  By  cross-sectioning  rods. 

4.  By  using  a  stadia  telescope  and  rod  to  measure  distances  in  place 
of  a  tape-line,  in  either  the  first  or  second  methods. 

To  these  may  be  added — 

5.  By  using  an  altazimuth  in  place  of  the  slope-level  or  hand-level  in 
the  first  or  second  methods.  It  may  also  under  special  circumstances  be 
used  to  advantage  with  cross-section  rods. 

56 


882    CHAP.   XXXI.— TOPOGRAPHY :  ITS  USES  AND  ABUSE. 


Fig.  290. 


1229.  In  rugged  and  broken  topography,  as  where  there  is  much  rock 
and  large  scales  are  to  be  used,  the  third 
method,  by  cross-section  rods,  is  much 
the  best.  These  rods  are  in  principle 
nothing  more  than  a  horizontal  measur- 
ing-rod of  a  fixed  length,  sometimes  10 
but  better  12  ft.,  carrying  a  level  bubble, 
so  that  it  can  be  set  exactly  horizontal. 
This  is  carried  by  one  assistant  while  an- 
other reads  with  a  light  vertical  rod,  B, 
Fig.  290,  the  rise  or  fall  of  the  ground 
in  the  given  distance.  In  practice,  to  prevent  warping  of  the  rod  A,  it 
is  usually  made  in  one  of  the  forms  shown  in  Fig.  291. 

These  rods  are  convenient  to  have  with  a  locating  party  in  rough 
country,  and  they  are  especially  suitable  for 
cross-sectioning  a  located  line,  but  the  pro- 
cess is  much  slower  than  any  of  the  others 
specified,  which  are  in  general  better  for 
ordinary  topography. 

1230.  A  wise  choice  between  the  slope- 
level  and  hand-level  methods,  also,  depends  a 
good  deal  upon  circumstances,  and  the  character  of  the  topography  to  be 
taken,  although  each  method  has  its  partisans  who  will  rarely  use  any 
other.  By  the  use  of  the  altazimuth  either  method  can  be  used  at  will, 
which  is  one  of  the  distinguishing  merits  of  that  instrument.  Much 
more  depends,  however,  upon  the  individual  skill  of  the  topographer  than 
upon  the  use  of  any  particular  method.  Where  the  country  is  rough, 
with  irregular  slopes,  the  hand-level  method  is  to  be  preferred,  since  it  is 
more  positive.     Otherwise,  the  slope-level  is  best. 

1231.  The  topography  based  on  these  slope-notes,  by  whatever 
method  taken,  should  invariably  be  drawn  in  the  field  directly 
UPON  the  working  maps  of  the  line,  which  should  be  the  first  and 
only  direct  use  made  of  the  cross-section  notes.  As  a  safeguard  in  case 
of  doubt,  the  rodman  may  well  keep  a  note-book  record  of  them,  but  this 
should  be  strictly  restricted  to  such  use  only.  The  habit  of  taking  the 
cross-sections  in  the  field  and  drawing  in  the  topography  in  the  office 
cannot  be  too  strongly  discouraged.  It  is  certain  to  result  in  more  or 
less  imperfect  work,  as  well  as  loss  of  time.  After  a  little  practice  a 
skilled  topographer  ought  to  be  able  to  keep  up  with  a  transit  and  level 
party  without  much  diflEiculty,  unless  circumstances  require  a  wide  belt 


Fig.  291. 


CHAP.    XXXI.— TOPOGRAPHY :  ITS  USES  AND  ABUSE.    883 


of  exact  topography  to  be  taken,  when  he  should  be  furnished  with  a 
double  cross-section  party.  The  main  requirement  for  doing  work 
quickly  and  well  is  to  train  the  eye  and  judgment  so  that  needless  cross- 
section  work  need  not  be  done  while  yet  taking  all  that  is  essential. 

1232.  The  topographer  is  provided  with  a  thin  drawing-board,  hav- 
ing a  leather  or  oil-cloth  pocket  on  the  back,  in  which  are  carried  the 
sheets,  about  19  X  24  inches  in  size  (par.  1240),  on  which  the  line  has  been 
plotted  the  night  before,  the  stations  marked  off,  and  the  elevation  of 
each  station  and  plus,  as  taken  by  the  level,  lightly  pencilled  on  it.  The 
topographer  must  thus  work  behind  the  level,  but  a  good  topographer 
will  endeavor  to  keep  very  close  up  to  it.  One  sheet  at  a  time  is  pinned 
upon  the  board  for  use.  A  6-in.  scale,  preferably  of  paper,  lead  pencils, 
and  rubber  complete  his  outfit.  His  two  assistants  (or  four  if  need  be) 
have  nothing,  necessarily,  but  tape  and  hand-level,  with  a  small  hatchet. 
A  small  compass  for  taking  bearings  is  in  general  desirable. 

1233.  In  taking  cross-sections,  the  elevation  of  each  station  is  given 
to  the  rodman  (or  has  been  previously  taken  off  by  him),  and  an  offset 

measured  off  to  a  point,  as 
indicated  by  the  hand-level, 
where  the  contour  next 
above  or  below  the  eleva- 
tion of  the  given  station 
falls.  Thus,  in  Fig.  292, 
with  contours  10  ft.  apart, 
elevation  of  station  704.2, 
contour  710  is  5.8  ft.  above 
it,  and  contour  700  4.2  ft. 
below  it.  The  distance  out 
in  which  the  ground  rises  or 
falls  these  amounts  should 
in  general,  on  rough  ground, 
be  directly  determined,  and 
then  the  distances  to  a  suc- 
cession of  other  points,  fall- 
ing 5  ft.  at  a  time,  as  far  out  as  accurate  topography  is  taken.  On 
smoother  country  a  little  trouble  may  be  saved  as  below  spoken  of. 

The  points  where  the  contours  cut  the  centre-line  are  also,  at  the 
same  time,  noted  by  the  topographer.  He  then  makes  a  light  pencil 
guess  at  the  course  of  the  contour  lines  ahead,  and  passes,  perhaps,  two 
stations  ahead,  to  "  17.4,"  Fig.  292,  and  repeats  the  process,  the  rodmen 
in  the  mean  time  cross-sectioning  the  intermediate  station  if  it  seems 


Fig. 


884    CHAP.    XXXI.— TOPOGRAPHY :  ITS  USES  AND  ABUSE. 


essential,  or  more  properly  speaking,  unless  it  seems  unessential.  Until 
the  topographer  has  acquired  well-founded  confidence  by  practice  he  will 
save  nothing  by  taking  chances,and  be  liable  to  throw  discredit  on  his  work. 
Here  the  previous  guesses  are  checked  by  the  cross-sections  and  the 
course  of  the  contours  sketched  in  backward  ;  exactly  and  finally,  and 
lightly  ahead,  with  further  pencilled  guesses.  In  this  way  the  topographer 
trains  his  eye  and  his  hand,  and  forms  an  idea  of  where  accuracy  is  and 
is  not  essential,  and  if  he  be  once  properly  instructed,  and  has  a  capable 
assistant,  it  is  not  at  all  difficult  to  take  a  mile  or  two  of  topography 
a  day  in  ordinary  country.  When  he  has  to  take  more  than  200  to  300  ft. 
on  each  side  it  becomes  a  different  matter,  and  progress  is  much  slower. 

1234.  If  slopes  are  determined  by  a  slope-level  it  is  still  simpler  work. 
A  scale  is  then  constructed,  showing  for  a  series  of  different  slopes  from 
1°  to  20°,  the  horizontal  distance  apart  of  lo-ft.  contours,  which  is  10  X  cot 
S.  From  this  the  contours  can  be  put  down  upon  the  map  at  once,  at 
the  proper  distances  apart,  or  as  far  out  as  the  slopes  are  taken. 

1235.  Time  is  lost  and  accuracy  sacrificed  in  many  surveys  by  using 
too  small  scales.  The  standard  working  scale  may  be  said  to  be  400  feet 
per  inch,  or  -g-gVo  (nearly  the  same  thing)  when  the  metre  is  used ;  but 
this  scale  is  adhered  to  far  too  strictly.  In  rough  country  it  should  be 
at  once  doubled,  and  in  very  rough  country  should  be  increased  to  100  ft. 
per  in.  or  -j-gVo  (^3i  ^t.  per  in.).  These  latter  are  the  only  suitable  scales 
when  there  is  any  considerable  proportion  of  rock-work.  It  rather  saves 
work  in  taking  topography,  adds  but  little  to  the  drafting  work,  and 
adds  immensely  to  the  practical  value  of  the  maps  when  made. 

1236.  The  following  cautions  will  assist  in  taking  topography  correctly  : 
I.  One  contour  line  can  never  run  into  another  and  either  disappear 

altogether  or  afterwards  depart  from  it,  in  the 
manner  shown  at  AA,  Fig.  293,  but  must  always 
be  everywhere  a  separate,  distinct,  and  continu- 
ous line  until  it  either  runs  off  the  map  or  closes 
on  itself  so  as  to  form  an  irregular  ring  or  circle, 
as  at  B,  Fig.  293. 

There  is,  indeed,  one  case  in  which  two  or  a 
dozen  contours  may  so  run  together  into  a  single 
line,  viz.,  when  an  absolutely  vertical  slope  is  to 
be  represented.  There  is  even  a  possible  case — 
that  of  an  overhanging  cliff — in  which  the  con- 
tour lines  may  cross  over  each  other  and  back 
again,  as  in  Fig.  294.  But  both  of  these  cases 
are  so  rare,  although  they  do  occur,  that  it  is  unnecessary  to  consider 
them  as  normal  types  of  topography. 


Fig. 293. 


CHAP.    XXXI.— TOPOGRAPHY :  ITS  USES  AND  ABUSE.    885 


1237.  2.  It  is  impossible  for  a  contour  line  to  split  into  two  parts  which 
sooner  or  later  reunite  again,  in  the  manner  shown  in  Fig.  295.  It  is  a 
frequent  error  of  young  topographers,  and  an 
immediate  evidence  of  inexperience,  to  be- 
lieve the  contrary.  It  is  indeed  theoretically 
conceivable  that  a  surface  should  have  such 
^^^-  ^5'^*  form  as  to  make  a  sketch  like  Fig.  295  topo- 

graphically correct.  Thus,  if  we  imagine  it  to  be  a  representation  of  the 
crest  of  a  hill,  it  might  come  to  so  sharp  and  regular  a  ridge,  if  made  of 
dressed  stone  for  example,  that  only  a  single  mathe- 
matical line  at  the  peak  or  ridge  of  the  slope  should 
appear  above  the  water,  and  yet  that  the  ridge  should 
so  appear  above  the  water  for  a  considerable  distance, 
being  precisely  level,  and  should  at  a  certain  point 
swell  out  into  the  "  island  "  AA.  But  practically,  with 
natural  surfaces  as  they  actually  exist,  this  is  plainly 
impossible,  and  the  true  method  of  representing  the 
natural  surface,  which  is  erroneously  presented  in  Fig, 
295,  would  be  as  shown  in  Figs.  208,  216. 

1238.  Topography,  more  largely  than  almost  any 
other  mechanical  detail  of  engineering  work,  is  a  mat- 
ter of  practice.  The  young  engineer  who  ends  his 
first  day's  work  at  topography  discouraged,  with  but  a  few  stations  taken, 
and  that  so  badly  taken  as  to  be  worthless,  can  by  even  a  few  days'  de- 
termined  effort  to  understand  it,  and  do  what  he  does  do  well,  learn  to 
go  over  as  much  ground  as  an  ordinary  transit  party.  It  is  a  valuable 
drill  for  cultivating  the  faculties  most  needed  for  location,  and  good  to- 
pographers generally  make  the  best  chiefs  of  party.  In  country  at  all 
rough  the  topographer  fills  the  most  responsible  position  on  the  party 
below  its  chief,  and  he  should  so  rank.* 


Pig.  295. 


*  The  art  of  taking  topography  should  be  taught  in  schools  more  thoroughly 
than  it  is.     There  is  no  better  drill  for  cultivating  those  faculties  of  mind  which 


make  the  engineer. 


886   CHAP.   XXXII.— MAPPING  AND  PROJECTING  LOCATION, 


CHAPTER    XXXII.  ^ 

MAPPING    AND    PROJECTING    LOCATION. 

1239.  But  two  methods  of  mapping  railroad  surveys  are  to  be  com- 
mended, which  are : 

1.  For  large-scale  working  jnaps :  plotting  lines  by  bearings  with  a 
large  paper  protractor  and  parallel  ruler. 

2.  For  small-scale  maps  :  by  latitudes  and  departures. 

Plotting  lines  of  any  length  by  laying  off  successive  angles — a  favor- 
ite way  of  laboriously  making  a  bad  map  among  inexperienced  men — 
should  never  under  any  circumstances  be  permitted.  All  work  should 
be  plotted  by  bearings  from  a  constant  North  and  South  line,  which  is 
transferred  from  sheet  to  sheet  by  prolongation  or  with  a  parallel  ruler. 
Cumulative  errors  are  thus  avoided. 

1240.  Except  in  cases  where  fully  8o  per  cent  of  a  line  is  tangent,  and 
there  is  little  topographical  detail,  a  survey-line  should  never  be  plotted 
on  long  strips  or  rolls  of  paper,  but  always  on  small  sheets,  about  19  x  24 
inches  in  size,  or  larger  if  there  be  little  curvature  and  topography — say 
19  X  36  inches.  These  sheets  are  added  one  after  another  as  the  plotting 
progresses,  lapping  one  side  or  corner  always  under  the  preceding  sheet, 
and  giving  its  axis  any  random  direction,  compared  with  the  other,  which 
will  best  serve  to  keep  the  centre  line  of  the  survey  in  the  middle  of  the 
sheets,  as  shown  in  Fig.  296,  The  two  sheets  are  pinned  together  with 
thumb-tacks,  and  two  or  three  X  marks  made  at  the  lap,  so  that  they  can 
be  replaced  at  any  time  in  exactly  the  same  position. 

A  North  and  South  base-line  should  then  be  laid  down  the  full  length 
of  the  sheet,  nearly  in  its  middle,  and  a  consecutive  number  for  the  sheet 
and  the  name  of  the  line  pencilled  on,  always  in  the  same  corner. 

1241.  The  large  paper  protractor  should  then  be  laid  down  in  the 
middle  of  the  sheet  on  the  North  and  South  lines,  from  a  clearly-marked 
permanent  centre-point,  and  the  computed  or  actual  bearings  of  all 
the  lines  which  are  likely  to  fall  on  the  sheet  laid  off  at  once.  If  omis- 
sions  are   discovered,  the  same   process   should   be   repeated  ;    lightly 


CHAP.    XXXII.— MAPPING  AND  PROJECTING  LOCATION.    88/ 


pencilling  in  the  degrees  and  minutes 
of  each  bearing  laid  off,  and  per- 
mitting the  points  thus  marked  to 
remain  permanently,  except  as  they 
interfere  with  the  mapping.  Should 
any  subsequent  error  be  discovered, 
they  may  then  all  be  checked  at 
once,  saving  much  time. 

With  a  good  parallel  ruler  (not 
the  cheap  and  poor  ones  which  are 
most  used,  but  a  heavy  metal  rule 
about  1 8  inches  long),  or,  failing 
that,  a  couple  of  triangles,  it  is  then 
but  a  few  moments'  work  to  transfer 
each  bearing  in  succession  to  its 
proper  point,  draw  in  the  line,  and 
plot  its  length.  The  angles  should 
then  be  roughly  checked  with  a 
small  protractor  to  guard  against 
the  large  errors  which  are  alone 
likely  to  occur.  The  bearing  of 
each  line  and  the  plus  at  each  angle 
should  then  be  pencilled  on. 

Every  station  should  then  be 
pricked  off  and  indicated  by  a  light 
check-mark,  and  every  fifth  station 
should  be  numbered. 

Opposite  each  station  on  a  di- 
agonal line  should  then  be  lightly 
pencilled  in  the  elevation,  and  also 
the  elevation  of  any  pluses  taken. 
The  sheets  are  now  ready  to  turn 
over  to  the  topographer. 

This  work  should  be  done  every 
night.  It  takes  but  a  short  time 
after  a  little  practice.  The  lines  may 
be  inked  in  on  rainy  days  or  at  any 
convenient  time.  The  centre  line 
should  be  in  red. 

1242.  For  the  same  reason  that  Fig.  296. 

plotting  should  be  done  from  bearings,  it  is  well  to  do  all  the  transit 


888    CHAP,   XXXII.— MAPPING  AND  PROJECIING  LOCATION. 


work,  on  preliminary  lines  at  least,  by  reading  bearings  instead  of 
ANGLES  from  the  vernier.  In  starting  the  survey  the  vernier  is  set  at  o, 
and  the  lower  limb  clamped  on  a  North  and  South  line,  or  as  near  to  it 
as  possible.  Unclamping  the  upper  limb,  we  may  then  read  the  bearing 
of  the  line  either  with  the  compass  or  the  vernier,  and  the  two  should 
approximately  correspond.  Retaining  the  verniers  at  the  same  reading 
for  taking  a  back-sight  at  the  next  angle,  and  unclamping  above  to  take 
the  next  sight,  we  obtain  the  bearing  of  the  new  line,  likewise  either  by 
the  compass  or  the  vernier — the  one  approximate,  the  other  exact.  Thus 
we  may  continue  throughout  the  survey,  with  the  advantage  (i)  that  we 
can  check  our  work  at  any  time  by  simply  dropping  the  needle,  since 
the  needle  and  vernier  readings  should  always  correspond,  and  (2)  that 
our  "  computed  bearings"  are  already  computed.  We  should  work,  how- 
ever, by  180°  on  each  side  of  the  North  point,  and  not  be  troubled  by  the 
transition  from  N.  E.  to  S.  E.  This  is  the  best  way  to  do  in  any  case, 
and  it  is  easy  to  read  the  needle  so. 

1243.  In  inking  in  the  topography,  every  fifth  line  should  in  all  cases 
be  made  heavier  or  a  different  color.  Black  or  brown  for  every  fifth 
line,  and  brown  or  orange  for  the  intermediates,  does  very  v^-ell.  Where 
possible,  contours  should  only  be  five  feet  apart,  although  ten  feet  is 
usual.  The  values  of  every  fifth  line  should  be  frequently  written  on 
them,  in  rows  one  above  the  other,  preferably  by  leaving  a  gap  in  the 
line  for  inserting  the  figures,  or  otherwise  by  writing  them  directly  over 
and  across  the  line.  Much  of  the  prejudice  against  working  with  con- 
tour topography  arises  from  the  prevalent  neglect  of  these  simple  direc- 
tions, which  seem  almost  too  simple  to  mention.  Such  a  map  as  Fig. 
297,  for  example,  is  an  abomination.  It  reflects  just  discredit  on  any 
engineer  to  turn  in  one  in  that  condition,  which  makes  it  almost  worth- 
less to  the  engineer  and  incomprehensible  to  the  mere  observer.  It  should 
be  finished  up  as  shown  in  Fig.  208. 

A  light  case,  provided  with  three  or  four  drawers  of  the  proper  size 
to  hold  the  sheets,  should  be  provided  for  field  use.  Light-yellow  de- 
tail paper  makes  very  good  sheets,  and  is  less  trying  to  the  eyes  than 
white. 

1244.  Experience  has  clearly  shown  this  system  of  mapping  survey- 
lines  to  be  far  better  than  any  other.     Its  advantages  are  : 

1.  But  a  small  amount  of  paper  is  in  use  at  once  in  plotting,  while 
any  number  of  sheets  that  there  is  table-room  for  may  be  put  together 
if  desired. 

2.  A  very  small  table  is  all-sufficient. 


,  297— AN  IMPROPERLY  FINISHED  CONTOUR  MAP.    (A  spiral  located  on  the  Connellsville  &  Southern  Pennsylvania  Railroad.) 
.vholly  useless  for  practical  work,  or  for  giving  a  definite  idea  of  the  line  to  a  casual  examiner,  while  it  is  nearly  as  much  work  to  make  it  as 


t  properly,  as  shown  < 


Fig.  298.— the  SAME  MAP,  PROPERLY  FINISHED. 
[Stationing',  degree  and  central  angle  of  curves,  grade-contour,  position  of  tunnels,  elevation  of  contours,  and  heavy  line  for  every  fifth  c 
tangents,  variation  of  compass,  pluses  of  P.  C.  and  P.  T.,  the  position  of  bridges  and  culverts,  changes  of  channel  (as  probably  require 


added  on  a  full-scale  i 


Centre  line  and  radii 


CHAP.    XXXII.— MAPPING  AND  PROJECTING  LOCATION. 


3.  No  time  need  be  lost  in  studying  how  to  keep  the  line  on  the 
paper,  or  in  rubbing  out,  or  in  pasting  on  extensions. 

4.  The  map  need  not  be  covered  ov^er  with  prolonged  lines  for  laying 
off  angles,  but  only  the  actual  length  needed  is  drawn. 

5.  Great  accuracy  is  secured  without  effort,  and  cumulative  errors  are 
impossible.  If  an  error  is  made  on  one  sheet  it  in  no  way  injuriously 
affects  the  work  on  the  adjacent  sheets,  except  that  two  of  them  will 
have  to  be  re-matched. 

6.  If  matched  properly  the  greatest  precision  is  possible  in  laying  them 
together  again  whenever  desired.  For  all  practical  purposes  they  are  as 
a  single  sheet. 

7.  There  is  no  waste  paper,  and  the  line  is  always  in  the  middle  of 
what  is  used,  readily  accessible  for  office  work.  The  awkwardness  of 
working  with  wide  rolls  is  entirely  saved. 

8.  The  paper  is  never  rolled,  but  always  flat  and  clean,  in  good  con- 
dition for  working  on. 

9.  For  projecting  location,  the  ease  with  which  any  part  of  the  line 
desired  can  be  worked  with,  without  annoyance  from  what  is  not  wanted, 
and  from  change  of  scale  due  to  rolling,  gives  it  very  great  advantage. 

10.  The  miaps  are  readily  stowed  away  in  dust-tight  boxes  or  drawers, 
and  in  very  small  compass,  instead  of  taking  up  a  great  deal  of  room  and 
getting  into  a  practically  unserviceable  condition  in  a  short  time,  as 
rolled  maps  usually  do. 

1245.  For  making  small-scale  maps,  plotting  by  latitudes    and 

DEPARTURES  is  the  most  satisfac- 
tory way.  The  latitude  and  de- 
partures should  not  be  computed, 
however  (or  the  labor  would  be 
prohibitory),  but  read  off  mechanic- 
ally from  a  diagram  similar  to  Fig. 
299,  which  shows  the  principle  of 
an  apparatus  for  the  purpose  de- 
vised by  Mr.  Chas.  Francis,  Chief 
of  Office  on  the  Pacific  Branch  of 
the  Mexican  Central  Railway.  Any 
one  can  readily  make  it.  The  base 
is  a  sheet  of  accurate  cross-section 
paper,  10  or  20  squares  per  inch, 
F^*^-  299-  on  which  angles  are  accurately  laid 

off,  either  around  the  edge,  as  shown,  or  on  a  circular  arc  of  as  large  a 


890  CHAP.   XXXIT.— PROJECTING  LOCATION. 

radius  as  possible.     Values  are  given  to  the  lines  from  zero  to  100  or 
more.     The  straight-edge  is  laid  of!  with  the  same  scale. 

We  have  then  only  to  set  the  edge  of  the  straight-edge  at  the  angle 
corresponding  to  any  bearing ;  place  a  needle-point  or  sharp  pencil  at 
the  point  on  it  representing  the  length  of  a  given  line,  and  we  read  off 
from  the  sheet  below,  at  once,  latitudes  and  departures  for  the  line.  Lati- 
tudes and  departures  for  miles  of  line  can  thus  be  called  off  and  tabulated 
in  a  day  by  two  men,  and  the  absolute  position  of  every  point  on  the 
survey,  by  rectangular  coordinates  from  any  fixed  origin,  determined 
once  for  all.  From  these  notes  as  many  or  as  few  points  can  be  trans- 
ferred to  the  map  as  seems  desirable,  according  to  its  scale,  and  the  re- 
mainder sketched  in.  When  several  alternate  lines  are  to  be  mapped 
together  this  method  is  especially  useful,  as  the  trouble  of  closing  ac- 
curately is  so  greatly  reduced. 


PROJECTING   LOCATION. 

1246.  To  make  a  really  good  projection  on  a  topographical  map  in- 
volves a  great  deal  of  work  and  study,  and  errors  are  almost  as  easy  as 
they  are  on  the  ground.  In  fact  the  writer  has  no  belief  that  any  one 
ever  projected  a  location  on  paper  which  could  not  be  materially  improved 
by  study  on  the  ground. 

The  most  difficult  case  is  projecting  a  final  grade-line  in  which  curve 
compensation  is  to  be  introduced  as  it  advances.  In  very  difficult  coun- 
try a  first  projection  on  an  estimated  average  "  straight "  grade-line  is  often 
advantageous,  saving  time  and  giving  a  better  final  result  because  of  the 
double  study.  The  lower  (dotted)  spiral  of  Fig.  216  was  projected  in 
this  way. 

The  projection  should  begin  at  the  summit  or  other  fixed  point 
which  the  line  must  make.  Assuming  a  starting-point  and  elevation,, 
take  in  a  pair  of  dividers  the  distance  on  the  map  which  the  given  grade- 
line  takes  to  fall  10  ft.,  or  better  yet,  5  ft.  When  curve  compensation  is 
introduced  this  distance  will  be  different  on  a  tangent  and  on  every  curve, 
and  should  be  laid  off  on  a  strip  of  paper  so  that  the  dividers  can  be  set 
and  reset  without  trouble. 

With  the  dividers  thus  set,  step  off  a  distance  of  10  or  12  inches  on 
the  map,  following  as  nearly  as  may  be  where  it  is  thought  the  line 
will  lie.  On  favorable  topography  this  will  be  very  closely  along  the 
GRADE  CONTOUR,  or  line  where  the  plane  of  the  grade  strikes  the  natural 
surface.     In  that  case  we  can  step  off  quite  a  distance  at  once,  stepping 


CHAP.  XXXII.— PROJECTING  LOCATION,  89! 

down  a  contour  or  half-contour  at  a  time,  and  marking  by  a  small  cross- 
mark  where  the  grade-line  crosses  each. 

1247.  The  grade-contour  should  then  be  very  lightly  pencilled  in,  and 
a  curve  or  two,  or  a  long  tangent  and  the  beginning  of  one  curve,  pro- 
jected. Then,  setting  the  dividers  for  the  proper  distance  for  a  fall  of 
I,  2,  or  5  ft.  on  the  given  curve  or  tangent,  and  starting  from  the  fixed 
point,  step  along  the  projected  location  to  the  first  point  of  curve  and 
determine  and  write  down  its  elevation  to  the  nearest  foot  and  tenth  ; 
paying  no  attention  as  yet  to  stationing,  but  simply  to  determining  points 
where  the  grade-line  reaches  certain  even  elevations,  and  to  determining 
the  grade  at  the  points  of  curve. 

Having  reached  a  curve  from  a  tangent,  reset  the  dividers  for  the 
proper  distance  for  the  given  fall  on  the  curve  ;  start  from  the  P.  C.  cor- 
rectly by  straddling  the  dividers  over  it  according  to  its  fractional  eleva- 
tion ;  step  around  the  curve  to  the  P.  T.,  and  determine  and  lightly  note 
its  elevation.  Reset  the  dividers  for  the  next  tangent  or  curve,  and  so  on 
to  the  end  of  the  section  projected. 

1248.  Then  return  and  correct  the  grade-contour  according  to  the 
precise  points  at  which  the  elevation  of  each  contour  or  half-contour  is 
reached  on  the  actual  projection,  sketch  every  bit  of  it  in,  and  see  if  the 
projection  corresponds  to  the  corrected  grade-contour  as  well  as  is  possi- 
ble. Consider  everything  :  the  material  (above  all) ;  the  surface  slope  ; 
the  water-ways ;  whether  the  line  should  be  preferably  in  cut  or  fill, 
whether  the  tangent  or  the  centre  of  a  curve  cannot  be  slightly  changed 
so  as  to  fit  the  grade-contour  better,  or  avoid  a  rock-cut ;  whether  the 
form  of  the  gulches  is  correctly  represented  and  there  is  not  a  crossing 
point  slightly  more  favorable  above  or  below,  which  the  topography  does 
not  clearly  show  ;  whether  the  tangent  cannot  be  broken  up  by  a  slight 
curve  and  save  work  which  will  be  more  conspicuous  on  the  ground  than 
on  the  map  ;  or,  on  the  other  hand,  whether  the  line  cannot  be  thrown  out 
here  and  in  there,  so  as  to  take  out  curvature  and  yet  give  as  good  a  pro- 
file. Probably  some  little  modification,  at  least,  will  be  at  once  seen  to 
be  desirable,  and  the  whole  work  will  have  to  be  done  over,  perhaps 
three  or  four  times.     If  not,  it  may  be  for  the  time  being  left  behind. 

1249.  A  short  stretch  more  should  now  be  projected  in  the  same 
manner  as  before,  and  now  only  will  it  be  possible  to  give  proper  study 
to  the  first  section  ;  for  the  whole  relations  of  the  line  to  the  ground  can- 
not be  taken  in  until  the  projection  is  complete  for  a  considerable  dis- 
tance on  each  side  of  the  point  studied.  It  is  now  more  likely  than  be- 
fore that  modifications  will  suggest  themselves  in  the  first  section.    The 


892  CHAP.  XXXIL— PROJECTING  LOCATION. 

reader  who  is  quite  satisfied  with  his  first  or  second  or  third  trial  may 
justly  fear  that  he  is  doing  bad  work.  The  projection  in  Fig.  216,  for 
example,  while  good  enough  for  an  approximation,  is  by  no  means  good  for 
a  final  one,  being  capable  of  considerable  improvement  at  several  points. 

After  completing  several  miles  the  whole  should  be  studied  over  again, 
and  corrections  unnoticed  before  are  pretty  sure  to  suggest  themselves. 
Very  often  long  stretches  of  the  grade  can  be  raised  or  lowered  somewhat 
to  advantage,  at  the  expense  of  a  slight  break.  It  is  difficult  to  point 
out  every  danger  in  advance,  but  it  is  a  fact  that  men  will  differ  in  their 
projections  almost  as  much  as  in  field  location,  and  the  most  obvious  im- 
provements will  not  suggest  themselves  until  some  one  else  points  them 
out.  Without  an  accurate  personal  knowledge  of  the  ground,  it  is  folly 
for  an}'^  one  to  attempt  to  make  a  really  good  final  projection,  although 
contour  maps  have  the  great  negative  merit  that  glaring  errors  or  gen- 
eral incompetency  may  be  detected  at  sight  by  any  one  of  experience. 

Before  the  projection  is  considered  final  the  corrected  grade-contour 
should  be  made  exactly  right,  and  sketched  in  clearly  and  complete.  It 
is  very  bad  practice  to  sketch  in  only  certain  grade-points.  A  great  check 
against  error  is  thus  lost. 

1250.  The  line  should  now  be  stationed  and  a  profile  and  field-notes 
called  off.  The  latter  are  readily  made  up,  since  the  length  and  degree 
of  each  curve  is  known,  but  they  should  be  checked  and  corrected 
throughout  by  determining  the  bearings  of  every  projected  tangent  from 
the  original  North  and  South  line.  Except  when  errors  are  seen  to  be 
compensatory  the  bearings  thus  read  will  be  more  trustworthy  than  the 
stepped-off  lengths  of  the  curves,  and  the  latter  should  be  modified  to 
correspond. 

1251.  Curves  may  be  projected  either  (i)  by  compasses,  (2)  by  wooden, 
rubber,  or  metal  curves,  or  (3)  by  a  curve- protractor  made  on  a  large  clear 
sheet  of  isinglass  by  scratching  on  the  curves  and  rubbing  ink  in  the 
scratches.  The  latter  is  a  very  convenient  and  desirable  adjunct  to  the 
work,  but  not  essential  when  the  radii  are  not  too  large  for  compasses. 
With  cut  curves  it  is  far  more  important.  The  writer  personally  prefers 
a  pair  of  compasses  to  anything  else  when  the  radii  admit  of  their  use. 
The  transition  curves  should  be  projected  at  the  same  time  as  the  curves 
by  drawing  in  the  latter  not  quite  tangent  to  the  tangents,  but  at  a  slight 
offset  to  them,  as  in  Figs.  208  and  216.  What  this  precise  offset  may  be 
does  not  matter.  It  may  vary  from  0.5  to  3.0  or  4.0  feet  per  degree  of 
curve. 

1252.  Having  made  the  profile,  the  grades  should  be  put  on  it.     Re- 


CHAP.  XXXIL— PROJECTING  LOCATION.  893 

member  in  putting  grades  on  a  profile  that  it  is  a  great  deal  easier  to 
stretch  a  thread  to  cover  two  or  three  feet  of  a  profile  than  to  execute 
with  shovel  and  crow-bar  the  work  which  it  calls  for.  Long  shallow  cuts 
are  generally  a  mistake  of  judgment.  The  grade  should  rather  be  broken 
and  thrown  up  into  fill.  As  a  rule,  apices  in  grade-lines  should  never 
meet  on  a  fill  nor  a  hollow  in  them  appear  in  a  cut,  since  the  extra  depth 
of  the  cut  or  height  of  the  fill  is  so  much  work  thrown  away  in  order  to 
do  a  bad  thing — bring  grade-lines  to  a  sharp  intersection  ;  but  there  are 
exceptions  as  respects  fills,  when  it  is  desirable  (as  it  always  is)  to  give 
abundant  water-way  for  streams  without  carrying  the  whole  fill  on  too 
high  a  bank.  It  is  a  common  error  of  inexperienced  projectors  to  lay 
the  grade-line  too  near  to  the  supposed  high-watermark.  It  is  not  worth 
while  to  take  chances,  and  it  should  be  several  feet  above  all  the  ap- 
parent possibilities. 

1253.  It  is  always  desirable,  except  on  steep  side-hills,  to  have  the 
fills  exceed  the  cuts.  Heavy  fills  can  be  gotten  at  from  a  good  many 
points,  or  temporarily  trestled  and  filled  by  train,  but  large  cuts  are  very 
apt  to  delay  progress  (they  are  generally  the  last  work  finished),  and  give 
trouble  for  maintenance  later.  Long,  low  fills  should  never  be  laid  out 
to  average  less  than  two  *feet  high.  The  temporary  economy  is  a  dear 
one.  Grades  can  in  general  be  laid  out  just  as  well  as  not  at  some  even 
rate  and  starting  from  some  even  station,  but  the  trouble  often  taken  to 
this  end  is  perhaps  rather  worse  than  thrown  away,  as  it  is  a  simple 
matter  to  compute  the  grade  elevations,  and  economy  is  very  apt  to  be 
sacrificed  to  no  real  advantage.  Full  allowance  for  vertical  curves  should 
be  made  as  the  work  progresses  and  the  grades  for  stations  carefully 
looked  after,  especially  in  projecting  long  grades.  Table  125,  page  388, 
will  facilitate  doing  so.  The  original  grades  should  be  studied  over  and 
revised,  aided  by  the  cross-sections  of  the  final  location.  It  is  costly 
business  to  attempt  to  make  the  latter  without  accurate  knowledge  of  the 
material  under  the  surface,  but  this  trouble  is  too  frequently  not  taken. 
Simple  boring  and  drilling  appliances  for  investigating  the  material  now 
exist  in  plenty,  and  the  expense  is  very  slight.  Whenever  and  wherever 
there  is  danger  of  striking  rock  beneath  the  surface,  there  is  little  excuse 
for  not  determining  its  depth  and  limits,  as  it  can  often  be  avoided  with 
ease. 

1254.  Provided  with  the  profile  and  field-notes  of  the  paper  location 
the  final  location  is  proceeded  with.  The  profile  is  kept  close  up  to  the 
transit,  and  the  precision  of  the  work  as  compared  with  the  projection 
checked  mainly  by  it.     A  few  tie-notes  with  the  preliminary  are  usually 


894  CHAP.  XXXII.— PROJECTING  LOCATION. 

taken  off  for  each  day's  work,  but  it  is  not  worth  while  to  attach  much 
weight  to  them.  The  question  is  only :  Does  the  line  as  run  on  the 
ground  give  as  good  a  profile  as  was  expected  and  desired,  and  can  any 
improvements  be  made  in  it  ?  That  chief  of  party  is  not  a  very  good  one 
who  will  not  see  many  improvements  as  he  progresses.  Aided  by  the 
system  of  transition  curves  referred  to  in  the  previous  chapter,  these 
changes  are  rapidly  made;  but  if  there  be  any  doubt  at  all  about  them, 
they  should  be  left  for  a  later  revision.  In  fact,  the  better  way  is  always 
to  run  the  whole  location  over  twice  (par.  1193).  The  money  spent  will 
be  well  invested. 


CHAP.  XXXIII.— THE   ESTIMATION   OF  QUANTITIES.     895 


CHAPTER  XXXIII. 

THE    ESTIMATION    OF    QUANTITIES. 

1255.  The  purpose  of  preliminary  estimates  is,  first,  to  arrive  at  an 
approximate  idea  of  the  cost  of  the  work ;  seco7idly,  to  compare  alternate 
lines  together;  and  thirdly,  to  assist  in  fixing  the  grades.  For  neither  of 
these  purposes  is  any  great  exactitude  necessary,  especially  if  there  is 
certainty  of  having  the  quantities  at  least  large  enough.  For  estimating 
the  cost  of  the  work  an  excess  of  two  or  three  per  cent  is  rather  an  ad- 
vantage. For  comparing  alternate  lines  the  error,  whatever  it  is,  will 
make  no  difference  unless  there  are  causes  why  it  should  exist  on  one 
line  and  not  on  the  other.  For  fixing  grade-lines  a  slight  percentage  of 
error  is  equally  unimportant,  since  it  is  rarely  good  engineering,  under 
modern  methods  of  construction,  to  attempt  any  very  exact  balance  of 
cut  and  fill,  the  fill  being  ajways  laid  out  in  excess,  and  long  cuts  avoided 
as  much  as  possible.  The  only  exceptions  to  this  rule  are  when  both  the 
cuts  and  fills  are  short  and  heavy,  so  that  the  haul  will  not  be  long,  or 
on  a  steep  side-slope,  so  that  throwing  the  line  in  to  decrease  the  ci/ts 
will  increase  the  fills,  or  vice  versa.  Even  then  the  possibility  of  using 
temporary  or  permanent  trestles,  the  size  of  water-ways  required,  and  the 
differences  in  classification  will  ordinarily  have  more  effect  on  where  the 
line  is  laid  than  the  mere  question  of  balancing  the  profile. 

1256.  For  these  reasons  it  is  an  absurd  waste  of  time  to  use  the  pris- 
moidal  formula,  or  any  other  method  but  that  of  averaging  end-areas, 
for  making  preliminary  estimates,  and  this  method  should  be  used  in  the 
simplest  way  of  all — that  of  determining  centre-heights  directly  from  the 
profile,  unless  the  ground  is  quite  rough  and  irregular.  In  that  case, 
especially  if  the  material  be  rock,  plotted  cross-sections  may  appear 
desirable. 

In  working  merely  from  the  profile  centre-heights,  without  taking  the 
trouble  to  compute  them,  there  is  a  certain  lack  of  precision  which  on  an 
individual  solid  may  introduce  a  considerable  error,  but  we  introduce  no 
ieiidency  to  error  in  either  direction.  Our  readings  are  as  likely  to  be 
too  great  as  too  small,  and  when  that  is  so  we  know  from  the  theory  of 


Sg6.   CHAP.  XXXIII.— THE   ESTIMATION  OF   QUANTITIES. 

probabilities  that  if  the  average  error  on  each  individual  solid  be  i,  with 
no  tendency  to  either  excess  or  deficit,  the  probable  net  error  per  solid 
on  looo  such  solids  will  be  only  0.0316  cubic  yards,  and  on  10,000  solids 
only  o.oi  cubic  yards.  Thus  there  is  no  real  objection  to  working  from 
a  well-made  profile  for  any  preliminary  purpose. 

1257.  The  nature  of  the  error  in  the  method  of  computing  by  averag- 
ing end-areas  is  this  :  The  error  increases  as  the  square  of  the  difference 
in  centre-height,  and  is  not  in  the  least  affected  by  the  absolute  volume 
of  the  solid.  The  heavier  the  work,  therefore,  or  the  less  the  sudden 
changes  of  profile,  the  less  the  proportionate  error.  That  cut  is  an 
unusual  one  in  which  the  error  is  more  than  5  per  cent,  and  that  section 
of  road  would  be  very  unusual  on  which  the  error  was  more  than  i  per 
cent,  and  this  error  is  always  in  excess.  There  are  indeed  certain  pos- 
sible solids  in  which  the  error  will  be  in  deficiency,  and  certain  others 
(those  whose  width  on  top  is  the  same  while  the  centre-heights  differ,  or 
vice  versa)  in  which  the  end-area  method  is  precisely  correct,  while  cer- 
tain methods  by  the  prismoidal  formula  which  appear  much  more  exact 
will  give  a  deficiency ;  but  except  on  perhaps  one  solid  in  a  thousand, 
averaging  end-areas  always  gives  an  excess  of  volume. 

1258.  All  methods  of  computing  volume  by  first  transforming  the 
end  sections  into  equivalent  level-sections  introduce  a  constant  tendency 
to  deficiency,  and  for  that  and  other  reasons  are  a  worse  than  useless 
labor,  far  simpler  methods  giving  a  more  accurate  result.  The  proper 
method  of  computing  earth-work  in  construction  is  to  compute  by  end- 
areas  only,  and  then  at  any  later  time  when  convenience  serves,  to  deter- 
mine prismoidal  corrections  for  those  solids  which  need  it  only,  which 
are  those  differing  by  more  than  two  or  three  feet  in  centre-height. 
These  corrections  are  then  added  together  for  each  cut  or  section  and 
deducted  in  gross  from  the  end-area  volume.  The  reasons  which  make 
this  method  at  once  the  simplest  and  the  most  accurate  of  all,  and  the 
evidence  from  experience  that  it  is  so,  are  given  at  length  in  the  writer's 
treatise  on  the  computation  of  earth-work,  referred  to  elsewhere  in  this 
volume,  and,  so  far  as  he  knows,  are  given  nowhere  else. 

1259.  In  computing  quantities  from  profiles  for  preliminary  purposes 
the  cut  or  fill  should,  as  a  rule,  be  assumed  to  terminate  at  the  nearest 
hnlf-station  to  where  it  actually  does  terminate,  as  shown  in  Fig.  300^ 
whether  its  actual  length  be  a  little  more  or  less.  This  introduces 
another  element  of  slight  uncertainty,  but  it  is  justified  by  the  fact^ 
which  it  is  sometimes  difficult  for  young  engineers  to  realize,  that  the 
end  of  a  cut  makes  a  very  small  part  of  its  total  volume,  so  that  very 


CHAP.  XXXIII.—  THE  ESTIMATION   OF   QUANTITIES.     897 


Fig.  300. 
[Showing  the  manner  in  which  a  profile  cut  is  assumed 
to  be  transformed  into  equivalent  prisms  in  making  pre- 
liminary estimates.] 


trifling  errors  in  the  centre-heights  at  the  middle  of  the  cut  will  have  far 

more  effect.     Moreover,  as  the  error  is  as  likely  to  be  one  way  as  another, 

it  v/ill  be  in  the  end  com- 
pensatory, and  no  good  end 
will  be  attained  from  the 
considerable  extra  labor  of 
taking  account  of  such  de- 
tails, unless  the  material  is 
rock,  and  not  always  then, 
except  in  the  final  adjust- 
ment of  the  line. 

The  centre-heights  are 
then  read  off  at  each  sta- 
tion and  the  corresponding 
quantities  determined.  This 
is  in  effect  equivalent  to 
assuming  that   the    actual 

solid  in  Fig.  300  may  be  transformed  into  the  series  of  prisms  bisected 

by  the  dotted  lines. 

1260.  It  is  not  usual  nor  necessary,  in  preliminary  estimates  of  earth, 
to  make  any  part  of  the  estimate  for  fractional  stations.  When  neces- 
sary it  is  allowed  for  by  taking  the  centre-heights  a  little  higher  or  lower, 
as  is  also,  in  fact,  any  excess  or  deficiency  in  the  length  of  the  end-  sec- 
tion. In  this  way,  with  a  little  practice,  closely  approximate  results  to 
what  the  most  careful  work  will  give  can  be  readily  obtained.  There 
can  be  no  better  practice  for  the  student  than  to  determine  this  practi- 
cally. 

1261.  One  source  of  error  must  be  allowed  for  when  it  exists,  however 
—the  SURFACE  SLOPE.  This  may  be  done  either  by  using  a  coefficient 
to  multiply  the  quantities  when  obtained,  or  by  working  from  a  diagram, 
like  those  devised  by  the  writer,  which  give  quantities  at  once  for  any 
surface  slope.  When  the  surface  slope  is  level  or  under  10°,  a  table  of 
level-section  quantities  may  be  conveniently  used,  or,  still  better,  plotted 
as  a  diagram,  as  in  those  of  the  writer,  and  the  successive  quantities 
taken  off  by  an  odometer  or  on  a  strip  of  paper.  The  trouble  and  chance 
of  error  in  addition  is  thus  saved. 

1262.  In  ROCK-WORK,  or  wherever  these  methods  are  not  accurate 
enough,  by  far  the  better  way  is  to  plot  the  surface,  draw  in  the  road-bed 
and  slopes  with  a  template,  and  determine  the  areas  with  a  planimeter, 
which  is  a  very  rapid,  simple,  and  accurate  method.     Before  the  final 

57 


898     CHAP.  XXXIII.  — THE   ESTIMATION  OF   QUANTITIES. 

location  is  regarded  as  complete,  it  is  in  every  way  desirable  that  such 
sections  should  be  plotted  complete  for  the  entire  line  and  carefully 
studied. 

1263.  Culverts. — It  is  always  a  mistake  to  make  separate  estima- 
tions of  each  of  the  minor  masonry  structures.  It  is  but  two  or  three 
hours'  work  to  construct  a  diagram  on  a  single  sheet  of  cross-section 
paper,  which  will  enable  the  quantities  for  any  standard  type  of  culvert 
to  be  read  off  at  once  for  any  given  centre- height,  to  a  tenth  of  a  cubic 
yard  if  desired,  but  the  nearest  cubic  yard  is  sufficiently  precise  for  the 
requirements.  The  surface  slopes  would  make  a  material  difference 
with  the  length  of  these  structures,  except  that  when  the  surface  slope 
is  steep  it  is  rarely  good  practice  to  lay  a  culvert  in  the  deepest  hollow 
of  a  gulch.  It  may  usually  be  placed  somewhat  higher  and  at  one  side, 
and  often  well  up  toward  sub-grade,  with  very  great  advantage  and 
economy,  the  only  important  point  being  to  absolutely  secure  the  lower 
end  of  the  cwlvert  against  wash,  which  is  readily  done.  Therefore,  if  a 
culvert  be  taken  as  the  equivalent  of  one  under  the  deepest  centre  fill 
with  a  level  surface  slope,  it  will  ordinarily  be  sufficient.  If  not,  it  can  be 
taken  as  much  deeper  as  seems  necessary. 

1264.  To  construct  the  diagr'am,  the  volume  of  any  box  or  arch  cul- 
vert whatever  (assmmi-ng  it  to  be  level)  is  expressed  by  the  equation 

in  which  //"  =  the  centre  height,^/=  a  coefficient  depending  on  the 
cross-section  of  the  main  body  of  the  culvert,  and  C=  a  constant  (which 
may  be  either  plus  or  minus),  which  includes  the  modifying  effect  on 
volume  of  the  ends  of  the  culverts.  To  substitute  actual  values  in  the 
equation  for  any  given  type  of  culvert :  Compute  its  volume  complete 
with  an  average  depth  of  foundation,  under  any  height  of  fill  from  the 
natural  surface — say  10  feet.  Compute  also  the  addition  to  its  volume 
by  lengthening  it  3  feet  (with  \^  to  i  side  slopes),  or  by  whatever  other 
length  is  added  to  the  culvert  by  increasing  the  fill  i  foot.  We  then 
have  values  of  v,f,  and  HXo  substitute  in  the  equation,  and  C  can  be  de- 
termined at  once. 

Such  a  diagram  has  another  value  than  merely  to  save  labor.  It  keeps 
before  the  mind  the  proportionate  quantities  in  culverts  of  different  sizes, 
although  if  this  should  lead  to  using  smaller  ones  it  would  ordinarily  be 
unfortunate.  No  dry  work  should  be  estimated  for  if  cement  is  reason- 
ably accessible.     It  is  costly  economy. 

1265.  Bridge  Piers. — Any  bridge  pier  may  be  resolved  into  certain 


CHAP.   XXXIII.— THE  ESTIMATION  OF  QUANTITIES.     899 

parts  independent  of  height ;  a  rectangular  sohd  varying  directly  with 
height,  and  a  pyramid  or  cone.  In  other  words,  its  equation  of  volume 
is  of  the  form 

v=fH+f'H'  +C, 

with  values  of  letters  as  above.  Numerical  values  may  likewise  be  deter- 
mined in  the  same  way.  With  a  batter  of  i  inch  per  foot,  the  value  of 
/',  for  volumes  in  cubic  yards,  will  be  only  .00103.  For  a  pier  10  ft.  high 
this  gives  1.03  cubic  yds.  as  due  to  the  batter ;  for  a  pier  100  ft.  high,  1030 
cubic  yards. 

1266.  Bridge  abutments  and  open  culverts  may  have  their 
volume  expressed  for  constructing  a  diagram  in  precisely  the  same  way, 
as  may  also  pile  or  other  foundations.  It  may  not  save  any  great  amount 
of  labor  to  do  this,  but  it  does  furnish  a  check  against  errors  in  single 
computations,  and  is  information  which  it  is  very  convenient  to  have 
ready  for  instant  reference. 

1267.  Wooden  trestles  are  cheap  affairs.  The  effort  should  be  to 
estimate  them  liberally,  but  it  is  quite  unnecessary  in  a  preliminary  esti- 
mate to  waste  time  on  a  careful  design,  merely  for  the  purpose  of  getting 
quantities. 

In  any  wooden  trestle,  the  caps  and  all  the  floor  system  above  it,  as 
also  the  minimum  length  of  sill  and  all  wooden  parts  below  it,  are 
directly  as  the  length  of  the  structure  and  independent  of  its  height. 
The  same  is  true  of  the  cost  of  digging  foundations,  and  the  piling  or 
masonry  if  used  (as  one  or  the  other  always  should  be). 

At  a  certain  distance  below  the  cap,  say  10  feet,  there  is  a  system  of 
longitudinal,  transverse,  and  diagonal  ties  and  sway- brace  running  the 
entire  length  of  the  structure  on  a  line  about  10  feet  below  the  caps,  and 
(constructively)  a  certain  addition  to  the  length  of  the  sill.  All  this  may 
be  expressed  at  so  much  per  lineal  foot  on  a  horizontal  line  10  feet  below 
the  grade-line. 

Ten  feet  farther  down  there  is  a  similar  system,  nearly  duplicating  the 
first,  but  a  little  larger,  which  may  be  all  expressed  at  so  much  per  lineal 
foot  on  a  horizontal  line  20  feet  (or  whatever  the  distance  may  be)  below 
the  grade-line. 

So  we  may  proceed  until  we  have  provided  for  the  highest  trestles 
likely  to  occur  on  the  line  of  the  given  type,  and  we  shall  have  expressed 
the  feet  board  measure  in  any  width  in  an  equation  of  the  following 
form : 

Ft.  B.  M.  =fL  +fL'  +f"L"  -h  etc., 


900     CHAP.  XXXIII.— THE   ESTIMATION  OF  QUANTITIES. 

in  which  L,  L',  L"  —  the  respective  lengths  of  the  structure  on  the 
grade-hne  and  on  parallel  lines  lo,  20,  30  feet,  etc.,  below  it,  and /,/',/"= 
the  corresponding  measurement  per  lineal  foot. 

1268.  The  length  of  each  of  these  lines  below  the  grade-line  ought,  in 
theory,  to  be  measured  a  little  short  on  the  profile  to  allow  for  any  bents 
which  may  extend  below  one  system  and  not  quite  down  to  another,  but 
such  nicety  may  be  neglected.  At  the  bottom  of  the  trestle  there  will 
be  an  irregular  area  of  greater  or  less  extent.  To  include  this  in  the 
estimate,  transform  it  by  eye  into  a  rectangle  10  feet  high  and  of  equal 
area.  Any  one  familiar  with  the  construction  of  trestles  will  do  this 
with  great  accuracy;  and  the  results  of  this  method,  in  which  no  account 
is  taken  of  the  particular  number  or  position  of  bents,  come  surprisingly 
close  to  the  ultimate  measurement,  as  the  writer  has  tested  on  many 
structures. 

1269.  Trestles  should  invariably  be  built  with  side  stringers  and  ties 
about  12  ft.  long,  capped  with  a  guard  rail,  as  a  safeguard  against  de- 
railed trains,  foot-passengers  caught  on  the  structure  by  a  train,  and  the 
insidious  effect  of  decay,  as  well  as  for  its  material  addition  to  the  strength 
of  the  structure  even  when  new.  "  Split  "  stringers,  breaking  joints  with 
each  other,  are  invariably  used  in  good  practice,  and  split  caps  and  sills 
boxed  into  the  posts  and  bolted  through  make  a  far  stiff er,  better,  and 
more  easily  renewable  structure  than  the  common  form  of  mortise 
joints.  "  Cluster-bent"  trestles  made  of  8  x  8  inch  timber  are  the  best 
for  high  structures. 

The  ends  of  all  trestles  and  bridges  should  be  protected  by  Latimer's 
rerailing  safety  frogs,  a  cheap  cast-iron  watchman  which  may  be  relied 
upon  to  put  derailed  wheels  back  upon  the  track,  if  not  too  far  displaced, 
as  has  been  proven  by  many  instances. 

1270.  Iron  Trestles. — Iron  trestles  may  be  estimated  in  much  the 
same  way  as  wooden  trestles,  and  it  is  of  practical  value  to  do  so  to 
bring  out  how  little  the  height  of  trestles  has  to  do  with  their  weight  or 
cost, — a  fact  which,  if  it  be  fully  realized  and  taken  advantage  of,  may 
often  be  an  immense  assistance  in  obtaining  a  favorable  line,  by  enabling 
it  to  be  carried  high  above  what  are  apt  to  be  the  most  serious  obstacles — 
the  deep  gorges. 

Iron  trestles,  for  some  occult  reason,  are  usually  planned  for  bents  30 
feet  apart,  each  successive  pair  of  bents  being  braced  together  into  a 
kind  of  pier.  Sometimes  the  intermediate  spans  are  made  45  or  60  feet, 
and  occasionally  the  bents  are  60  feet  apart,  continuously.  Sometimes 
the  intermediate  spans  are  mcreased  to  100  or  more  feet. 


CHAP.  XXXIII.— THE   ESTIMATION  OF  QUANTITIES     9OI 

1271.  However  these  details  are  varied,  there  is  wonderfully  Httle  dif- 
ference in  the  total  weight  of  the  structure,  which  usually  comes  out  much 
the  same,  barring  a  slight  percentage,  as  if  the  simple  type  of  30-foot  bents 
had  been  used  throughout.  What  is  gained  in  the  bents  is  lost  in  the 
floor-system,  or  vice  versa.  This  is  strikingly  illustrated  even  in  so  widely 
different  a  structure  from  the  ordinary  trestle  as  the  Kentucky  River 
bridge.  The  total  weight  of  iron  corresponds  very  closely  with  what 
would  have  been  required  to  cross  the  gorge  with  a  trestle  with  30-ft. 
bents — not  equally  safe  by  any  means,  but  of  the  same  average  weight 
per  lineal  and  vertical  foot  as  in  the  minor  structures  on  the  same  road, 
built  to  sustain  the  same  rolling  load  ;  so  that  in  estimating  structures 
for  large  and  small  gorges,  by  the  same  rule,  we  do  not  go  far  astray. 

1272.  This  fact  has  led  Mr.  Geo.  H.  Pegram  to  propose  the  following 
formula  for  the  weight  of  iron  trestles,  which  he  states  that  he  has  found 
to  give  close  results  when  tested  on  a  considerable  number  of  actual 
•structures  : 

IVt.  in  lbs.  =  (3Z  +  2//)  no  for  Mogul  engines  and  1820  lbs.  per  ft.; 
in  which  Z  =  the  total  length  of  the  structure  between  centres  of  end- 
pins  and  11=:  the  sum  of  the  total  bent  weights  from  top  of  masonry 
pedestal  to  top  of  columns,  taken  as  30  feet  apart,  whatever  they  may 
actually  be.  For  Consolidation  engines  we  may  take  IV={;^L  +  2II) 
125  to  130. 

These  formulae  give  the  total  shipping  weight  of  iron,  and  will  ordi- 
narily approximate  within  5  to  10  per  cent.  They  will  be  most  in  error 
(too  small)  for  very  large  structures. 

1273.  To  this  estimate  is  to  be  added  the  timber-floor  system  and  the 
pedestals.  The  pedestals  are  usually  of  the  best  quality  of  cut  stone 
masonry,  and  on  the  Cincinnati  Southern  Railway,  where  all  such  details 
were  ver}'-  carefully  looked  after,  averaged  1.6  cubic  yards  per  lineal  foot  of 
trestle  and  ranged  from  4  to  8  ft.  high,  above  the  natural  surface.  The 
floor  system  is  readily  estimated  according  to  the  design  adopted,  which 
should  include  plenty  of  timber. 

On  the  Cincinnati  Southern  Railway  (Mogul  rolling-load,  which 
proved  too  small  almost  before  the  road  was  opened)  the  average  con- 
tract prices  for  viaducts  were  $25  per  foot  horizontal  and  $10  per  foot 
vertical,  including  the  floor.  Adding  to  this  the  cost  of  masonry  pedes- 
tals, we  have,  by  a  similar  method  of  estimation  to  that  recommended 
for  wooden  trestles  : 

Per  foot  horizontal  at  grade-line $40  00 

Per  foot  horizontal  at  intervals  of  lo-ft.  below  grade... .         3  33 


902     CHAP.  XXXIII.— THE  ESTIMATION-  OF  QUANTITIES. 


1274.  We  may  see  from  this   method   of  expressing  the  cost  more 
clearly  than  otherwise  how  little  the  height  of  trestles  has  to  do  with 


^^J9522__^^RAIN  OF  BOX  CARS 
FoTl-RAIN  OF  COAL  URS 


-wwc 


Fig.  301.— Main  Pier  of  Niagara  Cantilever  Bridge,  showing  the  Slight  Effect  of 
Height  on  the  Total  Cost  of  the  Structure. 

TOTAL  WEIGHT  OF  STRUCTURE. 

Span,  248  ft.  (2920  lbs.  per  ft.), 724,000  lbs. 

Pier,  130  ft.  4  in.  (1304  lbs.  per  ft.), 170,000   " 


Total  of  pier  and  cantilever  span,        894  000  lbs. 

Additional  per  ft.  extra  height,  about, I'coo  "  * 

or  \  of  one  per  cent.  *     '  ' 


CHAP.   XXXIII.— THE  ESTIMATION   OF  QUANTITIES.     903 

their  cost.  Singularly  enough,  it  appears  from  comparisons  of  the  con- 
tract prices  on  that  road  that  it  has  more  effect  on  the  cost  per  foot 
horizontal  than  per  foot  vertical,  which  latter  were  very  little  affected ; 
in  part,  no  doubt,  because  erection  is  much  more  expensive  per  pound 
with  low  trestles.  Fig.  301  will  show  how  little  the  height  has  to  do  with 
the  cost  of  even  the  largest  structures. 

T275i  It  is  probable  that  pedestals  of  very  superior  concrete  would  be 
cheaper  as  well  as  better  than  masonry.  One  difficulty  in  the  use  of  concrete, 
which  is  a  very  serious  one  with  masonry  also,  is  that  under  the  usual  form  of 
contract  the  contractor  furnishes  his  own  cement.  He  is  therefore  under  a  con- 
stant temptation  to  skimp  the  work  in  that  vital  detail,  both  in  quantity  and 
quality.  The  true  way  is  for  the  company  to  purchase  its  own  cement,  furnish 
it  to  the  contractor  liberally,  and  require  him  to  use  it  so.  He  will  then  be  as 
anxious  to  make  the  work  good  in  that  respect  as  he  is  now  to  make  it  poor. 
Much  dispute  and  inspecting  annoyances  will  thus  be  saved,  the  cost  of  the 
work  little  if  any  increased,  and  its  quality  materially  benefited. 

1276.  Bridges. — In  Fig.  247,  page  767,  there  has  already  been  given 
a  diagram  prepared  by  the  writer,  mainly  from  the  formulae  determined 
by  George  H.  Pegram,  C.E.,  and  given  in  a  paper  before  the  American 
Society  of  Civil  Engineers.  In  addition  to  what  is  stated  in  connection 
with  the  diagram,  it  may  be  added  that  the  West  Shore  specifications 
called  for  rolled  I-beams  up  to  20  ft.  span,  plate  girders  from  20  to  50 
feet,  lattice  girders  from  50  to  75  ft.,  and  thereafter  pin-connected  trusses. 
There  was  naturally  a  slight  jump  in  passing  from  one  to  another.  The 
weights  of  bridges  of  various  spans  were  computed  to  be  of  first-class 
construction,  without  any  additions  of  doubtful  utility,  so  that  while  a 
bridge  might  weigh  more  than  that  given  through  some  special  excel- 
lence, it  should  not  weigh  much  less.  The  following  are  the  formulae 
deduced  by  Mr.  Pegram,  in  all  of  which 
S  —  the  span  centre  to  centre  of  bed-plates  or  end-pins,  as  the  case 

may  be. 
W  =  the  total  or  "  shipping"  weight  of  iron  or  steel  in  pounds. 

For  iron  bridges  under  200  ft.  span  : 

in  which 

a  =    7  for  Class  T,  Fig.  248,  page  769. 

a  =    9  for  Class  C, 

a  —  \2  for  Class  M,         "  " 

For  Class  N,  three  fourths  of  the  weight  as  given  for  Class  T  was 
taken — a  very  rough  process. 


904     CHAP.  XXXIII.— THE   ESTIMATION   OF  QUANTITIES. 

I 

For  irofi  bridges  over  200  ft.  span  :  1 

^=(5  +  1)^'- 

in  which 

^  =  100  for  Class  C, 

^  =    80  for  Class  T. 
For  steel  bridges  over  300//.  spa7t: 

W  =  cS\ 
in  which 

c  =  6  for  Class  C, 

•     c  =  6.7  for  Class  T. 

1277.  The  type  of  bridge  assumed  was  as  follows  : 

For  spans  below  75  ft. :  deck-plate  girder  bridges,  8  ft.  wide,  con- 
nected with  angle-iron  bracing,  and  with  cross-ties  resting  on  the  top 
chords. 

Above  75  ft.  up  to  150  ft.:  through -truss  bridges,  Pratt  or  single 
quadrangular  trusses. 

Over  150  ft.:  Whipple  or  double  quadrangular  trusses. 

The  widths  assumed  were:  For  standard-gauge  spans  under  255  ft., 
14  ft.  in  the  clear;  for  320-ft.  span,  18  ft.  centre  to  centre  of  trusses; 
for  420-ft.  span,  21  ft.  centre  to  centre,  and  for  520-ft.  span,  25  feet  centre 
to  centre.  The  floors  of  the  spans  consisted  of  cross  floor-beams  at  the 
panel  points,  with  a  line  of  iron  stringers  under  each  rail,  except  for  spans 
over  300  ft.,  which  had  three  lines  of  stringers. 

Differences  in  depth  affect  the  weight  less  than  would  be  supposed. 
Thus  in  a  6o-ft.  girder  span,  for  Class  T,  the  difference  in  total  weights 
between  depths  of  5  ft.  and  $^  ft.  was  practically  nothing,  and  for  an 
8o-ft.  girder  span,  calculated  for  Class  C,  with  depths  of  6  ft.,  6|-  ft.,  and 
7  ft.,  the  difference  was  less  than  i  per  cent.  In  a  i8o-ft.  truss  span,  the 
difference  in  weights  between  depths  of  26  and  28  ft.  was  less  than  2  per 
cent. 

In  a  520-ft.  steel  span,  for  Class  T,  the  difference  in  weight  between  a 
depth  of  50  ft.  and  one  of  58  ft.,  was  about  3  per  cent. ;  a  depth  of  56  ft. 
was  finally  taken  in  this  case. 

1278.  Modifications  for  other  conditions  than  those  specified  may  be 
made  as  follows : 

If  wooden  stringers  are  used,  deduct  195  lbs.  per  ft.  for  Classes  M.and 
C,  210  lbs.  for  Class  T,  and  140  lbs.  for  Class  N. 

For  safety  stringers  add  100  lbs.  per  ft.  for  all  classes. 


CHAP.  XXXIII.  — THE   ESTIMATION   OF   QUANTITIES     905 

For  deck-truss  bridges  add  10  per  cent,  and  for  double-track  bridges 
90  per  cent,  to  the  formula  weight. 

Through-plate  girder  bridges  will  not  differ  materially  from  deck 
bridges  in  weight,  where  the  cross-ties  are  made  to  serve  as  floor  beams. 
When  an  iron  stringer  floor  is  used,  it  will  be  a  close  approximation  to 
add  200  lbs.  per  foot  to  the  weight  given  by  the  formula. 

For  bridges  of  less  than  150  ft.  span,  the  only  part  of  the  rolling  load 
which  affects  the  weight  of  the  bridge  greatly  is  the  engine  load.  For 
spans  of  over  200  or  250  ft.,  an  average  of  the  engine  and  car-load  per 
foot  will  come  nearer  to  expressing  the  ratio  by  which  the  weight  of  the 
bridge  is  affected. 

1279.  The  weight  of  a  drawbridge,  including  turn-table,  wheels  and 
machinery  to  turn  by  hand,  will  be  very  nearly  the  same  as  for  a  fixed 
span  of  the  same  total  length  to  carry  the  same  live  load.  This  rule  is 
stated  by  Mr.  Pegram  to  have  been  remarkably  exact  in  tests  on  a  num- 
ber of  drawbridges  of  150  to  400  feet,  both  single  and  double  track. 

1280.  The  cost  of  bridges  per  pound  is  far  from  fixed  for  all  classes 
of  structures,  but  may  be  said  to  be  made  up  as  follows : 

Cts.  per  lb 

1.  Raw  material,  rolled  and  plate  iron 2^  to  3 

2.  Work  on  same  in  shop f  to  i^ 

3.  Transportation  by  rail i  to    ^ 

4.  Falseworks  and  erection i  to  i 

q.  Profit  and  administration , -i-  to  ij 

Total 4    to  7 

The  lowest  of  these  prices  are  sometimes  cut  under,  especially  in  dull 
times  and  for  large  orders  of  a  simple  class  of  work.  For  example,  on 
the  Manhattan  Elevated  Railway,  involving  immense  weights  of  a  very 
simple  class  of  work,  contracts  were  let  at  2  to  3  cents  per  pound,  while, 
on  the  other  hand,  fat  contracts  at  much  higher  rates  than  those  given 
above  are  not  uncommon  ;  but  these  are  fair  averages  for  average  work 
in  moderately  good  and  bad  times. 

It  will  be  seen  that  only  items  i  and  3  above,  and  not  always  even 
those,  increase  directly  with  the  weight  of  the  bridge.  We  may  say  in  a 
general  way  that  10  per  cent  increase  in  weight,  with  its  several  times 
greater  increase  in  safe  rolling  load,  will  mean  not  more  than  5,  or  at 
most  6,  per  cent  in  the  cost  of  the  bridge  to  the  company,  and  propor- 
tionately for  greater  or  less  differences  of  weight. 


906      LHAP.    XXXIII.— THE  ESTIMATION  OF  QUANTITIES. 

1281.  Station  buildings,  yards,  track  and  track-laying,  and  many  other 
minor  details  of  construction,  must  likewise  be  included  in  any  complete 
estimate,  but  to  consider  them  here  would  lead  us  too  far  from  our  sub- 
ject, which  has  had  to  do  with  those  details  only  which  are  connected 
with  and  affected  by  the  location  of  the  road. 

In  all  such  details,  it  has  been  intended  to  go  far  enough,  and  not  too 
far,  to  at  least  fairly  prepare  the  patient  reader  to  make  a  decent  approxi- 
mation to  the  true  economy  of  alignment.  To  do  more  than  this  can 
only  be  a  happy  accident  with  any  one.  To  do  less  than  this  the  writer 
hopes  he  may  have  rendered  unnecessary.  He  has  not  spared  his  own 
labor  to  do  so,  and  for  wherein  he  may  have  fallen  short  he  can  only  say 
with  the  heroine  of  "  A  Winter  s  Tale  :  I  speak  as  my  understanding 
instructs  me,  and  as  mine  honesty  puts  it  to  utterance.' 


APPENDICES. 


APPENDIX    A. 


EXPERIMENTS    ON    THE    RESISTANCES    OF    ROLLING-STOCK. 

[Made  by  the  author  on  the  Lake  Shore  &  Michigan  Southern  Railway,  at  Cleveland,  O.j 
June-July,  1878.    Abbreviated  from  Trans.  Am.  Soc,  C.  E.,  Feb.,  1879.] 

The  mode  of  test  was  by  what  may  be  termed  the  "drop  test;"  start- 
ing cars  from  a  state  of  rest  down  a  known  grade,  and  deducing  the 
resistances  from  the  velocity  acquired.  The  principle  of  this  method  has 
often  been  employed  before,  sometimes  merely  to  determine  comparative 
resistances,  without  attempting  to  measure  their  absolute  amount,  and 
sometimes  to  determine  a  single  average  resistance  from  the  average 
velocity  for  the  whole  descent.  In  the  present  tests  it  was  attempted, 
with  entire  success,  to  extend  this  method  to  the  determination  of  a  series 
of  successive  resistances  at  successive  points  (eleven  in  most  cases)  in  the 
path  of  the  vehicles,  during  which  their  velocity  varied  from  o  to  30 
miles  per  hour.  Great  accuracy  in  time  observations  was  necessary  for 
this  purpose,  which  was  fully  secured  by  the  aid  of  electricity,  so  fully, 
in  fact,  that  the  margin  for  error  in  the  latter  half  of  the  experiments 
is  hardly  more  than  -^  lb.  per  ton.  It  must  be  added,  however,  that 
about  half  the  tests  were  made  before  the  apparatus  was  fully  perfected, 
and  are,  hence,  less  minutely  accurate,  but  the  maximum  errors  in  these 
latter  can  hardly  exceed  ^  lb.  per  ton  in  any  case,  as  will  be  evident  from 
the  record  plates,  and  all  errors  of  any  kind  in  this  mode  of  test  are 
necessarily  compensatory,  any  excess  in  one  resistance  causing  a  corre- 
sponding deficiency  in  the  succeeding  one,  and  vz'ce  versa. 

It  is  believed  that  equal  accuracy  is  unattainable  by  any  other  mode 
of  test,  since  it  is  plain  that  every  step  in  this  process  is  free  from  any 
sensible  source  of  error  other  than  carelessness.  The  accelerating  force 
(gravity)  is  uniformly  applied,  and  exactly  known  from  formulae,  without 
measurement.  This  force  is  necessarily  all  consumed  (i)  in  overcoming 
the  resistances  to  be  measured,  or  (2)  in  communicating  velocity.  The 
amount  of  force  represented  by  a  given  velocity  is  known  by  formulae, 
without   measurement,  and    the  velocity   itself   is   exactly   recorded    by 


91 0  APPENDIX  A. 


electricity,  beside  a  synchronous  record  of  seconds,  from  which  intervals 
of  time  may  be  easily  read  off  to  -^  second.  Errors  from  carelessness 
in  computation  are  always  possible,  but  three  checks  existed  against  them: 
(i)  All  formulae  used  were  first  tabulated  by  "constant  differences  ;"  (2) 
most  of  the  resistances  were  computed  independently  by  two  distinct 
methods,  and  (3)  all  the  computations,  when  completed,  were  plotted 
on  the  record  diagrams  (Plate  IX.),  and  so  many  resistances  were  deter- 
mined for  each  test  at  gradually  increasing  velocities,  that  any  consider- 
able error  of  computation  revealed  itself  graphically.  Finally,  any  errors 
which  still  occur  are  not  cumulative,  any  excess  in  one  resistance  causing 
a  corresponding  deficiency  in  the  next  following,  and  vice  versa. 

The  tests  were  made  under  as  great  a  variety  of  conditions  in  respect 
to  load,  number  of  cars  in  a  train,  area  of  cross-section,  etc.,  as  it  was 
possible  to  secure  with  the  limited  time  at  command,  and  give  due  cer- 
tainty to  each.  This  variety  of  conditions  was  secured  in  order  to  facili- 
tate, as  far  as  possible,  one  of  the  objects  which  was  held  especially  in 
view,  viz.,  a  more  correct  separation  than  heretofore  of  the  aggregate 
resistance  from  velocity  only  (excluding  the  normal  axle-friction)  into  its 
constituent  elements,  air  resistance,  oscillatory  resistance,  etc.  This  ob- 
ject, it  is  thought,  has  been  quite  successfully  attained,  and  with  some- 
what surprising  results. 

[The  great  length  to  which  this  volume  has  grown  forbids  the  reproduction 
of  the  body  of  the  paper,  and  those  desiring  to  follow  it  are  referred  to  the 
paper  itself.  The  determination  of  the  possible  air  resistance  especially  is 
believed  to  have  been  sufficiently  exact  to  make  it  certain  that  it  has  less  effect 
on  the  movement  of  trains  than  is  commonly  supposed.  The  following  are  the 
conclusions  of  the  paper:] 

Summary. 

We  may  summarize  the  various  conclusions  reached  in  the  preceding 
paper  as  follows  : 

I  St.  The  axle  and  rolling  friction  of  empty  freight  cars  may  be  taken 
as  6  lbs.  per  ton  of  2000  lbs.  The  axle  and  rolling  friction  of  coaches 
and  loaded  freight  cars  may  be  taken  as  4  lbs.  per  ton.  The  fluctuations 
from  these  limits  are  small,  rarely  exceeding  i  lb.  per  ton  in  single  cars, 
or  i  to  ^  lb.  per  ton  in  a  train. 

2d.  The  initial  resistance  at  the  instant  of  starting  is  several  times 
greater  than  this,  and  greater  for  loaded  than  for  empty  cars,  being  at 
least  18  lbs.  per  ton  for  loaded  cars,  and  14  lbs.  per  ton  for  empty  cars, 
as  an  average,  but  fluctuating  considerably.  Its  amount  probably  varies 
with  the  length  of  stop,  according  to  unknown  laws. 


APPENDIX  A.  911 


3d.  Most  of  this  initial  resistance  is  almost  wholly  instantaneous,  and 
consumes  little  power.  Enough  of  it  still  remains,  however,  to  increase 
the  normal  axle-friction  in  the  first  few  car-lengths  by  at  least  2  lbs.  per 
ton.* 

4th.  The  air  resistance  against  such  a  surface  as  the  end  of  a  box  car 
(about  80  sq.  ft.)  is  less  than  \  lb.  per  square  foot  at  a  velocity  of  10  miles 
per  hour,  and  (presumably)  increases  as  the  square  of  the  velocity.  The 
current  estimates  of  this  resistance  (i  lb.  to  i  lb.  per  square  foot)  are 
erroneous  by  from  250  to  500  per  cent,  when  applied  to  surfaces  of  that 
size. 

5th.  About  two  thirds  of  the  velocity  resistance  proper,  excluding  the 
normal  axle-friction,  is  due  to  oscillation  and  concussion.  The  resistance 
due  to  this  latter  cause  alone  may  be  estimated  at  \  lb.  per  ton  at  a 
velocity  of  10  miles  per  hour,  varying  as  the  square  of  the  velocity. 

6th.  The  resistance  of  curves  decreases  materially  with  the  velocity, 
and  appears  to  be  greater  by  a  considerable  percentage  in  the  first  200  to 
500  feet  than  on  the  rest  of  the  curve. 

7th.  The  resistance  of  a  1°  curve  is  over  i  lb.  per  ton  at  a  velocity  of 
12  miles  per  hour,  and  decreases  to  about  \  lb.  per  ton  at  a  velocity  of 
22  miles  per  hour.  The  resistance  of  an  8°  curve  is  over  8  lbs.  per  ton  at 
a  velocity  of  9  miles  per  hour,  and  decreases  to  about  6\  lbs.  per  ton 
(probably)  at  a  speed  of  19  miles  per  hour. 

8th.  The  average  resistance  of  a  i''  curve  to  4-wheel  trucks,  having  a 
5-foot  rigid  wheel-base,  and  to  6-wheel  trucks  having  a  lof-foot  rigid 
wheel-base  (except  for  the  play  of  the  boxes  in  the  pedestal-jaws),  appear 
to  be  almost  identical. 

9th.  It  appears  possible  that  the  act  of  coupling  together  cars  by  a 
loose  link  slightly  decreases  the  axle-friction,  and  hence,  presumably 
the  oscillating  friction  at  high  velocities.  The  average  reduction 
observed  from  coupling  four  or  five  cars  together  appeared  to  be  as 
much  as  \  lb.  per  ton.  [The  tests  appeared  to  indicate  this,  but  the 
author  now  regards  it  as  very  doubtful.] 

loth.  There  appear  to  be  good  grounds  for  suspecting  that  a  slight 
superelevation  of  one  rail  on  a  tangent  may  have  the  effect  of  appre- 
ciably reducing  the  resistance  to  motion  even  at  velocities  of  ten  or 
twelve  miles  per  hour. 

*  This,  of  course,  does  not  include,  nor  in  any  way  refer  to,  the  additional 
power  demanded  to  get  up  speed,  which  is  2  lbs.  per  ton  to  give  a  speed  of  10 
miles  per  hour  in  3340  feet,  or  4.5  lbs.  per  ton  to  give  a  speed  of  15  miles  per 
hour  in  the  same  distance. 


912  APPENDIX  A. 


nth.  Roller-journals  of  various  forms  appear  to  be  very  effectual  at 
velocities  of  o  +,  tut  lose  nearly  all  their  theoretical  advantage  as  the 
velocity  increases.  Such  journals  appear  to  be  more  effective  as  the 
load  is  decreased,  and  reduce  the  resistances  of  empty  horse  cars  by 
about  one  half. 

1 2th.  Forty-two-inch  wheels  seem  to  be  even  more  effectual  than 
theory  would  indicate  in  reducing  extra  friction. 

13th.  The  equation  of  resistance  for  average  trains  (twenty  cars)  of 
loaded  box  cars  may  be  taken,  approximately,  as 


R  = +  4; 

130 

or,  for  trains  of  forty  empty  box  cars, 

i?  =  —-  +  6. 
106 

The  velocity  resistances  of  flat  cars  increase  somewhat  more  rapidly, 

being  for  twenty  loaded  flat  cars ,  and  for  forty  empty  flat  cars  -^— . 

These  formulae  are  believed  to  be  closely  approximate  up  to  velocities 
of  thirty  miles  per  hour.     No  tests  were  made  at  higher  velocities. 

14th.  The  coefficient  of  axle-friction  is  about  .02  for  loaded  freight 
cars  and  passenger  coaches  at  speeds  of  over  five  miles  per  hour,  about 
.03  for  empty  freight  cars,  about  .065  for  horse  cars,  and  about  .12  for 
freight  trucks  without  load.  The  coefficient  is  two  to  three  times 
greater  at  the  instant  of  starting.  It  decreases  rapidly  as  the  load  per 
journal  increases. 


APPENDIX  B.  913 


APPENDIX    B. 


EXPERIMENTS  WITH   NEW  APPARATUS  ON  JOURNAL-FRICTION 
AT    LOW  VELOCITIES. 

[A  Paper  by  the  author,  read  before  the  American  Society  of  Civil  Engineers,  June  4,  1884. 
Abbreviated  from  Trans.  Am.  Soc.  C.  E.,  Dec,  1884.] 

The  following  experiments  were  undertaken  by  the  writer  in  the  winter 
of  1878,  primarily  to  test  the  correctness,  especially  in  respect  to  initial 
friction  at  low  velocities,  of  a  series  of  other  tests  of  rolling-stock  resist- 
ances (see  Appendix  K.)  made  in  a  totally  different  manner,  on  the  Lake 
Shore  &  Michigan  Southern  Railway,  under  the  direction  of  Charles 
Paine,  Member  and  ex-President  of  the  Society,  who  kindly  furnished 
the  writer  all  necessary  facilities. 

The  apparatus  used  is  shown  with  sufficient  clearness  in  Fig.  302.  It  is 
extremely  cheap  and  simple,  but  fulfils  its  purpose  as  perfectly  as  could 
be  desired,  and  is  believed  to  be  entirely  novel.  The  axle  A  to  be  tested 
is  placed  in  an  ordinary  lathe,  having  as  great  a  variety  of  speeds  as 
possible.  The  testing  apparatus,  as  actually  constructed,  consisted  of  an 
oak  beam,  C,  about  4"  x  4"  in  size,  and  about  5  ft.  long,  carrying  the  com- 
pound lever,  LU,  each  of  which  multiplies  the  load  applied  about  1 1  times, 
or,  in  the  aggregate,  125  times.  The  yoke  E  encircles  the  axle  and  bears 
against  the  brass  B  underneath  it,  thus  furnishing  the  necessary  resist- 
ance to  the  action  of  the  levers  and  throwing  the  same  load  upon  the 
lower  brass  B  as  is  imposed  by  the  levers  directly  on  the  upper  brass  by 
transmission  through  the  pin  D,  the  latter  being  passed  through  a  hole 
in  the  beam  C.  The  pressure  was  transmitted  to  both  the  upper  and  the 
lower  brass  by  suitable  iron  blocks  (shown  in  the  cut  directly  above  and 
below  the  brasses),  representing  as  nearly  as  might  be  the  ordinary  form 
of  the  top  of  a  journal-box. 

As  thus  constructed,  it  will  be  seen  that  the  entire  apparatus  (when 
properly  balanced,  which  is  perfected  by  the  light  counterpoise  H)  is 
poised  in  unstable  equilibrium  on  the  axle  A,  and  opposes  no  resistance 
to  motion  in  either  direction,  except  such  as  arises  from  friction.  A  very 
heavy  load  may  be  thrown  on  the  bearings  viz.,  6000  lbs.  (3000  lbs.  on 
58 


914 


APPENDIX  B. 


each  bearing)  for  every  24  lbs,  of  load,  W  placed  on  the  extremity  of  the 
compound  lever,  but  the  only  weight  thrown  upon  the  lathe-centres 
is  the  dead  weight  of  the  apparatus  itself,  which  was  kept  constant  at 
205  lbs. 

[Some  further  details  are  omitted  here,  and  throughout  the  remainder  of  the 
paper.] 

When  the  axle  A  is  caused  to  revolve,  the  lever  C  is  held  stationary 
by  the  platform -scale,  and  it  is  obvious  that  the  pressure  produced  upon 


Fig.  302. — Apparatus  for  Testing  Journal-Friction  in  a  Lathe. 

the  scale  furnishes  an  exact  and  direct  measure  of  the  journal-friction 
It  was  found  in  practice  that  this  pressure,  varying  from  10  to  140  lbs., 
with  the  proportions  actually  adopted,  could  be  weighed  with  as  much 
delicacy  and  ease  as  if  it  were  a  material  substance  resting  upon  the 
platform  of  the  scale.  Under  a  given  load  and  speed  of  journal  the 
friction  produced,  although  it  did  not  remain  absolutely  stationary, 
varied  so  very  little  and  so  slowly  that  the  beam  of  the  scale  would 
sometimes  vibrate  slowly  and  gently  between  the  guards  (sometimes 
touching  the  upper  one  and  again  returning  to  the  lower,  but  for  the 
most  part  touching  neither)  for  10  or  15  minutes  at  a  time.  On  the 
other  hand,  when  the  brass  was  growing  hot,  by  continuing  the  test  for 
a  considerable  time  the  friction  would  continue  to  increase  so  that  the 
scale-weight  had  to  be  continually  moved  ;  but  the  change  was  never  so 
rapid  but  that  it  could  be  easily  followed  and  studied  with  the  scale,  with 
an  absolute  certainty  that  the  friction  existing  for  the  moment  was  being 
accurately  weighed.  The  difference  in  friction  caused  by  temperature 
was  found  to  be  very  great,  but  in  the  absence  of  arrangements  for 
accurately  determining  the  temperature  no  very  close  results  as  to  its 
precise  effect  were  attempted. 


APPENDIX  B.  915 


As  the  failures  in  designing  such  apparatus  are  as  instructive  as  the 
successes,  it  may  be  noted  that  the  entire  success  of  this  apparatus  de- 
pends upon  the  use  of  the  platform-scale,  or  some  equivalent  device  for 
weighing  the  strains,  in  which  the  measurement  of  the  strains  is  as  nearly 
as  may  be  absolutely  statical,  no  motion  of  the  bearing  whatever  being 
necessary  in  order  to  express  a  variation  of  friction.  It  was  at  first 
attempted  to  use  spring-scales  to  measure  the  friction,  with  the  idea  that 
variations  of  friction  could  be  more  delicately  and  readily  read.  The 
vibration  which  would  almost  instantly  set  up,  seemed  to  indicate  quick 
and  great  irregularities  of  friction,  and  absolutely  forbade  any  useful  in- 
dications from  the  readings. 

It  has  been  preferred  in  this  paper  to  deal  with  resistances  in  pounds 
per  ton,  instead  of  the  coefficient  of  friction,  for  two  reasons  : 

ist.  The  determination  of  these  resistances,  and  not  investigations  of 
the  general  laws  of  all  friction,  was  the  end  in  view  in  the  experiments. 

2d.  The  coefficient  proper  is  a  minute  decimal,  conveying  no  im- 
pression to  the  mind  in  itself,  whereas  resistances  per  ton  are  something 
that  engineers  are  already  familiar  with,  and  being  expressible  with  few 
digits  and  in  integral  numbers,  the  mind  much  more  easily  grasps  and 
follows  their  relations  to  each  other. 

For  the  same  reasons,  the  velocities  here  spoken  of  are  miles  per  hour 
of  train-speed.  Multiplying  the  velocities  given  by  9  gives,  very  approx- 
imately, the  journal-speed  in  feet  per  minute. 

In  the  comparisons  which  follow,  with  various  experiments  the  ap- 
proximate formula,  R  =  200C  has  been  used  to  convert  the  recorded  co- 
efficients into  pounds  per  ton.  This  is  only  correct  when  the  diameter 
of  a  railroad  journal  is  10  times  the  diameter  of  the  wheel.  In  general, 
at  the  present  time,  it  ranges  from  less  than  9  to  9.6  times,  the  latter 
having  been  the  ratio  in  the  present  test ;  so  that  the  use  of  the  approxi- 
mate formula  for  converting  coefficients  obtained  by  others  into  pounds 
per  ton  gives  a  result  about  4  per  cent  too  small.  In  view  of  the  fact, 
however,  that  these  results  differ  300  to  400  per  cent  from  each  other,  in 
many  cases  under  circumstances  which  seem  to  entitle  them  to  equal 
credit,  this  error  has  not  been  deemed  of  moment,  provided  its  existence 
be  remembered. 

The  apparatus  heretofore  described  is,  when  properly  constructed, 
believed  to  possess  every  important  advantage  of  the  various  testing 
machines  in  use,  with  some  peculiarly  its  own.  It  is  very  light  and 
cheap ;  the  actual  weights  to  be  handled  are  very  small,  so  that  they  are 
readily  changed,  and  but  little  strain  is  produced  on  the  machine ;  it  can 


gi6  APPENDIX  B. 


be  used  in  any  ordinary  lathe  and  with  an  ordinary  platform  scale, 
enough  varieties  of  which  can  be  obtained  without  special  construction  to 
satisfy  every  requirement;  it  is  positive  in  its  action  throughout,  and  no 
delicate  computation  and  construction  of  scales  is  necessary  for  its  use  ; 
and  it  admits  of  any  desired  delicacy  of  readings  by  tlie  simple  substitution 
of  more  delicate  scales.  The  common  platform-scale  of  the  shop  where 
the  tests  were  made  was  deemed  sufficient  in  this  instance,  since  the 
stresses  actually  weighed  ranged  so  high  that  the  error  of  observation 
from  lack  of  delicacy  in  the  scales  could  rarely  exceed  a  fraction  of  one 
per  cent.  The  axle  was  set  very  slightly  eccentric,  so  as  to  imitate  the 
effect  of  an  imperfectly  centred  wheel.  This  probably  somewhat  in- 
creased the  coefficient,  although  very  slightly  at  the  low  speed  used. 
The  effect  of  end  play  in  distributing  lubricants  was  imitated  by  the  oc- 
casional use  of  manual  force.  It  was  found  possible  to  do  this  in  great 
degree,  and  it  was  generally  found  to  have  a  slight  beneficial  effect  upon 
the  coefficient,  but  only  slight ;  especial  pains  was  at  all  times  taken  to 
have  the  journal  well  lubricated  before  beginning  each  test.  The  jour- 
nals and  brasses  were  fairly  well  polished  by  use  up  to  their  average  con- 
dition in  service,  but  no  more. 

The  tests  made  are  shown  in  Table  I.  (omitted),  and  graphically  in 
Fig-  303-  Three  different  loads  only  were  used  in  testing,  corresponding 
as  nearly  as  might  be  to  the  loads  on  bearings  of  a  loaded  car,  empty  car 
and  truck  alone.  Each  one  of  these  it  was  designed  to  test  a  number  of 
times  at  all  the  speeds  which  the  lathe  used  admitted  of.  Whenever  a 
bearing  heated  above  150°  F.  the  tests  were  suspended  and  the  bearings 
cooled,  since  no  means  had  been  provided  for  accurate  measure  of  tem- 
perature. Each  test,  at  any  given  speed  and  load,  was  continued  for 
from  5  to  even  30  minutes,  when  the  bearings  were  cool,  in  order  to  be 
certain  that  it  was  a  fair  average.  When  the  bearings  were  hot  the  tests 
were  shorter,  and  the  bearings  were  retained  as  nearly  as  might  be  at  the 
same  temperature  by  waiting  a  considerable  interval  between  each  test. 
During  a  test  the  resistance  would  generally  fluctuate,  slowly  and  gently, 
from  10  per  cent  to  sometimes  20  per  cent  higher  or  lower  than  the 
average  afterwards  taken.  This  change  was  considered  normal,  and 
arose  from  no  discernible  cause.  When  the  fluctuations  were  greater 
than  this  they  were  generally  very  much  greater,  and  arose  from  heating 
of  the  bearings. 


APPENDIX  B. 


917 


The  intensity  of  the  strain  per  sq.  in.  of  journal  (longitudinal  section) 
is  indicated  graphically  in  this  (and  the  following)  diagrams,  as  follows  : 


Heaviest  Load,  2JC)  lbs.  per  sg.  ill. 
Medium      "       154  "      "      "     " 
Light          "        29  "      "      "     " 
ine  of  each,  Jotcrnal  hot,  120°  to  150°  F. 
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9i8 


APPENDIX  B. 


Note. — In  all  the  diagrams  below,  as  also  in  Fig.  303  giving  results  of 
the  writer  s  tests,  the  Jour7tal-speed  has  been  reduced  to  its  equivalent 
train  velocity  in  miles  per  hour  and  the  coefficient  of  friction  to  its 
equivalent  in  pounds  per  ton  tractive  resistance  to  the  locomotive. 

Intensity  of  Load  Per  Sq.  Inch  indicated  by  Thickness  of  Lines. 


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Figs.  305,  306. 

Figs.  304-30?,  Results  of  Mr.  Beaucha^mp  Tower's  Tests,  giving  Effects  of  High 
Velocity,  Variation  of  Pressure  and  Differences  of  Lubrication  upon  Coefficient  of 
Friction. 


APPENDIX  B. 


919 


Vel.  Miles  perhour. 


Fig.  307.— Co:>iparative  Result  of  Pkof.  R.  H.  Thurston's  Ti;sTS  with  Sperm  Oil  and 
Mr.  Beauchamp  Tower's  Tests  with  Sperm  Bath;  the  Latter  indicated  thus — o — 0—0 — 

(The  most  notable  fact  in  this  diagram  is,  that  while  Thurston's  and  Tower's  tests 
agree  almost  precisely,  with  sperm-oil,  at  90°  temperature  and  100  lbs.  per  sq.  in,,  in- 
creasing the  pressure  to  200  lbs,  per  sq.  in.  caused  a  marked  ntcrease  of  coefficient  in 
Thurston's  tests  and  an  equally  marked  decrease  in  Tower's  tests.) 


Deduction  from  the  Tests. 
(  Tons  of  2000  lbs?) 

Initial  Friction.— ^\i^  writer's  observations  under  this  head  were  ex- 
ceptionally complete,  and  the  conclusions  reached  were  as  follows: 

1.  Friction  at  very  low  journal-speeds  of  o  -f-  is  abnormally  great, 
and  more  nearly  constant  than  any  other  element  of  friction,  under  vary- 
ing conditions  of  lubrication,  load,  and  temperature.  It  varies  from  i8 
to  24  lbs.  per  ton  (coefficient,  .09  to  .12)  for  loads  of  from  30  to  280  lbs. 
per  square  inch.  Within  those  limits  it  is  not  greatly  modified  by  load 
or  temperature. 

2.  This  abnormal  increase  of  friction  is  due  solely  to  the  velocity  of 
revolution  continuing  unchanged  so  long  as  the  velocity  is  unchanged, 
and  returning  to  the  same  amount  whenever  the  velocity  is  reduced  to 
the  same  rate,  barring  exceptionally  slight  variations,  probably  due  to 


920  APPENDIX  B. 


differences  of  lubrication  and  temperature.  It  is  not  appreciably  affected 
by  the  fact  that  the  journal  may  be  just  starting  into  motion,  or  is  just 
coming  to  rest,  or  is  temporarily  reduced  to  a  velocity  of  o  +  during 
continuous  motion. 

3.  At  velocities  higher  than  o  +,  but  still  very  low,  the  same  general 
law  obtains.  The  coefficient  falls  very  slowly  and  regularly  as  velocity 
is  increased,  but  is  constantly  more  and  more  affected  by  differences  of 
lubrication,  load,  and  temperature. 

4.  A  very  slight  excess  of  initial  friction  proper  (varying  from  \  lb. 
to  2  lbs.)  could  generally  (but  not  always)  be  observed  over  that  which 
continued  to  exist  at  the  nearest  approach  to  a  strictly  infinitesimal 
velocity  which  it  was  possible  to  obtain.  This  difference  was,  by  analogy, 
ascribed  solely  to  the  fact  that  the  lowest  continuous  velocity  attainable 
was  not  strictly  infinitesimal,  and  the  final  conclusion  was  drawn  that — 

5.  There  is  no  such  phenomenon  in  journal-friction  as  a  frictio7i  of 
rest,  or  a  friction  of  quiesce7ice,  in  distinction  from  (i.e.,  differing  in 
amount  from)  friction  of  motion  at  slow  velocities,  and  due  to  the  fact 
of  quiescence.  Consequently,  the  use  of  such  a  term,  although  con- 
venient, is  scientifically  inaccurate,  in  that  it  ascribes  the  phenomenon 
to  the  wrong  cause,  and  to  a  cause  which  is  not  necessary  for  its  exist- 
ence. The  fact  that  friction  pi  rest,  as  such,  appears  to  exist,  is  due 
solely  to  the  fact  that  no  journal  or  other  solid  body  can  be  instaittly 
set  into  rapid  motion  by  any  force,  however  great.  There  must  be  a  cer- 
tain appreciable  instant  of  time  during  which  the  velocity  is  infinitesimal 
and  gradually  increasing. 

This  interesting  fact,  which  is  believed  to  have  been  here  observed 
for  the  first  time  (no  other  apparatus  being  known  to  have  been  used 
suitable  for  determining  it),  was  determined  with  great  completeness  by 
many  tests.  Very  slow  motion  could  be  produced  at  any  time  by  re- 
volving the  driving-pulley  of  the  lathe  by  hand  when  geared  for  a  slow 
speed.  With  a  little  experience,  the  weight  on  the  scale-beam  could  be 
placed  in  advance  at  a  point  which  would  be  a  trifle  less  than  the  initial 
friction  proper,  and  (when  properly  placed)  it  would  barely  lift  when 
motion  first  began,  and  then  have  to  be  moved  back  a  notch  or  two  only, 
to  weigh  the  friction  which  continued  to  exist  indefinitely.  Similarly, 
when  a  test  at  comparatively  high  speed  was  about  to  be  concluded,  the 
scale- weight  would  be  placed  to  measure  the  same  pressure,  or  a  little 
less,  as  existed  in  starting,  and  it  was  always  found  to  indicate  in  stop- 
ping substantially  the  same  friction  as  in  starting.  The  same  test  was 
made  by  interrupting  tests  at  speed,  so  as  to  give  a  continuous  motion. 


APPENDIX  jB. 


921 


but  to  suddenly  reduce  the  speed  to  o  +.     These  tests  were  repeated 
again  and  again,  with  practically  identical  results. 

Comparing  these  results  with  others,  they  agree  very  closely  indeed 
with  the  writer's  conclusions  from  the  results  of  his  gravity  tests,  as  will 
be  seen  below : 

"  hiitiar'  Journal-friction  (i.e.,  at  velocity  of  o  +). 
Writer's  conclusions  from  journal  tests,  above,  say. .      19    to     25  lbs.  per  ton. 
Writer's  conclusions  from  gravity  tests  of  rolling-stock 

(see  Trans.  Am.  Soc.  C.  E.,  February,  1879),  "  ^•t 

least" o    .14    to    18     " 

Prof.   R.  H.  Thurston  ("Friction  and  Lubrication," 

page  175),  W.  Va.  oils 22    to    28     " 

Prof.  R.  H,  Thurston  ("Friction  and  Lubrication," 

page  175),  sperm 14    to    28     ** 

Prof.  R.  H.  Thurston   ("Friction   and   Lubrication," 

page  175),  lard 14    to    22     " 

Prof.  Kimball  (yAm.  Jour.  Sci.,   March,    1878,   or  Fr. 

and  L. ,  page  186) 22    to    31     " 

In  addition,  it  may  be  noted  that  the  writer  has  taken 

pains   to  observe  with  some  care  at  various  times 

that  in  ordinary  service  no  railroad  cars  can  start 

themselves  from  rest,  nor  can  they,  in  general,  be 

started  without  the  use  of  much  force,  on  a  grade 

of  .7  per  cent  {=  14  lbs.  per  ton,  36  ft.  per  mile), 

but  that  they  will  generally  (but  not  always)  start 

of  themselves   on   a  grade   of  i.i  to  1.2  per  cent 

(=  22  to  24  lbs.  per  ton,  58  to  63  ft.  per  mile),  in- 
dicating an  "  initial"  friction  of 20    to    24     "       "     " 

These  results  agree  wonderfully  well  with  each  other,  the  averages 
running  18,  16,  25,  20,  18,  25^,  and  22  lbs.  per  ton,  the  average  of  all  being 
18.0  to  25.0  lbs.  per  ton,  or  2o|-  lbs.  as  the  general  average  of  all.  This 
corresponds  to  the  accelerating  force  of  gravity  on  a  i  per  cent  (52.8  ft. 
per  mile)  grade,  and  that  being  also  the  lowest  grade,  by  universal  rail- 
road experience,  upon  which  cars  can  be  relied  on  to  start  off  from  a 
state  of  rest  with  little  or  no  assistance,  the  correctness  of  this  coefficient 
may  be  considered  as  well  determined.* 

*  On  a  0.7  per  cent  grade  (14  lbs.  per  ton)  the  writer  found  it  impossible  in 
several  instances  for  six  men  pushing,  two  with  pinch-bars,  to  start  two  loaded 
box  cars  into  motion.  In  no  single  instance  out  of  over  sixty  did  cars  start 
without  some  assistance. 


922  APPEXDTX  B. 

Normal  Coefficient  of  Journal-friction  at  Ordinary  Operating  Veloci- 
ties.— Certain  general  facts  seem  to  be  clear  from  all  the  various  tests^ 
here  considered : 

The  first  of  these  is,  that  (i)  the  character  and  completeness  of 
lubrication  seems  to  be  immensely  more  important  than  the  kind  of 
the  oil,  or  even  pressure  and  temperature,  in  affecting  the  coefficient. 

This  is  very  clear  from  the  diagrams  (Figs.  303  to  307)  showing  the 
various  results.  Mr.  Tower  found  that  lubrication  by  a  bath  (whether 
barely  touching  the  axle  or  almost  surrounding  it)  was  from  six  to  ten 
times  more  effective  in  reducing  friction  than  lubrication  by  a  pad.  By 
this  method  of  lubrication  Mr.  Tower  succeeded  in  reducing  the  co- 
efficient in  a  large  number  of  tests  to  as  low  a  point  as  .001,  equivalent 
to  only  0.2  lb.  per  ton  of  tractive  resistance,  and  the  general  average  in 
the  bath  tests,  under  all  varieties  of  load  and  speed,  is  given  as  only 
.00139  or  0.278  lb.  per  ton,  against  1.96  to  1.95  lbs.  per  ton  with  siphon- 
lubricator,  or  pad  under  journal.  These  results  are  very  far  below  any 
heretofore  reported,  as  will  be  seen  from  the  following  general  average 
of  results;  not  considering  now  the  comparatively  minor  variations  pro- 
duced by  ordinary  working  differences  in  temperature,  load,  etc. 

The  normal  journal-friction,  under  favorable  conditions,  deduced 
from  various  series  of  tests,  may  be  summarized  as  follows  for  velocities 
greater  than  10  miles  per  hour,  or  90  ft.  per  minute,  journal  speed : 

Beauchamp  Tower,  bath  of  oil..  , 278  lbs.  per  ton. 

"  "         pad  or  siphon 1.9 

Thurston,  light  loads 2.75 

"  heavy  loads i-75 

Wellington  (gravity  tests  of  cars  in  service),  light  loads 6.0       "      "     ** 

heavy  "     3.9        "      "     *' 

direct  tests  (as  shown  in  Fig.  2) -j        '  ,,      ,^     ,, 

Thurston,  inferior  oils  (Fr.  and  Lub.,  p.  173) ]        '^        .,      ,.     ,, 

Morin,  continuous  lubrication 6.0  to  10.8 

These  discrepancies,  especially  as  they  are  accompanied  by  many 
minor  ones,  are  very  instructive,  as  showing  that  the  character  of  lubri- 
cation is  the  great  cause  of  variation  of  coefficient. 

Resistance  of  Freight  Trai?is  in  Starting.— It  will  be  seen  in  Fig.  303 
that  the  abnormally  high  coefficient  of  friction  at  starting  continues 
during  the  period  of  getting  up  speed,  and  thus  constitutes  an  extra  tax 
upon  tractive  power  for  some  little  distance  after  getting  under  way. 


APPENDIX  B.  923 


The  following  conclusions  may,  it  is  believed,  be  drawn  (already  sum- 
marized in  par.        ). 

Effect  of  TeinperaUire  on  Coefficient  of  Friction. — So  far  as  can  be 
estimated,  the  results  agree  very  closely  with  Prof.  Thurston's  formula 
that  the  coefficient  increases  as  the  square  of  the  increase  of  heat  over 
90°  to  100°  F.  at  speeds  under  12  miles  per  hour. 

Effect  of  Load  per  Square  I?ich  of  Bearing  on  Coefficient  of  Friction. — 
Comparison  of  the  results  obtained  by  the  writer,  and  by  Messrs.  Thurs- 
ton and  Tower  and  others,  as  shown  in  Figs.  303  to  307,  develop  this 
curious  fact :  that  while  the  results  differ  quite  widely,  in  fact  by  several 
hundred  per  cent,  in  what  may  be  called  the  typical  or  average  co- 
efficient of  friction,  they  all  agree  quite  closely  in  finding  that  the  effect 
of  increased  load,  within  working  limits,  is  to  ver^'  materially  diminish 
the  coefficient.  Mr.  Tower,  in  fact,  goes  so  far  as  to  state,  as  one  of  the 
results  of  his  tests,  that  it  almost  seemed  at  times  as  if  it  was  approxi- 
mately true  that  the  absolute  loss  by  friction  was  entirely  independent  of 
load,  the  coefficient  falling  almost  to  half  when  the  load  was  doubled. 
But  it  seems  plain,  from  the  diagrams  given  herewith,  that  this  result  is 
only  true  on  account  of  the  unprecedentedly  low  coefficients  which  he 
obtained  by  his  very  perfect  lubrication.  Inspection  of  the  diagrams  will 
show  that  the  general  law  of  variation  from  increase  of  load  is  not  mate- 
rially different  in  the  different  tests,  despite  the  wide  variations  in  the 
average  coefficients. 

Effect  of  Velocity  over  Twelve  Miles  per  Hour. — Figs.  303  to  307,  taken 
in  connection,  seem  to  show  the  following : 

1.  The  velocity  of  lowest  journal-friction  is  10  to  15  miles  per  hour. 

2.  With  bath  or  other  very  perfect  lubrication  there  is  a  very  slight 
increase  of  journal-friction  accompanying  velocities  up  to  55  miles  per 
hour  (Figs.  306  and  307). 

3.  With  less  perfect  lubrication,  as  with  pad  or  siphon,  greater 
velocity  is  as  apt  to  decrease  as  to  increase  the  coefficient  (Figs.  304,  305, 
and  307).  The  latter  being  more  like  the  ordinary  lubrication  in  railroad 
service,  we  may  say,  without  sensible  error,  that  the  coefficient  of  journal- 
friction  is  approximately  constant  for  velocities  of  15  to  50  miles  per 
hour. 

This  has  been  the  assumption  which  all  investigators  of  railroad  fric- 
tion, to  date,  have  been  compelled  to  make,  and  it  is,  in  some  respects, 
fortunate  that  it  proves  not  far  from  true. 

Higley  Roller- f our nal  Bearings. — The  direct  tests  of  this  apparatus 
confirmed  exactly  the  correctness  of  the  writer's  previously  stated  con- 


924  APPENDIX  B. 


elusions,  that  the  Higley  bearing  was  nearly  as  efficient  as  theory  would 
indicate  in  reducing  initial  friction,  but  loses  nearly  all  of  this  advantage 
under  speed. 

[The  paper  was  followed  by  a  long  discussion,  which  it  is  necessary 
to  omit,  bringing  out  many  further  points  of  interest.] 


APPENDIX   C.  925 


APPENDIX  C. 


THE  AMERICAN  LINE  FROM  VERA  CRUZ  TO  THE  CITY  OF 
MEXICO,  VIA  JALAPA,  WITH  NOTES  ON  THE  BEST  METHODS 
OF  SURMOUNTING  HIGH  ELEVATIONS  BY  RAIL. 

[Read  by  the  author  at  the  Annual  Convention  of  the  American  Society  of  Civil  Engi- 
neers, July  3,  1886.     See  Trans.  Am.  Soc.  C.  E.,  Nov.  1886.] 

The  line  described  in  this  paper,  and  illustrated  in  the  accompanying 
maps  and  profiles,  is  one  located  by  the  writer,  as  consulting  and  after- 
ward chief  engineer,  from  the  Port  of  Vera  Cruz  to  the  city  of  Mexico, 
vm  the  city  of  Jalapa,  being  a  parallel  line  to  the  existing  Mexican  Rail- 
way— the  first  railway  built  in  Mexico — in  the  sense  of  connecting  the 
same  termini,  although  following  a  very  different  route  and  of  a  very 
different  character. 

All  the  features  of  interest  and  of  difficulty,  both  in  the  line  here  de- 
scribed and  in  the  line  of  the  Mexican  Railway,  are  confined  to  the 
mountain  grade  by  which  the  necessary  abrupt  ascent  from  the  level  of 
the  sea  to  the  level  of  the  plateau,  8000  feet  above  the  sea,  is  accom- 
plished. Once  on  the  plateau  there  is  no  great  difficulty  in  going  almost 
anywhere  with  very  light  work ;  many  high  mountains  being  scattered 
around,  even  on  the  plateau,  but  disconnected,  with  flat  lands  between. 

The  elements  which  appear  to  make  the  mountain  grade  of  this  line 
particularly  worthy  of  description  are  these  : 

First.  It  is  believed  to  be  by  far  the  longest  continuous  grade-line 
ever  located;  116.9  kilometres  (72.64  miles)  having  been  located  on  an 
unbroken  2  per  cent  grade  (105.6  feet  per  mile),  rising  in  that  distance 
from  elevation  600.4  feet  (183  metres)  to  elevation  7923.3  feet  above  the 
sea  (2415  metres).  The  accompanying  plate  (Fig.  232)  shows  graphically 
the  extent  of  the  contrast  in  this  respect  with  some  of  the  other  great 
inclines  of  the  world. 

Secondly.  It  is  believed  to  be  on  the  lowest  rate  of  grade,  by  about 
2  per  cent,  ever  successfully  attempted  for  accomplishing  within  a 
limited  distance,  either  by  a  continuous  grade-line  or  otherwise,  a  rise 


926  APPENDIX   C. 


of  over  one  half  as  much  as  was  attained  on  this  line.  The  gronnds  for 
this  belief  also  are  shown  in  the  accompanying  plate  (Fig.  232). 

Thirdly.  The  line  is  believed  to  be,  by  probably  one  half  at  least, 
the  cheapest  line  per  mile  which  has  ever  been  actually  located,  with 
-equally  favorable  alignment,  for  attaining  within  a  limited  distance  as 
much  as  one  half  the  rise  actually  attained  by  this  line,  either  by  con- 
tinuous or  broken  grade-lines,  on  any  rate  of  grade.  As  for  this,  Table 
190,  Figs.  309  and  310,  and  the  general  knowledge  of  engineers  are  the 
only  evidence  that  can  conveniently  be  appealed  to,  or  which  it  is  worth 
while  to  attempt  to  present. 

Finally.  It  appeared  that  the  manner  in  which  the  line  was  obtained 
might  have  a  certain  instruction  and  encouragement  to  those  who  may 
be  dismayed,  as  was  the  writer,  by  having  similar  problems  of  unusual 
difficulty  suddenly  thrust  upon  them,  and  it  was  also  desired  to  give,  in 
connection  with  the  description  of  the  line,  certain  conclusions  which 
the  observation  and  experience  of  the  writer  has  indicated — not  only  on 
this  incline,  but  on  eight  or  ten  others  of  considerable  rise,  which  have 
been  located  or  relocated  in  part  or  whole  under  his  supervision,  aggre- 
gating over  24,000  vertical  feet — in  regard  to  the  most  advantageous  and 
economical  manner  of  dealing  with  great  inclines,  under  which  may  be 
Classed  anything  exceeding  1200  to  1500  feet  of  vertical  rise. 

It  is  one  of  the  unfortunate  features  of  the  department  of  engineering 
to  which  this  paper  refers — that  of  laying  out  railway  lines  to  the  best 
economic  advantage — that  a  mere  description  of  a  located  line  has 
usually  little  technical  interest  or  instruction,  since  it  is  ordinarily  im- 
possible to  so  carefully  describe  any  line  on  paper  as  to  enable  even  an 
intelligent  impression  to  be  formed  as  to  the  real  character  of  the  work. 
If  the  grades  and  work  be  light,  it  may  be  because  the  line  was  well  laid 
out,  or  it  may  be  simply  because  there  were  no  serious  natural  obstacles 
in  the  way.  On  the  other  hand,  if  the  grades  and  work  be  heavy,  it  may 
be  due  to  bad  engineering,  and  so  discreditable;  or  it  may  be  due  to  the 
existence  of  gigantic  difficulties,  and  so  an  evidence  of  skill.  It  is  but 
natural,  however,  that  the  magnitude  of  the  natural  difficulties  to  be 
-overcome  should  in  general  be  regarded  as  bearing  some  nearly  constant 
ratio  to  the  magnitude  of  the  works  constructed  to  overcome  them  ;  and 
hence,  that,  even  when  the  construction  of  a  very  costly  line  may  have 
been,  as  a  matter  of  fact,  an  avoidable  extravagance,  due  to  lack  of  skill 
or  foresight,  the  very  magnitude  of  the  works  gives  more  instead  of  less 
reputation  to  the  line  as  an  engineering  work. 

Only  in  the  comparatively  rare  cases  when  two  independent  alternate 


APPENDIX   C.  927 


lines  exist  between  the  same  termini,  is  it  possible  for  the  engineer  to 
find  in  printed  descriptions  of  located  lines,  however  perfectly  mapped, 
any  rational  basis  for  intelligent  judgment.  The  present  happens  to  be 
one  of  the  cases  in  which  this  is  possible,  owing  to  the  existence  of  the 
parallel  Une  before  mentioned,  but  in  order  to  avail  of  it,  it  becomes 
necessary  to  enter  somewhat  into  what  would  otherwise  be  an  invidious 
— because  unnecessary — comparison  with  the  parallel  and  previously 
constructed  line.  The  writer  feels  the  less  embarrassed  in  doing  this, 
as,  owing  to  the  checkered  history  of  the  line,  no  one  engineer  can  be 
held  responsible  for  its  character,  and  there  were  certain  circumstances 
tending  to  impede  entire  freedom  of  choice  and  proper  investigation. 

The  whole  interior  of  Mexico  is  a  vast  plateau,  at  an  elevation  of  5600 
to  9000  feet  above  the  sea,  bounded  by  an  abrupt  escarpment  from  which 
the  descent  to  sea-level  is  almost  immediate.  The  edge  of  the  plateau  is 
higher  and  sharper  on  the  Atlantic  than  on  the  Pacific  Coast,  and  at  no 
point  on  either  the  Atlantic  or  Gulf  Coast  is  it  higher  or  sharper  than 
directly  in  line  between  the  capital  of  the  country,  Mexico,  and  its  chief 
port,  Vera  Cruz.  Here  two  stupendous  natural  obstacles,  the  Pico  of 
Orizaba  on  the  south  (17,873  feet  high),  and  the  Cofre,  or  "  Box,"  of 
Perote  (12,500  feet  high),  both  of  them  described  in  physical  geographies 
as  volcanoes,  although  both  are  temporarily  extinct,  and  the  two  con- 
nected by  a  ridge  over  10,000  feet  high  at  its  lowest  saddle — combine  to 
forbid  a  direct  line  inward. 

Orizaba  is  one  of  the  three  mountains  in  Mexico  covered  with  per- 
petual snow,  the  other  two  being  Popocatepetl  (17,884  feet),  and  Ixtac- 
cihuatl  (15,705  feet),  overlooking  the  valley  of  Mexico.  These,  however 
start  from  a  plain  8000  feet  high,  whereas  Orizaba  starts  practically  from 
sea-level  on  the  coast  side,  making  it  in  that  sense  by  much  the  highest 
mountain  on  the  North  American  Continent,*  and  among  the  highest  in 
the  world.  Its  snow-clad  peak  is  visible  60  miles  out  at  sea,  long  before 
there  is  any  other  evidence  of  land,  and  with  the  morning  sun  shining  on 
it  is  a  very  striking  sight.  Its  last  violent  eruption  was  in  1546,  soon 
after  the  Spanish  conquest,  although  it  now  occasionally  throws  out 
smoke.  Only  one  or  two  men  have  ever  ascended  to  its  crater,  the  first 
one  having  been  Lieutenant  Reynolds,  U.S.A.,  in  1848.  The  line  of  the 
Mexican  Railway  passes  to  the  south  of  this  mountain,  as  shown  in  Fig. 
308. 

*  Mount  St.  Elias,  in  Alaska,  in  a  possible  exception,  being  only  about  30 
miles  inland,  and  its  height  variously  given  as  14,970,  16,900,  17,850,  "over 
i8,ooq"  (U.  S.  Census  Report),  and  19.500. 


928  APPENDIX  C. 


The  Cofre,  or  "  Box,"  of  Perote  (so  named  from  a  cylindrical  basaltic 
needle  about  300  feet  in  diameter  and  300  feet  high  which  caps  the 
mountain,  like  a  box  laid  on  its  peak),  although  formerly  one  of  the  most 
active  volcanoes  in  the  world,  and  classed  as  still  active,  is  perhaps  per- 
manently extinct,  its  last,  and  probably  also  its  greatest,  eruption  having 
been  to  form  what  looks  to  be,  and  is  in  fact,  a  frozen  river  of  lava,  shown 
in  Fig.  309,  extending  to  and  running  into  the  sea  50  miles  distant,  filling 
up  an  enormous  barranca  or  deep  gulch  in  the  process,  in  a  manner 
which  was  very  convenient  for  subsequently  carrying  the  line  over  it,  as 
may  be  seen  in  Fig.  309.  The  natural  variations  in  the  width  of  this 
gulch  have  caused  lakes  and  frozen  "water-falls"  of  lava,  which  makes 
it  difficult  to  believe,  as  one  looks  up  the  slope  upon  it  from  some  com- 
manding point,  that  the  mass  is  not  still  flowing,  making  it  a  unique  and 
impressive  bit  of  natural  scenery.  Vessels  have  been  frequently  wrecked 
in  the  toe  of  this  flow  where  it  enters  the  sea.  It  has  still  hardly  any 
deposit  of  sand,  soil,  or  vegetation  on  it,  that  and  other  facts  evidencing 
that  the  flow  is  geologically  very  recent,  not  antedating  much  the 
historic  era. 

Around  the  north  side  of  this  mountain,  and  directly  over  this  lava 
flow,  the  line  here  described  passes,  as  shown  in  Figs.  308  and  309,  being 
about  sixty  miles  north  of  the  Mexican  Railway  line  at  its  greatest  diver- 
gence, the  two  beginning  to  come  together  again  very  soon  thereafter. 
The  summit  of  Perote  is  just  below  the  limit  of  vegetation  and  of 
perpetual  snow,  and  it  is  very  easily  ascended  on  horseback  to  the  foot 
of  the  "  cofre,"  or  box,  that  fact  alone  being  an  evidence  to  the  engineer 
of  how  different  the  topography  of  its  slopes  must  be  from  those  of  its 
southerly  companion.  Evidences  abound  of  tremendous  flows  of  lava  in 
remote  geologic  times,  which  are  now  covered  to  a  considerable  depth 
with  soil,  and  in  the  kind  of  pocket  formed  between  the  foot-hills  of  the 
two  great  mountains,  in  which  lie  Jalapa  and  Coatepec,  the  detritus  of 
ages  has  accumulated,  including  probably  great  amounts  of  volcanic  ash, 
so  that  no  rock  exists  over  large  areas,  as  was  afterwards  discovered,  ex- 
cept in  isolated  points. 

Cortez  followed  this  route  on  his  first  invasion,  as  did  General  Scott 
328  years  later ;  but  from  an  early  date  after  the  conquest  of  Cortez  two 
leading  routes  have  existed  between  the  interior  and  Vera  Cruz,  follow- 
ing substantially  the  two  railway  lines  here  described,  one  through  Jalapa, 
rounding  Perote  to  the  north,  and  the  other  via  Orizaba,  rounding  the 
mountain  of  that  name  to  the  south.  The  northerly  line  was  first  con- 
structed, and  over  it,  for   300  years  (between  1521  and  1812-20)  passed 


:44:»%i4-^-l. 


■■^W:     -  -'■'."  "^K^  '::$0 


APPENDIX   C.  929 


vast  sums  of  silver  and  gold,  practically  the  entire  product  of  the  Mexican 
mines,  amounting  in  the  aggregate  to  $3,000,000,000,  or  nearly  half  of 
the  value  of  silver  in  the  whole  world,  which  in  1876  was  estimated  at 
$7,232,071,674,  exclusive  of  what  existed  before  1520,  which  was  rela- 
tively little.  During  all  this  time  the  southerly  route  was  an  insignifi- 
cant trail,  but  early  in  this  century  the  southerly  route  took  prominence, 
and  the  Jalapa  caniino  real,  or  "  King's  highway"  (as  the  leading  roads 
are  still  called  in  republican  Mexico),  was  suffered  to  fall  into  decay.  It 
had  originally  been  paved,  guttered,  and  curbed  for  the  entire  distance 
from  Jalapa  to  Vera  Cruz,  some  73  miles,  and  from  Jalapa  up  the  moun- 
tain a  fine  macadamized  road,  likewise  curbed  and  guttered,  existed,  and 
still  exists  in  fine  order,  having  been  recently  repaired.* 

Within  fifteen  or  twenty  years  after  the  abandonment  of  the  north- 
erly highway,  as  earl)^  as  1837,  the  movement  for  a  railway  between  Vera 
Cruz  and  Mexico  was  begun  by  Don  Francisco  Arrillaga,  and  very  nat- 
urally, but  very  unfortunately,  the  route  which  had  by  that  time  become 
the  only  one  generally  known,  assumed  a  prominence  which  it  held  to 
the  end.  The  very  facts  which  made  it  best  suited  for  a  highway,  that  a 
very  comfortable  valley  ran  directly  up  into  the  bowels  of  the  mountains, 
from  which  the  ascent  was  abrupt  and  sharp  to  the  plains  above,  made  it 
unsuited  for  a  railway  line,  but  this  could  hardly  be  appreciated  at  that 
early  day. 

By  1854  the  construction  of  a  tramway  from  Vera  Cruz  had  been  be- 
gun, Don  Antonio  Escandon,  a  wealthy  Mexican  banker,  who  was  chiefi}^ 
instrumental  in  pushing  the  project  through  to  completion,  having  then 
taken  hold  of  the  enterprise.  Don  Antonio  had  a  large  estate  near  Ori- 
zaba, and  his  property  mterests  may  well  have  somewhat  influenced  the 
final  decison.  However  this  may  be,  in  1857,  Colonel  Andrew  H.  Tal- 
cott,  an  American  engineer,  arrived  with  a  staff  of  assistants,  the  only 
member  of  which  now  living,  the  writer  believes,  is  Mr.  S.  Wimmer,  M. 
Am.  Soc.  C.  E.,  then  a  very  young  man,  after  whom  one  of  the  leading 
bridges  of  the  line  was  subsequently  named.  According  to  one  of  the 
published  histories  of  the  road,  all  these  engineers  confined  their  labors 
to  the  Orizaba  line,  that  via  Jalapa  being  mtrusted  to  a  Mexican  engi- 

*  On  the  lower  part  of  this  highway  a  splendid  stone  bridge,  the  Puente 
Real,  or  as  now  described,  the  Puente  Nacional,  which  has  been  not  unreason- 
ably claimed  to  be  "  worthy  of  the  best  days  of  Rome,"  still  exists  in  perfect 
order,  and  as  showing  the  fine  quality  of  the  Mexican  lime,  the  joints  are  con- 
siderably harder  than  the  stone  itself  (which  is  durable  but  rather  soft),  and  are 
worn  less. 
59 


930  APPENDIX   C. 


neer,  Don  Pascual  Almazon.  According  to  other  accounts,  a  commis- 
sion of  engineers  examined  both  lines.  If  the  first  was  the  case,  it  is  less 
surprising  that  "  on  comparing  the  separate  surveys,"  as  the  history  of 
the  road  states,  that  by  Orizaba  was  finally  adopted,  on  the  grounds,  first, 
that  there  was  more  traffic  to  be  secured  on  it  (which  is  rather  more 
than  doubtful,  although  the  local  traffic  at  best  is  an  insignificant  ele- 
ment), and  secondly,  that  "  notwithstanding  it  requires  great  and  costly 
works,  the  line  presents  greater  facilities  than  that  by  Jalapa,  where  the 
larger  tiumber  of  raviiies  and  the  harder  nature  of  the  soil  would  have  re- 
quired jnuch  heavier  outlay y  A  greater  mistake  than  is  contained  in  the 
italicized  part  of  the  quotation  could  not  well  be. 

Colonel  Talcott's  e-stimate  of  the  line  was  $15,000,000,  but  nothing 
more  was  done  than  to  build  about  ten  miles  of  surface  line  out  of  Vera 
Cruz,  until  August,  1864,  when  the  military  necessities  of  the  Emperor 
Maximilian  led  to  a  real  beginning  and  prompt  pushing  of  the  work 
under  English  engineers,  and  by  an  English  company,  which  still  con- 
trols it.  Beyond  a  statement  that  the  resumption  was  "after  rectifying 
the  plans  of  Colonel  Talcott,"  the  official  history  contains  no  record  of 
the  second  examination  of  the  whole  question  of  route,  which  was  in 
fact  made,  although  how  thoroughly  the  writer  cannot  state. 

By  1867  the  line  was  opened  from  Vera  Cruz  to  Paso  del  Macho,  47!- 
miles,  and  from  Mexico  to  Apizaco,  86i  miles,  the  rails  for  the  latter 
being  hauled  by  wagons  an  average  of  200  miles  inland,  at  enormous 
cost — a  hard  condition  imposed  by  the  Mexican  Government.  A  third 
change  of  engineers  took  place  about  this  time,  while  the  heavier  parts 
of  the  work  were  still  unexecuted.  In  1868,  the  Puebla  branch,  29  miles, 
was  opened,  the  rails  for  it  having  been  hauled  in  the  same  manner.  In 
1870  the  line  was  opened  to  Atoyac,  54  miles  from  Vera  Cruz ;  in  1871  to 
Fortin;  in  1872  to  Orizaba,  and  on  the  last  day  of  that  year  the  entire 
line  was  opened  with  great  ceremony. 

Shortly  thereafter,  in  1874,  Don  Ramon  Zangronez,  of  Vera  Cruz, 
succeeded  in  getting  a  branch  line  to  Jalapa  well  under  way,  and  in 
having  it  assumed  by  the  Mexican  Railway,  which  completed  it,  as  shown 
in  Fig.  308,  in  May,  1875.  It  is  operated  solely  by  animal  power,  being 
probably  by  far  the  longest  horse  railway  in  the  world.  Its  grades  are 
very  severe  (16  per  cent),  and  its  curves  of  ordinary  horse-car  radii. 
It  is  laid  for  a  great  part  of  its  length  along  the  old  camino  real, 
and  exhibits  the  same  trait  as  the  main  line  of  the  Mexican  Railway  to 
the  foot  of  the  mountains — that  is,  it  runs  obliquely  across  the  drainage 
lines,  thus  materially  increasing  the  difficulties  of  both  lines,  but  making 


APPENDIX   C.  931 


the  Jalapa  line  absolutely  impracticable  for  an  ordinary  railway,  even 
with  gigantic  work.  It  was  probably  some  such  erroneous  treatment  of 
the  lower  part  of  the  descent  which  led  to  the  condemnation  of  the  route, 
as  it  seems  impossible  that  an  ascent  from  Jalapa  on  a  4  per  cent  grade 
could  have  been  deemed  as  serious  as  that  from  Orizaba  on  the  adopted 
line. 

The  main  line  thus  constructed  is  still  one  of  the  most  massive  and 
costly  in  the  world.  Its  cost  was  abnormally  increased  by  two  causes  : 
First,  the  political  condition  of  the  country,  which  was  so  much  disturbed 
that  it  no  doubt  added  much  to  the  cost ;  and  secondly,  the  absurd  re- 
quirement that  construction,  including  track-laying,  should  begin  from 
both  ends  at  once,  necessitating  the  enormous  expense  referred  to  for 
hauling  rails  over  execrable  roads  from  Vera  Cruz  to  Mexico  and  Puebla. 
In  all  some  15,000  tons  of  rails  were  thus  hauled,  at  a  cost,  the  writer 
believes,  of  some  $80  per  ton,  amounting  to  some  $1,200,000  in  all.  On 
the  other  hand,  there  was  little  direct  inflation  of  the  capital  account, 
most  of  the  share  capital  representing  actual  money  paid  in.  The  gross 
nominal  cost  of  the  line  was,  as  nearly  as  may  be,  $40,000,000.  Reducing 
this  by  one  half,  we  shall  make  an  ample  allowance  for  the  effect  of  all 
abnormal  causes  tending  to  increase  cost  of  line,  and  for  the  cost  of  the 
Jalapa  horse  railway  and  the  small  amount  of  rolling-stock  (65  engines, 
810  cars),  leaving  $20,000,000  to  represent  the  actual  cost  of  264  miles 
of  main  line  and  29  miles  of  branch.  Of  this  the  section  between  Paso 
del  Macho  and  Boca  del  Monte  alone,  some  60  miles,  is  in  any  sense 
difficult  or  costly  work.  The  remaining  223  miles  is  light  work,  with  i^ 
per  cent  grades,  which  latter  are  quite  unnecessarily  high. 

On  this  basis  we  may  distribute  the  actual  cost  (taken  at  half  the 
nominal)  about  as  follows  : 

223  miles  light  work,  at  $40,000  per  mile $8,920,000 

60  miles  very  heavy  work,  at  $184,667  per  mile 11,080,000 


283  miles  in  all,  at  $70,670  per  mile $20,000, 


000 


Both  the  grades  and  curves  on  this  line  are  very  severe.  Only  10  miles 
out  of  Vera  Cruz  1.5  per  cent  grades  begin,  which  shortly  thereafter 
are  increased  to  2  per  cent,  2.5,  3,  and  at  last  to  4  per  cent,  which  latter 
is  entirely  unbroken  for  the  last  13  miles  of  rise,  and  used  also  at  several 
other  points  on  the  ascent.  Curves  as  sharp  as  325  to  350  feet  radius 
(16  degrees  30  minutes  and  17  degrees  40  minutes)  are  used,  and  six  or 
eight  reversed  curves  of  these  radii  often  succeeding  each  other  without 
any  tangent  between  them,  and  without  any  grade  compensation,  making 


932  APPENDIX  C. 


the  virtual  gradient  fully  6  per  cent.  Fairlie  engines  are  used  to  operate 
this  grade  between  the  summit  at  Boca  del  Monte  (107  miles  from  Vera. 
Cruz)  and  Cordova.  The  remaining  157  miles  to  the  city  of  Mexico,  as 
well  as  the  lower  and  easier  part  of  the  mountain  grade  (which,  however,, 
has  2-I-  to  3  per  cent  grades,  increased  by  unreduced  curvature),  is 
operated  by  American  engines.  Very  naturally  both  the  freight  rates 
and  the  expenses  are  fabulously  high,  receipts  ranging  from  10  to  12 
cents  per  ton-mile  and  as  high  as  $8  per  train-mile,  expenses  being  from 
50  to  60  per  cent  of  receipts.  To  show  how  radically  the  cost  and 
revenue  from  the  operation  of  this  line  differs  from  anything  with  which 
we  are  familiar,  it  was  calculated  in  1883  that  with  the  Mexican  rates  the 
New  York  Central  would  earn  $27.25  and  the  Erie  $28.50  per  freight 
train-mile,  and  their  total  freight  earnings  would  have  been  in  one  year 
$297,025,000  and  $244,300,000  respectively — $168,000,000  more  than  the 
Central's  whole  capital  account,  and  $93,000,000  more  than  the  Erie's. 

There  are  fourteen  tunnels  in  all  on  the  line,  none  of  them,  however,, 
very  long,  and  about  as  many  viaducts.  The  grading  is,  for  miles  to- 
gether, almost  wholly  rock,  and  the  work,  as  a  whole,  can  only  be  de- 
scribed as  Titanic,  so  that  it  is  small  matter  of  surprise  that  almost  every 
one  who  writes  about  the  line  describes  it  in  much  the  same  terms  as 
does  Mr.  George  William  Curtis  in  a  late  number  of  Harper's  Magazine 
(February,  1886),  who  chances  to  be  the  last  writer  whose  remarks  in. 
respect  to  it  have  come  to  the  Writer's  knowledge. 

"If  it  is  magnificent  scenery  that  you  seek,  here  at  hand,  with  no  inter- 
vening ocean,  is  the  railway  from  Vera  Cruz,  260  miles,  to  the  city  of  Mexico 
— a  marvellous  feat  of  scientific  skill,  crossing  the  mountains  at  a  height  of  8500 
ft.,  and  bearing  you  through  every  climate,  amid  unimaginable  luxuriance  and 
brilliancy  of  vegetation,  changing  into  temperate  hues  of  hardier  growths,  with 
awful  mountain  abysses  between  and  snow-clad  peaks  beyond  against  the  deep 
blue  sky." 

The  line  located  by  the  writer  rises  to  almost  precisely  the  same 
height  of  summit  as  the  Mexican  Railway,  and  is  as  nearly  as  may  be  of 
the  same  length,  but  in  almost  every  other  detail  stands  in  broad  con- 
trast with  it,  thus : 

Grade. — Continuous  2  per  cent  (uncompensated)  against  a  broken  4  per  cent 
(uncompensated) ;  including  the  effect  of  curvature  or  of  compensation  there- 
for, 2.6  per  cent  against  6  per  cent. 

Curves. — Curves  of  2S9  ft.  radius  (19°  50)  connected  by  minimum  tangents 
of  40  metres  (131  ft.),  against  16°  30'  to  17°  40'  curves  (325  to  350  ft.  radius)  con- 
nected by  no  tangents  at  all  for  many  successive  reversions.     The  writer  con- 


^^w 


// 

r- 

'  "BS'S'pSs'k  _     _ 

^^ 

1  /       e-yO    ^ 


'^^. 


■^•>^j : . 


APPENDIX   C.  933 


rsiders  that  the  difficulty  and  expense  of  maintaining  these  two  limits  is  about 
equal,  but  that  the  latter  is  decidedly  the  most  objectionable. 

Amount  of  Curvature. — On  Mexican  Railway  143  curves  on  the  last 
20.14  kilometres  of  the  ascent,  against  82  curves  on  the  upper  ig  kilometres  of 
the  Jalapa  line,  shown  on  Figs.  309  and  310.  The  lower  portions  of  the  line  will 
be  seen  in  Fig.  309  to  have  much  more  favorable  alignment. 

The  number  of  curves  indicates,  what  is  the  fact,  that  there  is  hardly  any 
tangent  on  the  upper  portion  of  the  Mexican  Railway  grade,  whereas  on  the 
upper  third  of  the  line,  shown  on  Figs.  309  and  310,  41-^  per  cent  of  the  line  is 
tangent  (the  average  tangent  being  96.3  metres  or  320  ft.),  and  on  the  whole  54 
kilometres  which  have  been  engraved  48  per  cent  of  the  line  is  tangent.  The 
comparative  degrees  of  curvature  cannot  be  given. 

Distance. — The  distance  between  Vera  Cruz  and  San  Marcos,  where  the 
two  lines  as  actually  surveyed  connect,  was  just  20  kilometres  (12^  miles)  longer 
via  the  Jalapa  line,  viz.,  262  against  242  kilometres.  Had  the  purpose  in  view 
been  the  same,  however,  merely  to  get  to  Mexico,  this  difference  might  have 
been  more  than  eliminated,  as  will  be  clear  from  the  dotted  line  above  San 
Marcos  on  Fig.  308. 

Gauge. — The  Jalapa  line  was  intended  to  be  laid  to  3-ft.  gauge,  correspond- 
ing to  the  gauge  of  the  Mexican  National  Railway,  whereas  the  Mexican  Rail- 
way was  4-ft.  8i-in.  gauge.  No  difference  was  made  in  the  location,  however,  on 
account  of  the  gauge,  the  road-beds  having  been  taken  as  14  and  18  ft.,  slopes 
I  to  I  in  cuts  and  \\  to  i  in  fills,  and  rails  estimated  at  56  lbs.  The  ties  were 
■estimated  at  $1  each,  only  7  ft.  long,  which  was  the  only  item  estimated  in  any 
way  lower  because  of  the  gauge. 

Cost. — In  Table  No.  i  (omitted)  is  given  an  abstract  of  the  large  estimate 
blank  prepared  from  the  careful  paper  location  of  the  entire  mountain  grade. 
Table  No.  2  is  an  abstract  closing  a  report  by  the  topographer,  giving  in  detail 
the  material  on  the  line,  from  which,  in  connection  with  Fig.  310,  its  very  favor- 
•able  character  will  be  seen.  From  these  and  the  maps  and  profiles  submitted, 
which  even  in  the  reduced  engravings  show  the  estimated  quantities  at  each 
point,  any  engineer  can  form  his  own  judgment  as  to  whether  the  estimate  in 
Table  No.  i  (omitted  to  save  space)  is  adequate.  The  writer's  belief  was,  and 
still  Is,  that  it  is  entirely  adequate,  and  if  so  the  cost  of  the  entire  mountain 
grade,  with  30  per  cent  added  for  engineering  and  contingencies,  amounts  to 
less  than  $40,000  per  mile,  against  $184,677  per  mile  for  the  actual  cost  of  the 
mountain-grade  of  the  Mexican  Railway,  or  in  the  ratio  of  r  to  /\\.  A  ratio  of 
3  to  I  is  believed  to  be  the  very  lowest  which  could  be  claimed  to  correctly 
represent  the  relative  work.  Unfortunately  the  writer  was  never  able  to  obtain 
exact  figures  of  the  quantities  on  the  Mexican  Railway.  Therefore  he  is  re- 
luctant to  claim  more  than  is  certainly  just.* 

*  The  general  route  of  both  lines  here  described  is  shown  in  Fig.  308.     In 


934  APPENDIX  C. 


Make  what  allowances  one  will,  there  is  a  great  contrast  in  these  two 
lines,  and  it  therefore  becomes  of  interest  to  consider  how  this  latter  line 
was  obtained. 

In  March,  1881,  the  writer  was  engaged  by  the  Mexican  National  Rail- 
way Company  to  act  as  engineer  in  charge  of  location  and  surveys  on  the 
various  lines  for  which  they  had  concessions,  extending  from  the  city  of 
Mexico  to  the  United  States  and  to  the  Pacific  coast.  On  landing  at 
Vera  Cruz,  with  a  large  staff,  under  orders  to  report  in  Mexico,  he  was 
surprised  at  the  receipt  of  a  letter  of  instruction  to  the  effect  that  a  corps 
were  engaged  in  examining  a  line  from  Vera  Cruz  to  Mexico  via  Jalapa, 
and  that  he  should  detach  another  corps  for  service  on  this  line,  sending 
forward  the  remaining  parties  by  rail ;  that  he  should  then  make  a  re- 
connaissance "  sufficient  to  determine  the  general  possibilities  of  the 
route,  taking  such  escort  as  might  seem  necessary ;"  set  the  new  and  old 
parties  at  work ;  and  not  delay  date  of  report  in  Mexico  "  more  than  six 
days." 

Fig.  309  is  given  a  reduction  to  one-fifth  scale,  or  g^^Qo  {1^  inches  per  mile, 
within  I  per  cent),  of  the  large  topographical  map  on  a  scale  of  xxj^^tt  ^f  ^^^ 
upper  54  of  the  117  kilometres  of  the  mountain  grade.  This  in  turn  was  re-^ 
duced  from  the  original  field-sheets  on  the  large  scale  of  y^Vs"  ^^  83^  feet  per 
inch,  which  the  difficult  character  of  the  work  made  necessary.  The  topog- 
raphy was  very  accurately  taken  by  a  skilled  topographer,  Mr.  Max  Chapman^ 
M.  Am.  Inst.  M.  E. 

In  Fig.  310  is  given  a  photographic  reduction  of  the  original  profile,  which 
was  called  off,  station  by  station,  in  the  usual  way  from  a  paper  location  on  the 
original  field-sheets^  and  estimated,  station  by  station,  from  tables,  with  allow- 
ance for  surface  slope,  which  often  more  than  doubled  the  level-section  quanti- 
ties. The  estimated  quantities  for  each  cut  and  fill  are  given  on  the  profile  and 
nature  of  material  indicated.  Retaining-walls  were  estimated  for  at  every  point 
where  a  fill  would  not  catch,  and  are  indicated  by  a  thick  line  on  the  profile. 
The  small  amount  of  masonry  is  due  for  the  almost  entire  absence  of  surface 
drainage  and  running  water,  as  elsewhere  noted. 

The  hne,  profile,  and  estimate  here  shown  were  not  finalities,  but  prepared 
for  a  special  purpose.  Compensation  for  curvature  had  not  yet  been  introduced.. 
It  was  fully  expected  to  do  still  better  at  points,  and  in  fact  the  location  shown 
was  greatly  improved  in  the  upper  section  (9)  by  a  new  line,  run  just  before  the 
suspension  of  work  which  threw  the  line  back  from  the  ragged  cliff-work  near 
the  summit.  As  maps  and  profiles  of  this  improvement  cannot  be  given,  no 
claim  in  respect  to  it  is  made,  but  only  for  what  had  been  actually  secured  and 
recorded  in  black  and  white. 


rib     :       s,',^  im?:     : 


^^^ 


1 

■f' . 

jri 

- 

^ 

"    -3  4-\lff^ 

M44tl 

^'-""^^ 

Ui-j  jH"^ 

t4-:l.Tr:-t- 


#^^ 


APPENDIX   C.  935 


To  one  landing  in  Mexico  entirely  ignorant  of  the  language  and  the 
country ;  provided  with  no  map  or  profile  of  the  existing  line,  and  know- 
ing nothing  more  of  its  character  than  the  general  fact  that  it  was  one  of 
the  heaviest  and  most  costly  railways  in  the  world;  unaware  that  its 
engineers  had  even  given  a  thought  to  a  route  vm  Jalapa,  or  even  that 
there  was  such  a  place,  until  he  finally  learned  that  the  route  had  been 
examined  only  to  be  abandoned,  and  that  the  branch  which  had  been 
built  to  Jalapa,  at  the  foot  of  the  mountain  proper,  had  lo  per  cent  grades, 
and  was  practicable  only  by  horse-power ;  unaccustomed  to  a  tropical 
climate  and  to  the  saddle ;  provided  with  no  map  of  the  region  better  or 
much  larger  than  Fig.  308  which  accompanies  this  paper;  and  innocent 
of  all  knowledge  as  to  how  large  an  escort  would  insure  safety,  if  indeed 
any  could — these  were  sufficiently  formidable  instructions,  and  could 
never  have  been  successfully  carried  out,  as  fortunately  they  were  to  the 
letter  (barring  two  days'  delay  from  an  unseasonable  rain),  had  recon- 
noitring such  lines  been  in  fact  so  entirely  lawless  a  matter  that  there 
was  nothing  for  it  but  to  look  over  the  whole  country  and  then  decide 
what  to  do,  or  at  least  to  try  for. 

The  line  which  was  found  to  be  under  examination  is  indicated  by 
dotted  lines  on  the  general  map  herewith,  and  was  at  once  rejected  as  im- 
practicable and  absurd .  It  ran  from  the  coast  north-easterly  to  Jalapa,  4500 
ft. ;  then  descended  southerly,  850  ft.  in  about  10  miles,  to  an  elevation  of 
about  3650  ft.  at  Coatepec  ;  then  was  expected  to  ascend  somehow,  some 
7000  ft.  to  the  "  pass"  between  the  volcanoes  of  Orizaba  and  Perote,  at  an 
unknown  elevation,  estimated  at  10,700  ft.  in  an  air-line  distance  of  some 
15  miles ;  and  then  to  descend  some  2000  or  3000  ft.  on  the  back  slope  of 
the  mountain,  to  the  general  level  of  the  plateau.  Very  naturally  the 
best  grades  which  it  was  even  hoped  to  obtain  were  those  of  the  Mexican 
Railway,  or  4  per  cent  uncompensated. 

It  was  at  once  clear  that  either  something  considerably  better  than 
this  must  be  obtained,  or  the  line  should  be  reported  as  impracticable  and 
the  whole  staff  withdrawn.  And  it  seemed  equally  clear  to  the  writer  that 
either  a  considerably  better  gradient  than  on  the  existing  line  must  be 
obtained,  and  lighter  work  as  well,  or  the  project  reported  as  unde- 
serving of  any  consideration  financially.  A  reasonable  hope  for  a  maxi- 
mum grade  of  not  over  2^  per  cent  at  most  was  therefore  fixed  upon  as 
the  highest  one  justifying  setting  parties  at  work  on  it,  and  hence  to  be 
considered  at  all ;  and  this,  to  make  the  project  a  meritorious  one,  re- 
quired that  2  per  cent  should  be  sought  for.  This  made  it  indispensable  to 
gain  considerable  development  for  the  ascent,  and  this  in  turn  made  it  out 


93^  APPENDIX   C. 


of  the  question  j:o  ascend  between  the  two  volcanoes,  even  had  the  saddle 
between  them  been  cleft  down  to  the  level  of  the  main  plateau,  which 
was  known  not  to  be  the  case.  The  whole  problem,  therefore,  turned 
upon  the  question  of  whether  or  not  it  would  be  possible  to  turn  north- 
ward at  Jalapa  (assuming  that  point  to  have  been  successfully  reached  by 
the  required  grade,  which  seemed  a  minor  question)  and  run  parallel 
with  the  coast  line  and  the  coast  range,  gradually  ascending  with  all 
possible  development,  and  turn  the  mountain  of  Perote  to  the  north. 

This  possibility  the  writer  was  satisfied  would  turn,  negatively  at  least, 
upon  the  simple  question  of  whether  or  not  there  was  some  kind  of  an 
esiablished  highway  ascending  from  Jalapa  to  the  plateau,  following  in  a 
general  way  the  same  course,  and  turning  the  mountain  to  the  north. 
Tliat  is  to  say,  the  existence  of  a  highway  would  not  prove  the  line  was 
practicable,  but  the  absence  of  it  would  go  far  to  prove  that  it  was  im- 
practicable. In  respect  to  highways,  the  writer  had  even  then  learned 
by  sad  experience,  and  had  repeated  occasions  in  the  next  three  years 
to  realize  still  more  fully,  that  the  route  of  a  highway  is  ordinarily  the 
worst  possible  guide  for  a  locating  engineer,  except  as  it  may  serve  the 
negative  purpose  of  a  danger  sign  to  warn  him  away.  He  now  recalls  no 
less  than  twenty-three  instances  on  the  lines  in  Mexico  under  his  charge 
where  the  existence  of  a  travelled  road  proved  merely  a  snare  to  deceive. 
Some  of  these  instances  were  of  a  very  curious  character  and  of  much 
technical  interest,  but  description  must  be  forborne. 

But  in  regions  of  real  difficulty,  where  the  elevations  to  be  surmounted 
become  serious  even  for  animal  power,  and  even  after  all  avoidable  rise 
and  fall  has  been  eliminated,  the  case  is  different.  The  writer's  experi- 
ence and  conviction  is  that  in  such  cases  the  aggregate  intelligence  of 
the  cows  and  the  natives  thereabout  may  safely  be  trusted  to  discover  and 
utilize  the  very  best  route  there  is  for  surmounting  the  elevation  with  the 
least  amount  of  work.  Even  what  would  be  regarded  in  Mexico  or 
Colorado  as  so  simple  a  problem  as  that  of  making  the  900  ft.  rise  over 
the  Allegheny  Mountains  in  Pennsylvania,  is  a  case  in  point.  The  pass 
above  Altoona  and  Hollidaysburg  was  discovered  and  utilized  in  the  very 
earliest  days  of  the  settlement  of  the  country,  and  four  generations  of 
engineers  on  four  successive  public  works  have  been  able  to  do  no  bet- 
ter. 

The  first  question  asked  by  the  writer,  therefore,  after  learning  the 
details  of  what  was  doing,  was  whether  there  was  a  travelled  highway 
turning  the  mountain  to  the  north,  the  map  before  him  not  extending 
far  enough  north  to  show  that  region  distinctly  at  all.     He  was  informed 


APPEXDIX  c.  937 


at  once  that  there  was,  and  a  ver}^  old  and  good  one.  Had  the  response 
been  otherwise,  he  should  have  regarded  the  result  of  the  reconnaissance 
as  practically  decided  then  and  there.  The  statement  was  coupled  with 
another,  however,  that  this  route  had  been  examined  by  the  engineers 
of  the  Mexican  Railway,  and  reported  far  less  practicable  than  the  line 
afterwards  adopted  and  built,  so  that  the  middle  line  described  was  under 
examination  as  the  only  hope  left. 

This  was  discouraging  enough  ;  but  on  further  learning  that  the  high- 
way had  been  for  three  centuries  preceding  the  railway  era  the  leading 
one  between  the  interior  and  the  coast ;  that  there  was  no  succeeding 
descent,  but  rather  a  gentle  rise  in  it  for  many  miles  after  the  mountain- 
grade  proper  was  surmounted  ;  that  the  summit  was  (this  afterwards 
proved  an  error)  several  hundred  feet  lower  than  that  of  the  Mexican 
Railway  ;  and  some  other  facts  which  seemed  hopeful, — there  appeared  to 
be  a  fighting  chance,  which  was  at  least  the  only  chance  that  the  line 
might  be  developed  to  give  the  requisite  grade. 

The  more  immediate  question  became  then  to  make  the  ascent  of  4500 
ft.  to  Jalapa,  and  it  was  at  once  apparent  that  to  have  any  hope  of  doing 
this  on  such  favorable  grades  as  were  alone  worthy  of  consideration  under 
the  circumstances,  the  line  must  be  carried  down  to  as  low  an  elevation 
as  possible,  parallel  with  the  coast  and  the  mountain  slope,  by  running 
south  from  Jalapa  toward  Coatepec  before  beginning  to  lose  distance  by 
turning  eastward  to  the  sea.  It  appeared  probable  that  the  850  ft.  of  fall 
between  these  two  points,  as  to  which  some  definite  knowledge  was 
available,  could  not  be  made  on  a  steeper  grade  than  2  per  cent,  and  it 
was  this  fortunate  fact  (as  it  proved)  which  first  led  to  conducting  the 
reconnaissance  from  the  beginning  on  the  fighting  chance  of  obtaining  a 
2  per  cent  grade. 

It  was  now  determined,  therefore,  that  the  line,  if  there  w-as  to  be 
any,  must  pass  from  Vera  Cruz  to  Coatepec,  and  thence  to  Jalapa,  instead 
of  to  Jalapa  direct.  Coatepec  lies  at  the  head  of  a  river  of  considerable 
size,  the  Rio  Antigua,  which  runs  from  it  directly  east  to  the  coast;  and 
the  map  and  known  elevation  of  the  town  made  it  at  once  clear  that  there 
was  no  physical  impossibility  in  descending  this  valley  directly  on  a  2\ 
per  cent  grade,  or  perhaps  less,  if  the  valley  had  a  tolerably  uniform  de- 
scent. It  needed  but  the  most  moderate  knowledge  of  the  general  laws 
of  topography,  however,  to  make  it  practically  certain  that  no  even 
approximately  uniform  descent  could  be  hoped  for  in  a  river  flowing  in  a 
deep  gorge,  cut  through  what  was  practically  only  a  narrow  footing  to 
the  most  tremendous  mountain  slope  on  this  continent.     The  foot-hills 


938  APPENDIX   C. 


of  a  slope  which  reached  a  height  of  17,873  ft.  and  started  practically 
from  the  level  of  the  sea,  was  certain  to  have,  like  all  such  slopes,  a  de- 
cidedly concave  profile. 

Nothing  less  than  5  per  cent  could  be  rationally  hoped  for  in  follow- 
ing the  bed  or  immediate  slopes  of  the  valley,  and  it  therefore  became 
quite  certain  that  the  line  descending  from  Coatepec  must  start  from  the 
lowest  point  at  the  head-waters  of  the  Rio  Antigua  which  it  was  possible 
to  obtain,  but  speedily  rise  up  on  the  higher  slopes  of  the  valley  and  out 
of  the  influence  of  the  stream,  until  at  last— and  probably  within  a  short 
distance — it  would  rise  above  all  supporting  ground.  No  resource  would 
then  remain  but  to  turn  across  northwardly,  at  some  favorable  point  on 
the  dividing  ridge,  into  the  valley  of  the  next  river  to  the  north,  the  Rio 
Chachalacas,  with  the  view  of  gaining  only  such  limited  development  as 
might  be  necessary  to  catch  upon  some  high  point  on  what  were  known 
to  be  the  gentle  slopes  of  the  lower  valley  of  that  river,  from  which  the 
line  could  descend  eastwardly  on  the  required  grade  to  sea-level  at  a 
point  as  near  to  the  coast  as  possible.  The  only  fear  in  this  process,  be- 
sides the  danger  of  heavy  work,  was  that  it  might  be  unavoidable  to  make 
a  long  horseshoe  development  up  the  valley  of  the  Chachalacas,  bring- 
ing the  foot  of  the  grade  far  inland  from  the  sea,  and  causing  just  so 
much  unnecessary  loss  of  distance  on  a  level  before  reaching  the  foot  of 
the  mountain  grade.  The  existence  of  these  two  parallel  and  deep-lying 
streams  made  it  certain  that  the  general  scheme  below  Coatepec  would 
be  practicable,  if  not  too  costly  ;  and  the  immense  depth  of  the  southerly 
valley,  which  varied  from  1000  to  2000  ft.,  together  with  the  absence  of 
all  supporting  ground  to  the  south  of  it,  made  it  certain  that  the  line 
could  at  no  point  turn  south  between  Coatepec  and  the  coast. 

Thus,  by  a  process  of  exclusion,  the  entire  line  was  projected  and 
sketched  upon  the  map,  with  most  dismal  apprehensions  of  the  charac- 
ter of  the  work  which  would  be  encountered,  but  with  absolute  confi- 
dence, expressed  at  the  time  to  the  gentlemen  who  accompanied  the 
writer  on  reconnaissance,  in  the  face  of  some  opposition,  that  if  this  line 
was  not  practicable,  there  was  nothing  in  the  region  which  was  suffi- 
ciently defensible,  from  an  economic  point  of  view,  to  make  it  even  worth 
examination.  The  line  shown  on  the  general  map  (Fig.  308)  which  the 
writer  now  has  the  honor  to  lay  before  the  Society,  does  not  dififer  by 
its  own  width  at  any  point  in  the  entire  ascent  of  nearly  8000  feet  to  the 
plateau  from  that  which  the  writer  thus  sketched  upon  the  map  in  the 
city  of  Vera  Cruz,  and  showed  to  several  gentlemen,  on  the  evening  of 
the  day  when   he  first  landed  in    Mexico :  within  two  hours  after  first 


APPENDIX  C.  939 


learning  that  there  was  such  a  place  as  Jalapa,  or  that  there  was,  or  ever 
had  been,  such  a  project  as  an  ascent  to  the  plateau  through  that  region, 
and  with  the  elevation  of  only  two  points  on  the  line,  Jalapa  and  Coate- 
pec,  approximately  given.  Neither  does  the  line  on  Fig.  308  differ  by 
much  more  than  its  own  width  at  any  point  from  the  position  of  the  line 
as  finally  surveyed,  as  shown  on  the  detailed  maps  and  profiles  which  are 
herewith  laid  before  the  Society  complete,  the  more  difficult  upper  half 
of  the  mountain  grade  only  having  been  engraved  on  Figs.  309  and  310. 

The  writer  would  not  be  understood  to  assert  or  imply  tliat  equal 
positiveness  in  defining  in  advance  the  limitations  of  reconnaissance  is 
often  possible.  On  the  contrary,  he  has  never  known  another  instance 
just  like  it,  although  it  became  his  duty  later  to  consider  projects  for 
several  other  lines  of  a  similar  but  less  exacting  character.  But  the 
peculiar  conditions,  it  will  be  seen,  left  no  escape  at  any  point  from  the 
chain  of  reasoning.  Had  there  been  no  existing  parallel  line,  one  might 
have  justifiably  taken  the  region  for  better  for  worse,  and  borne  with 
equanimity  finding  it  a  great  deal  worse  than  he  took  it  for.  As  it  was, 
the  fighting  chance  for  a  low  grade  was  the  only  one  economically  worthy 
of  attention,  and  this  primary  fact  given,  the  conditions  left  no  escape 
at  any  point  from  the  train  of  reasoning  that  it  was  that  one  route  or 
nothing. 

The  next  morning  at  daybreak  the  reconnaissance  began,  and  was 
pushed  through  with  increasing  confidence  as  fast  as  the  animals 
could  stand  it,  or  at  the  rate  of  some  40  miles  per  day,  the  entire  ex- 
amination of  the  mountain  grade  occupying  three  days — such  haste 
being  merely  in  fulfilment  of  the  writer's  positive  instructions,  and  nat- 
urally against  his  inclination.  Less  time  was  required,  however,  be- 
cause the  only  real  purpose  of  the  reconnaissance  was  not  to  find  a  route, 
but  to  examine  on  the  ground  the  features  of  what  was  already  known 
to  be  the  only  route  affording  a  rational  chance  of  success.  The  first 
1500  feet  of  rise  was  seen  to  be  on  slopes  smooth  in  detail,  but  suffi- 
ciently steep  for  laying  down  a  surface  line  on  almost  any  grade,  and 
were  not  examined  critically.  The  dividing  ridge  was  then  followed  up, 
to  judge  of  what  was  really  the  only  critical  point  of  the  lower  descent 
(from  the  point  of  view  of  possibility  and  not  of  cost),  the  passage  from 
one  water-shed  to  the  other.  A  long  and  sharp  spur  ridge  running 
eastwardly  from  Coatepec  about  half  way  to  the  coast,  having  a  crest 
5000  or  6000  feet  high,  and  standing  at  right  angles  to  the  main  slope, 
was  found  to  define  the  point  where  this  passage  must  occur  pretty  defi- 
nitely, and  the  material  and  topography  was  seen,  with  much  relief,  to 


940  APPENDIX   C. 


be  favorable  for  making  this  passage  with  as  much  or  as  little  develop- 
ment as  might  be  necessary,  with  considerable  latitude  in  elevation  and 
easy  work.  The  south  slope  of  this  mountain,  where  the  line  would  lie, 
was  found  to  be  almost  impracticable  for  passage  on  horseback  without 
-camp  equipage  and  time ;  but  observing  the  north  side  to  be  fairly  favor- 
able, and  taking  it  to  be  very  unlikely  that,  in  a  ridge  of  this  character, 
the  topography  would  differ  widely  on  the  two  slopes,  it  was  passed  by 
with  a  confidence  that  the  result  fully  justified,  as  well  as  such  very  lim- 
ited information  as  was  available  at  the  time.  It  will  be  seen  from  the 
.maps  and  profiles  of  this  section  (not  engraved)  that  on  the  surveys  now 
submitted,  a  few  of  the  most  costly  single  works  on  the  line  are  here,  and 
not  on  the  engraved  section  above  Jalapa,  which  was  really  the  critical 
section.  This,  however,  the  writer  is,  and  was  then,  satisfied  was  due 
chiefly  to  the  fact  that  the  lower  section,  not  being  a  source  of  much 
anxiety,  was  left  in  less  competent  hands.  In  part  it  was  radically  im- 
proved almost  at  the  conclusion  of  surveys,  and  the  writer  feels  no  doubt 
that  it  all  might  have  been  more  or  less,  although  he  makes  no  claim  in 
that  respect.  Owing  to  the  falling  away  of  the  country  to  the  south, 
before  referred  to,  and  the  existence  of  the  deep  barranca,  or  gorge,  in 
which  the  river  lay,  which  cut  down  almost  to  sea-level,  or  some  3000 
leet  below  the  line,  some  of  the  most  sublime  views  of  the  line  were  on 
this  section ;  but  its  difficulty  was  not  in  proportion,  in  part  because  of 
the  very  fact  that  the  line  lay  so  high  as  to  be  above  the  immediate  influ- 
ence of  the  barranca.  The  material  on  all  this  section  was  exceedingly 
favorable. 

The  region  between  Coatepec  and  Jalapa  was  known  to  be  not  very 
rugged,  and  to  oppose  no  difficulty  as  to  elevation,  so  that  it  also  was 
passed  by  with  a  confidence  which  the  result  justified,  and  the  project 
was  complete  to  Jalapa,  as  a  basis  for  surveys,  with  a  reasonably  favor- 
able 2  per  cent  grade-line  all  but  assured. 

For  the  critical  section  above,  the  distance  by  highway  was  found  to 
be  almost  one  half  too  short,  and  all  hung  upon  the  possibilities  of  de- 
velopment. The  material  and  topography  on  the  lower  half  was  found 
to  be  favorable  for  this  purpose,  being  earth  to  a  great  depth,  as  noted, 
and  sufficiently  broken  up  by  ridges  and  hills.  A  long  stretch  at  about 
the  middle  of  the  slope,  near  the  village  of  San  Marcos,  was  of  an  equally 
favorable  character,  being  literally  an  inclined  plane  on  a  slope  of  about 
I  in  10, — an  old  lava  flow  overlaid  with  soil, — and  not  much  broken  up 
in  detail.  The  upper  section  was  rugged,  but  short,  with  considerable 
•opportunities  for  rather  expensive  development. 


APPENDIX  C.  941 


The  whole  of  this  region  was  examined  on  the  third  day  of  a  very 
heavy  rain-storm,  the  end  of  which  could  no  longer  be  waited  for,  and 
the  examination  was  necessarily  restricted  to  salient  features  only.  On^ 
a  long  grade-line  of  this  character,  however,  the  possibilities  of  develop- 
ing on  practicable  ground  to  reach  certain  elevations  at  certain  frac- 
tional portions  of  the  available  distance,  can  be  judged  of  with  some 
certainty,  the  general  character  of  the  slope  being  the  main  feature;  and 
the  writer  felt  no  real  doubt  then,  or  at  any  later  time,  that  a  grade  in 
the  neighborhood  of  2  to  2^  per  cent  was  easily  practicable,  there  being 
a  certain  considerable  belt  of  favorable  territory  on  which  to  place  it, 
although  above  and  below  that  the  topography  was  much  more  forbid- 
ding. A  leading  factor  in  reaching  this  apparently  hasty  conclusion 
was  the  splendid  and  ancient  highway  already  referred  to,  by  far  the 
best  in  Mexico,  if  not  on  this  continent.  It  is  a  broad  macadamized 
road  with  paved  gutters,  and  a  stone  curb  or  masonry  w^all  at  the  side, 
and  the  writer  desires  to  pay  a  tribute  of  admiration  and  respect  to  the 
unknown  engineer,  whoever  he  was, — very  possibly  one  of  the  soldiers  of 
Cortez,  or  one  of  his  immediate  successors, — who  laid  it  out.  From  a 
point  near  Jalapa  to  the  summit,  near  Las  Vegas,  there  is  not  a  break  in 
the  steady  ascent,  and  there  are  few  points  on  it  where  a  fresh  team  of 
horses  would  not  readily  break  into  a  trot.  The  conclusion  was  natural, 
that  if  a  Spanish  soldier  in  1530  could  put  something  like  a  6  per  cent 
highway  down  that  mountain  slope,  an  American  engineer  in  1881  ought 
to  get  a  2  per  cent  railroad  line  down  it,  or  take  off  his  hat  to  his  prede- 
cessor. 

After  reaching  the  summit,  the  continuation  of  the  line  to  Mexico, 
or  any  other  point  on  the  plateau,  was  a  detail  offering  no  difficulties 
and  needing  no  immediate  stud^^  The  line  was  therefore  reported 
on  in  writing  to  Mr.  W.  C.  Wetherill,  chief  engineer,  three  days  later 
(March  28),  as  follows  : 

"The  line  under  examination  was  too  forbidding  to  be  worth  further  at- 
tention. ...  I  feel  no  doubt  that  the  proper  place  for  the  line  is  to  the  north 
of  Perote,  and  that  something  like  a  2^  per  cent  grade,  or  possibly  a  2  per  cent 
grade,  is  practicable  above  Jalapa.  Whatever  grade  is  there  obtained  can  cer- 
tainly be  continued  down  to  sea-level  and  slope  without  excessive  work.  I 
have  instructed  surveys  to  be  conducted  above  and  below  Jalapa  on  a  2  per 
cent  basis  for  the  present,  and  consider  the  prospects  for  a  fairly  favorable  line 
good." 

It  should  be  mentioned  further,  that  the  writer's  examination  had 
been  merely  in  a  consulting  capacity  (the  line  not  being  formally  a  part 


942  APPENDIX   C. 


of  the  Mexican  National  projects),  and  for  some  months  later  he  had  no 
permanent  connection  with  or  knowledge  of  the  progress  of  the  work, 
being  absent  on  the  Pacific  slope.  On  being  again  asked  to  examine 
the  line,  August  ist,  1881,  he  found  that  his  conclusions  had  been  re- 
ported on  as  impracticable,  and  that  a  3  per  cent  compensated  grade  had 
been  adopted,  located  in  part,  and  was  under  construction.*  Fortu- 
nately, however,  a  most  intelligent  assistant  engineer,  of  great  natural 
capacity  for  location,  Mr.  John  S.  Elliott,  was  in  charge  of  the  upper 
locating  party.  To  his  admirable  conduct  of  surveys  the  success  of  this 
line  was  very  largely  due.  Aided  by  information  he  had  acquired,  it 
was  soon  discovered  that  the  abandonment  of  the  2  per  cent  grade  had 
been  an  over-hasty  conclusion,  from  data  which  in  fact  assured  its  suc- 
cess. The  work  in  progress  was  therefore  stopped  by  the  writer's  advice  ; 
some  $30,000  of  completed  work  abandoned,  chiefly  in  the  approaches 
to  a  costly  tunnel  in  earth  ;  and  the  writer  appointed  chief  engineer,  con- 
tinuing in  charge  until  some  time  after  the  completion  of  the  surveys 
now  laid  before  the  Society,  when  the  abandonment  of  all  furtherance  of 
the  project  by  the  Mexican  National  Railway  compelled  his  resignation, 
and  shortly  afterward  led  to  the  stoppage  of  all  work.  But  for  the  fact 
that  he  was  favored  with  an  unusually  competent  assistant  in  immediate 
charge  of  surveys  on  the  more  difficult  section,  the  writer  fears  that  he 
should  never  have  been  able  to  carry  through  the  line  with  the  limited 
time  at  his  command. 

Two  features  on  the  upper  ascent  are  worthy  of  special  note :  One,  the 
great  lava  flow  shown  in  Fig.  309,  and  before  referred  to ;  and  the  other, 
a  still  grander  feature,  the  barranca  of  Zimilahuacan,  a  vast  sink-hole  in 
the  earth  some  2  or  3  miles  in  diameter,  and  some  3000  feet  deep  by  the 
barometer,  about  half  of  it  sheer,  with  no  transition  or  "ragged  edge" 
whatever  from  the  surrounding  surface  of  the  plateau,  which  was  as 
smooth  and  treeless  as  an  Illinois  rolling  prairie,  but  sloping  about  i  in 
12  or  15  in  the  chasm.  This  feature  was  encountered  some  miles  beyond, 
where  all  difficulties  had  ceased  at  the  summit;  and  so  smooth  was  the 
edge  that  the  line  skirted  it  with  a  mere  surface  line,  so  near  to  it  that 
a  stone  thrown  from  the  car-window  would  fall  sheer  full  1000  feet  before 
touching.  On  the  plateau  the  locality  was  so  cold  and  so  much  exposed 
that  it  was  stated  that  wheat  would  hardly  head,  while  immediately  be- 
neath one's  feet  bananas,  coffee,  oranges,  and  every  form  of  tropical 
vegetation  could  be  seen  growing  luxuriantly.     A  few  miles  beyond  was 

*  The  concession  permitted  of  no  delay  in  beginning  construction. 


APPENDIX   C.  943 


a  large  and  very  ancient  fortress  still  in  good  repair,  but  unoccupied, 
which  would  cost  perhaps  $5,000,000  or  $6,000,000  to  duplicate,  in  which 
for  two  centuries  the  great  bulk  of  the  silver  product  of  Mexico  was 
stored  pending  the  arrival  of  transports  at  Vera  Cruz.  Several  of  the 
old  line  of  visual  telegraph  towers  which  were  used  to  communicate 
between  the  two  points  are  still  pointed  out,  although  out  of  use  more 
than  a  century.  From  several  points  on  the  upper  ascent  the  city  of 
Vera  Cruz,  80  miles  off  in  an  air-line  and  6000  to  8000  feet  below,  is 
visible  in  clear  weather.  These  and  other  features  make  the  region  one 
of  the  highest  interest  to  the  tourist. 

In  view  of  what  has  preceded,  the  writer  hopes  that  he  may  not  be  sus- 
pected of  over-estimating  the  difficulties  of  securing  such  lines,  or  of  per- 
sonal inability  to  cope  with  them,  when  he  declares  his  conviction  that 
this  whole  method  of  taking  railway  lines  up  difficult  ascents  by  a  con- 
tinuous succession  of  curves  and  tangents  on  a  rising  grade,  over  which 
the  locomotive  keeps  up  a  steady  march,  is  fundamentally  wrong  and 
bad,  and  one  which  might  profitably  be  modified  in  nearly  all  cases  when 
an  elevation  of  over  1000  feet,  or  possibly  much  less,  is  to  be  surmounted. 
To  furnish  a  suitable  background  for  the  expression  of  these  conclusions, 
by  showing  that  they  are  formed  in  spite  of  fairly  successful  experience 
in  following  up  the  more  usually  approved  plan,  is  a  main  purpose  of 
this  paper. 

Three  generpl  methods  for  surmounting  such  elevations,  besides  the 
almost  universal  one,  are  more  or  less  in  use : 

First.   Rack  or  grip  railways. 

Second.  Inclined  planes  operated  by  stationary  engines. 

Third.  Switchbacks. 

The  first  of  these  was  proposed  in  a  practicable  form  over  thirty  years 
ago,  and  the  two  latter  antedate  the  locomotive  itself.  Either  one  of 
them  is  probably  deserving  of  more  use  than  is  given  it,  but  the  third 
(switchback)  the  writer  deems  worthy  of  adoption  by  engineers  as  the 
standard  plan  for  surmounting  considerable  elevations,  always  provided 
the  switchbacks  be  constructed  and  operated  in  quite  a  different  manner 
from  that  usual  in  the  few  which  exist,  which  have  for  the  most  part 
only  been  resorted  to  as  a  last  resource. 

One  feels  a  natural  hesitation  in  expressing  a  conclusion  which,  it 
must  be  admitted  at  once,  all  the  tendency  of  modern  practice  tends  to 
discredit.  The  accumulated  verdict  of  experience  is  rarely  wrong,  and 
it  is  undeniable  that  all  these  plans  have  been  in  many  cases  tried  and 
abandoned,  and  have  met  decreasing  favor.     Nevertheless,  causes  need- 


944  APPENDIX   C. 


less  to  go  into,  other  than  lack  of  real  merit,  may  explain  in  part  at  least 
this  result,  and  the  writer  sees  no  escape  from  believing  that  they  do  so 
wholly. 

The  capabilities  of  the  inclined  plane  or  cable  plan  have  been  greatly 
extended  in  recent  years,  as  applied  to  street  and  local  passenger  service^ 
and  it  is  clearly  destined  in  the  near  future  to  still  wider  use.  Super- 
ficially, the  record  of  its  use  in  connection  with  ordinary  railways  is 
most  discouraging  to  any  hope  of  its  future  usefulness  in  that  direction. 
In  the  early  days  of  railways  it  was  constantly  considered,  and  often 
used.  A  complete  plant  of  the  kind  existed  over  the  Allegheny  summit 
of  the  Pennsylvania  Railroad  before  that  line  was  built,  and  was  aban- 
doned in  favor  of  locomotive  traction,  even  to  connect  two  lines  of  canals^ 
Several  complete  railways  operated  by  successive  inclined  planes  and 
gravity  inclines  were  built  in  Pennsylvania  and  elsewhere — two  in  North- 
ern Pennsylvania  of  considerable  length,  one  of  which  is  still  in  use  and 
the  other  only  recently  abandoned,  but  not  chiefly,  if  at  all,  for  reasons 
affecting  its  abstract  merit.  It  is  not  generally  known  that  the  existing 
main  line  of  the  Pennsylvania  Railroad  over  the  AUeghenies,  which  was 
built  long  after  the  old  planes  had  been  abandoned,  was  laid  out  with 
the  distinct  view  of  afterwards  adding  a  new  and  enlarged  system  of 
planes  for  freight  traffic  when  the  volume  of  traffic  had  increased  to 
justify  it.  This  policy  was  favored  by  its  distinguished  chief  engineer,. 
Mr.  J.  Edgar  Thompson,  and  some  elaborate  and  interesting  data  in  re- 
spect to  it  are  given  in  the  early  reports  of  that  road,  notably  in  a  report, 
by  the  then  Superintendent,  Gen.  Herman  Haupt,  in  which  the  ground 
is  distinctly  taken  that  it  is  a  mere  question  of  volume  of  traffic  whether 
inclined  planes  are  economical  or  not. 

That  view  the  writer  apprehends  to  be  the  true  one.  The  fixed  trac- 
tive plant  is  costly  to  construct,  maintain,  and  operate,  and  expenses  are 
not  greatly  affected  by  whether  the  tonnage  moved  by  it  be  large  or 
small.  It  by  no  means  follows  that,  because  the  system  was  wisely 
abandoned  in  favor  of  locomotive  power,  for  the  thin  traffic  of  those 
early  days,  that  it  is  wise  to  continue  to  neglect  it  at  points  where  almost 
a  steady  stream  of  laden  cars  is  to  be  carried,  first  up  and  then  down  a 
dividing  ridge,  day  and  night,  the  year  round,  as  on  the  Pennsylvania 
summit,  and  at  many  similar  localities.  At  such  points  it  is  demonstra- 
ble that  not  only  may  the  great  amount  of  power  used  in  lifting  locomo- 
tives be  saved,  but  that  the  descending  and  ascending  cars  may  be  bal- 
anced against  each  other,  thus  largely  eliminating  the  effect  of  the  rise  ; 
while  the  superior  economy  of  stationary  engines  will  largely  reduce  the 


APPENDIX   C.  945 


cost  per  horse-power,  after  allowing  for  the  friction  of  cables,  which,  on  a 
short,  steep  incline  is  a  minor  element.  Especially  now  that  the  making 
of  long  continuous  cables  is  so  well  understood,  so  that  as  long  an  in- 
cline as  the  topography  permits  may  be  readily  worked,  it  is  worthy  of 
the  most  serious  study  whether  a  very  large  economy  is  not  readily  pos- 
sible at  such  special  localities,  a  considerable  number  of  which  may  be 
counted  up. 

A  proper  switchback  system,  however,  seems  to  the  writer  the  most 
generally  useful  and  meritorious  for  lines  of  probably  thin  traffic,  as  well 
as  the  most  unquestionably  practicable  for  use  in  all  such  localities.  The 
germ  of  the  proper  system  was  contained  in  the  first  switchback  laid 
out  in  America,  if  not  in  the  world, — that  at  Mauch  Chunk, — which  was 
used  for  dropping  empty  coal-cars  down  into  the  Nesquehoning  Valley, 
before  the  tunnel  of  that  name  was  completed.  That  track  was  used  only 
for  cars  passing  in  one  direction  (descending),  and  was  operated  as  fol- 
lows : 

The  cars  were  started  from  A,  Fig.  311,  on  a  down  grade  of  about  i 
per  cent,  calculated  to  give  a  considerable  velocity.  At  B  an  automatic 
switch,  whose  exact  mechanism  the 
writer  cannot  give,  was  run  through  and 
the  car  brought  to  a  rest  by  the  next  suc- 
ceeding up  grade  at  C,  from  which  it  im- 
mediately started  back  towards  D,  pass- 
ing through  the  switches  B  and  D  until 
again  stopped  at  E  ;  and  so  on  indefinitely, 
the  cars  descending  several  hundred  feet 
in  all  without  the  slightest  attention, 
very  rapidly,  with  very  rare  accidents^ 
and  with  no  one  on  them  or  stationed 
along  the  track.  '^^^-  3"- 

Thus,  to  say  the  least,  every  advantage  was  gained  that  could  have 
been  gained  by  a  long  continuous  descent,  with  the  immense  advantage 
that,  owing  to  the  entire  liberty  of  choice  as  to  the  length  given  to  each 
plane,  the  best  alignment  and  lightest  work  available  on  any  part  of  the 
surrounding  country  may  be  chosen. 

But  more  than  this  was  gained.  Any  long  continuous  grade  which 
is  steep  enough  to  move  cars  with  journals  in  rather  bad  order,  must  be 
steep  enough  to  speedily  give  cars  in  good  order  a  dangerous  velocity. 
Thus  it  would  be  impossible  to  let  cars  run  of  themselves  down  a  con- 
tinuous grade  of  any  kind,  while,  on  the  switchback,  not  only  was  this 
50 


94^  APPENDIX  a 


very  readily  done,  but  a  pretty  high  average  velocity  could  be  safely 
used,  from  the  fact  that  it  in  any  case  could  not  exceed  a  certain  maxi- 
mum. Again,  when  necessity  required,  it  was  easy  to  stop  cars  at  any 
point. 

Analogous  advantages  are  readily  obtainable,  mutatzs  ?7zuta7idzs,  by 
.switchbacks  operated  by  regular  trains  running  in  both  directions,  but 
not  under  the  conditions  of  ordinary  practice,  which  necessitates  the 
complete  loss  of  all  the  vz's  viva  of  the' train  at  every  switch.  The  plan 
rhown  in  Figs.  312  and  313  will  apparently  obviate  this  necessity  com- 
pletely, and  introduce  no  new  elements  liable  to  cause  difficulty,  but,  on 
the  contrary,  give  smooth,  easy,  and  rapid  motion.  The  details  of  this 
plan  are  as  follows  :  ' 

As  Respects  the  Switches.— Th.^  switches  should  be,  and  are  easily 
made,  entirely  automatic.  Their  normal  position  should  be  that  in  Fig. 
312,  in  position  for  running  up  hill,  and  not  down  hill.  A  runaway  train 
or  car  cannot  then  pass  a  switch  and  continue  down  grade.  As  respects 
a  train  going  up  grade,  this  arrangement  presents  no  difficulty.  It  may 
simply  run  through  the  switch  Z>,  springing  the  points  over  to  let  the 
wheels  pass.  Simple  devices  of  many  different  forms  maybe  used  to 
restrain  too  rapid  return  of  the  points  after  the  passage  of  each  single 
wheel,  but  this  is  not  essential,  as  the  wear  and  tear  would  be  small. 

The  mechanism  here  outlined  acts  as  follows: 

Down      Trains. —  A         \ 
places  B  and  C  in  position        "  v     N. 
to  act,  which  are  otherwise  ^'N^-^yX^^ 

entirely  inoperative,  ^^^^'^^^''^'NS^ 

B.  when  first  made  op-  ^^^C/^**^^;:::^^- 

erative   by  A^  opens    the      f ^-v.^^^  .  — ■"■'-y    ■■— 

switch  D  for  track  C,  and        ^0^^^""^"^  ^     _^-^-~--,        ^    _ J^        . 

holds  it  open.  Jt 

C,  always  operative  Fjg.  312.— Mechanism  for  Automatically  Operating  the 
when  ^  is,  returns  ^,  ^,  Switches  of  Switchbacks. 

and  D  to  their  original  positions. 

A,  B,  and  C  are  supposed  to  be  located  with  reference  to  having  the  engine  always  at 
the  same  end  of  the  train.  If  the  engine  be  at  the  other  ends  the  switches  must  be  oper- 
ated by  hand. 

Up  Trains. — If,  by  carelessness,  the  engineer  of  ati  up  train  should  leave  the  switch- 
actuating  lever  down,  nothing  will  happen  except  to  set  A  as  if  for  a  down  train,  in  leav- 
ing the  switchback.  This  will  not  affect  following  trains,  either  down  or  up.  Should  a 
succeeding  up  train  be  equally  careless,  it  will  act  first  on  C  and  then  on  A,  thus  running 
through  the  switch  with  no  effect. 

A  train  descending  should  be  able  to  operate  the  switch,  so  as  to  con- 
tinue descent,  by  a  single  act  of  the  engineer,  but  only  by  intention  on 


APPENDIX  C. 


947 


l-  O'ZJ"^ 


'-} 


his  part.  This  may  be  accomplished  by  a  very  simple  and  inexpensive 
apparatus,  such  as  that  outlined  in  Fig.  312,  operated  by  a  lever  or  idler 
wheel  on  the  locomotive  controlled  by  the  engineman,  and  with 
mechanism  somewhat  similar  to  that 
of  the  simpler  forms  of  interlocking 
apparatus,  which  it  would  be  super- 
fluous to  describe  in  detail,  as  it  can 
be  designed  in  a  few  hours  by  any 
signal  engineer.  The  general  meth- 
od of  operation  is  described  beside 
Fig.  312,  the  whole  insuring  that  (i) 
up  trains  shall  always  pass  the 
switches  freely  and  automatically;  (2) 
that  runaway  down  trains  shall 
never  pass  them,  but  be  caught ; 
(3)  that  regular  down  trains  shall  be 
enabled  to  pass  the  switches  auto- 
matically by  a  single  act  of  the  en- 
gineer ;  (4)  that  careless  neglect  of 
this  act  shall  do  no  other  harm  than 
to  cause  the  train  to  run  back  again 
on  the  up  track ;  (5)  that  danger 
signals  shall  be  set  when  the  switches 
are  wrong,  or  any  part  of  the  appa- 
ratus broken ;  (6)  that  the  switches 
can  at  all  times  be  operated  by  hand 
if  desired,  or  if  the  mechanism  is  out 
of  order. 

As  respects  the  Adjustment  of  the 
Grades. — Fig.  313  shows  in  detail 
what  the  writer  regards  as  the  proper 
adjustment  of  grades  for  a  2  percent 
switchback,  and  the  principle  of  the 
adjustment  for  any  grade.  With 
this  arrangement  it  is  unnecessary 
for  an  up  train  to  use  brakes,  or  even 
shut  off  steam  at  all,  for  making  the 
stop  and  then  starting  backwards. 

It  will  be  seen  that  the  up  grade 
passed  the  switch  and  then  rises  in  a 


1-^ 


V> 


continues  unbroken-  until  it  has 
sharp  vertical  curve,  which  rises 


94^  APPENDIX  C. 


above  the  regular  grade,  slowly  at  first,  and  at  the  further  end — merely 
as  a  precaution  against  accidents — rises  very  rapidly  indeed.  This  is  to 
bring  the  train  to  a  stop  slowly  and  gradually,  but  certainly,  without 
either  shutting  off  steam  or  using  brakes.  The  rise  necessary  to  do  this 
for  any  given  train-speed  may  be  computed  exactly,  and  is  given  in  Table 
.ii8  of  this  volume. 

Suppose  a  train  to  be  ascending  the  2  per  cent  grade  at  a  uniform 
speed  of  15  miles  per  hour.  Then,  by  the  table,  a  lift  of  7.99  ft.  above 
the  regular  grade  will  bring  it  to  a  stop  even  with  the  engine  still  using 
steam.  If  the  velocity  be  only  10  miles  per  hour,  a  lift  of  3.55  ft.  only 
Tvrill  be  necessary,  and  this  will  or  can  readily  be  made  to  be  the  usual 
speed  of  approach.  In  that  case,  if  the  train  consist  of  10  cars  and  be 
400  ft.  long,  it  will  come  to  rest  with  the  steam  still  on,  unchanged,  when 
the  rear  of  the  train  has  passed  a  little  over  100  ft.  past  the  switch,  the 
centre  of  gravity  of  the  train  being  then  3.55  ft.  above  the  tangent  grade- 
line.  The  slack  of  the  train  will  be  taken  out,  under  these  conditions, 
very  gradually  indeed,  and  almost  at  the  instant  of  coming  to  rest. 

If,  then,  without  changing  the  throttle,  the  reverse  lever  be  thrown 
over  into  back  gear,  or  even  merely  into  mid-gear,  so  as  to  do  no  work 
at  all,  the  train  will  immediately  start  backward,  still  holding  all  the  slack 
out  of  the  train,  which  will  continue  out  until  forward  motion  is  resumed 
at  the  next  switchback.  If  the  lever  were  immediately  placed  in  the 
same  notch  of  back  gear  in  which  it  formerly  stood  in  forward  gear  (which 
would  be  unnecessary)  the  speed  which  the  train  would  have  acquired  on 
resuming  the  upper  straight  grade  at  T,  Fig.  313,  would  be  that  due  to 
the  height  c,  which  is  3.55  +  (8x4)=  35.55  ft.,  or,  as  per  Table  118,  3i|- 
miles  per  hour,  an  objectionably  high,  but  not  dangerous,  speed.  Had 
the  velocity  of  approach  from  below  been  15  miles,  this  speed  would  have 
been  that  due  to  37.99  ft.  or  only  32f  miles  per  hour,  and  had  the  velocity 
of  approach  (in  case  of  passenger  trains)  been  even  20  or  25  miles,  this 
speed  would  have  been  only  36  or  39  miles  per  hour.  Thus  the  switch, 
with  grades  arranged  as  shown,  can  be  run  through  at  any  speed,  making 
no  more  change  in  the  brakes,  steam  or  engine,  than  to  throw  over  the 
reverse  lever,  at  the  moment  the  train  comes  to  a  stop,  from  full  gear  for- 
ward to  full  gear  back.  , 

With  ordinarily  careful  and  safe  working,  the  speed  at  T,  Fig.  313, 
would  be  about  10  miles  per  hour  higher  than  the  speed  of  approach, 
a  gain  far  more  than  sufficient  to  obviate  all  loss  of  time  from  the  stop, 
and  equivalent  (for  speeds  of  10  miles  per  hour  approaching  and  10  miles 
leaving)  to  a  subtraction  of  10.65  vertical  feet  from  the  rise  in  the  next 


APPENDIX  C.  949 


grade — a  gain  which  will  considerably  increase  the  average  speed  or  haul- 
ing capacity,  or  both.* 

Fig.  313  equally  well  represents  the  conditions  at  the  next  ensuing 
switchback,  where  the  train  approaches  rear-end  to  it,  if  we  simply  as- 
sume the  engine  to  be  at  the  other  end  of  the  train.  It  reaches  the  po- 
sition shown,  backing  up  from  below,  with  all  slack  out  of  the  train.  In 
starting  forward  on  the  up  grade,  the  rear  end  of  the  train,  being  on  a 
steeper  grade  than  the  engine,  will  tend  to  crowd  slightly  upon  it,  and  by 
setting  the  reverse  lever  in  the  second  or  third  notch  of  forward  gear, 
the  slack  will  be  taken  out  in  the  gentlest  possible  way,  far  more  gently 
than  is  ever  possible  in  starting  on  a  level. 

Thus  the  ordinary  and  great  objections  to  sharp  hollows  in  grade-lines 
do  not  apply  in  this  case.  On  the  contrary,  the  action  is  smoother  than 
it  would  be  without  the  curved  profile.  Similarly,  the  still  greater  ob- 
jections to  a  stop  on  the  grade-line  do  not  apply  at  all  in  this  case.  We 
rather  gain  by  it,  because  the  whole  train  stops  and  starts  again  with  the 
gentleness  and  economy  of  energy  of  a  pendulum,  for  identical  mechan- 
ical reasons. 

This  being  so, — there  being  no  loss  of  time,  no  loss  of  distance,  no  loss 
of  hauling  capacity,  and  no  measurable  loss  in  smoothness  of  motion, — 
we  have  left  as  a  net  gain  two  things :  First.  A  great  additional  safe- 
guard against  collisions  with  and  derailments  of  runaway  trains  or  parts 
of  trains.  Accidents  resembling  the  terrible  one  on  the  Southern  Pacific, 
on  the  Tehachapi  grade,  some  years  ago,  in  which  nearly  all  of  a  train- 
load  of  people  were  killed  or  injured,  are  not  likely  to  occur.  Before  a 
train  can  attain  a  velocity  of  60  or  70  miles  per  hour  it  must  fall  128  or 
174  feet  in  excess  of  the  fall  required  to  overcome  its  resistance.  If  we 
estimate  its  average  resistance  in  acquiring  that  speed   at  20  lbs.  per 


*  If  the  train  were  running  up  a  straight  grade  ZOT'at  15  miles  per  hour 
(say  22  feet  per  second)  in  - —  =  18.2  seconds. 

Via  the  switchback  it  takes : 

o  —I—  22 
O  to  stop,  800  feet  at  average  speed  of  about  — - —  =  48.5  seconds. 

Stop  to  T,  1200  "         "         "         "         £+37  _  ^^^       ,, 

91.8       " 
Loss  of  time,  as  nearly  as  may  be,  ij  minutes. 
The  train  is  then  moving  10  miles  per  hour  faster,  so  that  it  will  save  this 
lost  time  almost  within  the  next  mile. 


950  APPENDIX   C. 


ton,  equivalent  to  the  acceleration  on  a  i  per  cent  grade,  a  train  must  de- 
scend a  2  per  cent  grade  for  2\  to  3i  miles  before  it  will  acquire  those 
velocities.  A  single  car  would  take  much  longer  yet,  so  that  a  switch- 
back every  3  or  4  miles  would  go  far  to  insure  against  the  worst  results 
from  such  catastrophes,  which  no  care  can  wholly  avoid. 

Second.  A  great  reduction  in  cost  of  construction  and  amount  of 
curvature,  and  usually  in  rate  of  gradient  as  well,  is  assured;  in  some 
cases  more  than  others,  but  always  considerable.  In  the  line  described 
in  this  paper,  the  writer  estimates  that  half  the  curvature,  and  nearly  half 
the  cost  of  construction  to  sub-grade,  might  have  been  saved  by  using 
not  more  than  eight  or  ten  switchbacks  on  the  whole  ascent  of  8ooa 
feet,  through  the  better  choice  of  ground  afforded.  An  entirely  different 
route  would  have  been  selected,  and  nearly  the  whole  line  might  have 
been  reduced  to  but  little  more  than  a  surface  line.    - 

On  the  other  hand,  there  is  the  unquestionable  disadvantage  in 
switchbacks,  that  engines  do  not  pass  curves  well  running  backward.  In 
part  this  is  remediable  in  the  design  of  engines,  and  by  leaving  the  rear 
drivers  blind,  but  the  only  proper  course  would  be  to  use  an  easier  maxi- 
mum curve  on  the  sections  on  which  the  engine  runs  backward,  which 
svould  be  the  same  both  ascending  and  descending,  and  to  make  those 
sections  as  short  as  possible. 

Thus,  the  writer  believes,  this  objection,  while  it  cannot  be  entirely 
removed,  may  be  reduced  to  very  small  dimensions  ;  and  should  it  again 
fall  to  his  lot  to  locate  a  line  of  railway  upon  an  ascent  of  8000  vertical 
feet,  or  even  a  half  or  a  quarter — or,  possibly,  even  an  eighth — of  that 
amount,  he  will  in  no  case  willingly  attempt  to  locate  it  for  an  unbroken 
locomotive  run,  but  either  use  switchbacks  for  a  light  traffic,  or  study 
with  great  care  the  possibilities  of  the  locality  for  inclined  planes  with  a 
heavy  traffic. 


INDEX. 


INDEX. 


References  to  tabtilar  matter  are  indicated  by  *   and  references  to  many  of  the  more 
important  conclusions  for  immediate  application  are  in  small  capitals. 

To  save  space,  many  page  references  are  marked  thus: 
500 -|-,  meaning  "  Page  500,  and  following  pages  not  in  the  immediate  context." 
500  — ,  "  "Page  500.  and  preceding  pages  not  in  the  immediate  context." 

500  ±,  "  "Page  500,  and  pages  both  preceding  and  following  not  in  the  imme- 

diate context." 
500  &,  "  "Page  500,  and  in  various  other  places  throughout   the  volume,   to 

which  more  specific  reference  under  this  head  did  not  seem  con- 
venient or  expedient.     See  elsewhere." 
q.v.  (which  see)  has  been  used  in   many  cases  for  giving  cross-references,  as  most 
economical  of  space. 

Because  there  are  many  cross-references  it  must  not  be  assumed  that  they  always  exist. 


Aba— Agr 

Abandonment  of  old  work,  786 

of  schedule  trains,  102 

Abrasion,    rails,  q.v.^  as  affected 

theory  of,  562     [by  speed,  561 

rate,  iron  and  steel,  320 

Abt  rack  railway,  descr.,etc.,  691, 

Abutments,  prelim,  ests.,  899  [932 

pile,  770 
Acceleration  of  g-ravity,laws,33i-3 
of  trains  on  grades,  342,  346-56 
{See  Virtual  Profile,  etc.) 
Accidents  as  affected  by  curv.,  245 
by  grades,  598,  949 
by  handling  locos,  359 

[900 
by  re-railing-  bridge  g'ds, 
by  superelevation,  300 
marvellously  few,  257 

Adams,  C.  F.,  as  to,  252-7 
p.  c.  pass,  and  ft.  trains,  ^248 
p.  c.  sum'r  and  winter,  ^249-56 
train,  13  years,  ^246 

east  and  west  of  Ohio,  252 
Accuracy  and  precision,  863  -|- 

instrumental,  not  an  end,  865 
Adams,  C.  F.,  on  accidents,  252-7 
Adhesion,  ratio  of,  436,   532,   551, 
Adiabatic  curve,  469  [598  & 

Admission,  period  of,  def.,  458  4- 
Advertising  and  agts,  cost,  full  de- 
by  easy  curves,276  [tails,*i72-6 
by  maint.  way,  124 
by  route,  charac.  of,  683 
Africa,  railways  of,  =^43 

rolling  slopes  in,  844  [*203 

Age,  effect  on  car  and  eng.  repairs. 

Agents    &    station    service,  cost, 

[full  details,  *i72-6 

.Agricultural  regions,  traffic  from, 

exception,  618  [618 


Ain— Ane 

Ainsworth,  D.  H.,  on  location,  11 
Air-brakes,  q.v.,  effect  on  sp'd,  370 
Air  resistance,  amount,  911 

knowledge  as  to,  513 

Alabama,  area,  populat'n,  sidings, 

per  cent  op'g  exp.,  earnings  per 

mile  and  head,  ^go;  wealth  per 

cap.,  *26 

Albany  &  Susq.,  align,  statist., ^259 

Alignments,  comparing  minor  de- 

[tails  and  grades,  581 

WHEN  NEARLY  EQUAL,  583 

crooked,  and  safety,  252 
{See  Curvature.) 

indicating  on  profiles,  862 

States  and  rys.  U.  S.,  *259 
{See  Curvature  Grades.) 
Alleghanies,  Altoona  pass.,  936. 

planes  on,  687,  699,  944 
Allegheny  river,  fall',  841 
Allegheny  Vallej'-  Ry.,  p.  c.  switch 
Alliteration  of  6's,  656  [miles,  *i8i 
Almazon,  P.  &  Mex.  Ry.,  930 
Alsace-Lorraine,  cost  rys..  etc.,*45 
Altazimuth,  use  of,  847,  881-2 
Altoona,  car  movement  at,  609 

grades  at,  618 

pass  at,  936 

pusher  service  at,  595 

shops  opened,  141 
Ameca  River,  descent  into,  682 
America,  railways  of,  *42-3  & 
American  line,V.C.  to  Mexico,  925 

loco.,  q.v.,  weights,  etc.,  *407 
American  C.  ry.,  align't  statist., 

[*262 

Ames  car-coupler,  489 
Andes  and  rough  country,  840 

summits  in,  698-9 
Aneroid,  use  of,  838,  877 


Ang-Ass 

Angles,  eye  exaggerates,  842  -\- 

plotting,  886 
Anthracite,  effect  on  fxre-box,*4i9 

lump  of,  449 

N.  Y.  supply  and  distance,  710 

traffic  west,  609,  615 
Apennine  railways,  profile,  698 
Apex  distance,  det'g  diffs.  in,  *644 
'Arbitraries,'  nature  of,  156,  218 


examples, 


820 


Arbitration  and  interl'k'g,  8124- 
Arc,  mental,  striking,  839 
Area,  miles  ry.  for,  world,  *43  & 
Arizona:  area,  pop'n,  sidings,  p. 
c.  op'g  exp.,  earnings  per  mile 
and  head,  ^go;  wealth  per  cap., 

*26 

Arkansas:  area,  pop'n,  sidings,  p. 
c.  op'g  exp.,  earniags  per  mile 
and  head,  *9o;  wealth  per  cap., 

*26 

Arkansas  river,  fall,  841 
Art  and  science,  831 
Ash-pan,  loco.,  q.v.^  wt.,  *4i4 
Asia,  railways  of,  *43 

rolling  slopes  in,  844 
Asphalt,  H.  U.  in,  ^450 
Assistant  engines,  585 

and  low  grades,  590,  659 
cost  of,  601 

and  train  wages,  671 
how  to  estimate,  604 
interest  charge,  604 
duty  of,  598  -1- 

and  light  traffic,  599 
separate  engs.  necessary, 

[598 
for  passenger  service,  592 

example,  607 
grades  for,  591 


954 


INDEX, 


Ass— Bac 

Assistant  engines— Conti>iued. 

GRADES,  BALANCE  OF,  593  — 

example,  604  + 
comparing  with  uniform 
[grade,  604  + 
curve  comp'n  for,  598 
projecting,  high,  669 

low,  596,  666 
as  afE'd   by  length  gr., 
[618-9 
duplicate  tracks,  691 
temporary  grades,  766 
when  wrong  to    reduce, 
old  lines,  introd'g  on,  788  [671 

CONCLUSION  AS  TO,  8o8 

operating  at  yards  and  sta'ns, 
block  signals  for,  601  [599 
cutting  trains  in  two,  599 
power  of,  491 

best  wt.,  597 
tank  engines  as,  592 
without  stopping  t'ns,  792 
presumpt'ely always  adv.,  586 
two  or  three  rarely  advisab., 
work  with  nature,  589    [669  & 
Assistants,  discred'g  rep's  of,  836 
Atchison,   T.  &  S.  F.  Ry.,  fluct. 
[in  stocks,  *46 
loco,  performance,  *439-4i 

"  Uncle  Dick  "  loco.,  421 
miles  and  earnings,  *7i9 
sharp  curves  on,  279 
Atkinson,  E.,  forecast  of  ry.  con- 
[struction,  *4i 
Atlantic  &  Gt.   W    as  Erie  con- 
[nection,  730 
loc'n  at  Springfield,  O.,  56 
strategic  disadvantage  of,  222. 
{See  New  York,  P.  &  O.) 
Atlantic,  M.  &  O.  Ry.,  alignm't 
[statist.,  *264 
Atlanta  &  W.  Pt.  Ry.,  loc.   per- 
[formance,  *439 
Australia,  Am.  Iocs,  in,  422 

pop'n,  railways,  wealth,  etc., 
rolling  slopes  in,  844  [^27,  ^43 
Austria,  bridges,  wt.  of,  767 

locos.,  no.  and  work  of,  *i6o 
pop'n,  r'ys,  wealth,  etc.,  *27, 

rolling-s'k  and  traffic,  etc.,  *43 

receipts  per  inhab't  pass,  and 

[frt.,  *io5 

Austrian  N.  W.  Ry.,  lub'n  tests. 

Automatic  brakes,  g.7'.,  4S8      [516 

couplers,  g.v.^  488-9 
Axiom  as  to  location,  660 
Axles,  accidents  from,  *246 

car,  cost  and  deprec'n,  *204 
maint.  of.  *i62 
w't  of.  *i63 
size  of  M.C.B.,  513 
effect,  on  fric,  513 
French,  521 
loco.,  life  of,  *42o 

w't  and  cost,  ^412  + 
radiating,  possible  effect,  283 
Axle-boxes,    loc.    w't    and    cost, 
[*4i3  + 
Axle-friction,  q.v.,  and  rolling,  515 
better  lub'n  needed,  509  -|- 
comp've  coeff.,  512  ± 

Babbitt  metal  in  loc,  *4i2-4 
Backing  locos,  q.v.,  950 
Backing  up  in  loc'n,  865-6 


Bac— Bel 

Back  pressure,  locos.,  q.v.,  472 
Baden,  cost  rys.,  etc.,  *45 
"  Bad  times"  and  ry.  const.,  763  & 
Baggage  cars,  g.v.^  dimen's,  etc., 
[*49i 
Balance  of  g-rades,  g.v.,  593,  608 
traffic,  g.v.,  flucts.  in,  loi 
slide-valve,  g.v.,  532 
Baldwin  Loco.  Wk's  and  Consol. 
catalogue,  422  [eng-?  278 

computing  cap'y  of  Iocs.,  442 
Decapod  loc,  det'ls,  *4io 
loco,  cost,  comp.  all  sizes, *564 
narrow-gauge,  *564-5 
per  ton,  *4ii 
dimens.,  etc.,  *4o8 
fast  pass.,  421 
performance  table,  *438 
test  of,  *46i  -|- 
wt.  of,  incr.  13  yrs.,  *466 
on  drivers  per  sq.  ft., 
Ballast,  cost  of,  773      [grate,  *452 
various  roads,  *i2o 
economy  of,  772 
imp't  in  practice,  114 
lining  with  string,  124,  277 
Ballast  trains,  handling  of,  773 
Baltimore  &  O.  rd.,  cars,  heaviest, 
wheels  on,  486,  513       [490 
curves,  sharpest,  278,  325 

Y  on,  279 
fastest  train,  *529 
flucts.  in  stock,  *46 
history    and    causes  success, 
inundations  on,  783  [730 

location,    Allegheny    incline, 
balance  of  grds.,  618  [*699 
for  pushers,  585 
profile,  condensed,  698 
temp'y  lines,  '700 
loco,  boiler  pres.,  ^408 

cost  and  miles  pr.  y.,  *i59 

mogul,  dimens.  etc.,  *4o8 

maint'ce  exps.,  34  yrs.,  *i29 

miles  and  earnings,  ^719 

opg.  exp.  and  trains  per  day, 

p.  c.  opg.  exp.,  *iio  [*i72 

why  low,  no 
per  train-mile,  cost,  *ii6 
train-load,  frt.  and  pass,  *2i7 
Bankrupt    lines,    pass    far   from 
[towns,  68  & 
never  from  curves,  655 
Bar-iron,  past  prices  of,  763 
Barranca,  def.,  928 
Blanca,  spiral,  678 
Zimilahuacan.  942 
Barometer,  use  of,  838,  847 
Basaltic  lava,  684 

river  of,  928 
Bath  lubrication,  q.v.^  eff'y,  509 
Bavaria,  cost  rys.,  etc.,  *45 

flange-fric.  tests,  516 
Beams,  comp've  strength,  742 
stiffness,  740 
Bearings,  compass, 

for  taking  off  paper  loc'n, 

for  transit  work,  888    [892 

use  always  for  map'g,  886 

loco.,  g.v.,  life  of,  420      [*i6o 

Belgium  locos.,  no.  and  work  of, 

popu.,  rys.,  wealth,  etc.,  ^27, 

L*43,  *45 

rolling-stock,  traffic,  etc..  =^43 

Bell,  loco.,  cost,  *4i3  [*262 

Belleville  &.  E.  rd.,  align't  statist., 


Bho— Bra 

Bhore  Ghaut  inclme,  *699 
Birmingham, Eng.,  stat'n  exp.  at, 
Bissell  truck,  g,v.,  430  &  [828 

Blackmail,  r'ys  built  to,  14 
Blast-nozzle,  sfze,  *409 
Block-signals,  interl'g,  g.v.,  and 
[assist,  engs.,  601 
Blue  Ridge  rd.,  60  ft.  &  6°  comb'n, 
'  Bogie'  truck,  g.v.,  421  [656 

Boiler,  loco.,  g.v.,  449 

cost  new,  details,  *i5o-5 
explosions,  *247 
life  of,  *4i9 

pres.,  effect  increas'g,  401 
repairs,  details,  *i46 
English,  *i44 
p,  c.  due  to  various 
[causes,  *203 
and  minor  det'ls,  *i49 
water  in,  wt.,  *40o  & 
marine,  efficiency,  *456-7 
Bonds  and  stock  per  mile,  sect'ns 
building  on,  30        [U.S.,  *io7 
nature  of,  29 
'  Boom'  and  inception  of  rys. ,34  & 

and  prices,  763 
Boot,  on  Mex.  ry.,  *699 
Boreas  summit,  descent  from,  696 
Boring  tools,  868,  893 
Borrowed  money,  intox'g  eflf't,  34 
Bosnia,  cost  r'ys,  etc.,  *45 
Boston— N.  Y.  traf.,  loss  bydist., 
side  track  at,  823  [709 

train-speed  to,  650 
Boston  &  Albany  rd.,  alignment 
[statist.,  *259 
curve  comp'n  on,  621 


flucts.  in  stock,  *46 


[*i59 


locos.,  cost  and  miles  per  yr., 
fast  pass.,  wt.,  etc.,  421 
slide-valve  tests,  532 
tubes  in,  *42o 
op'g  exp.  and  trains  per  day, 
rates,  fall  of,  *726  [*i72 

sidings  on,  *825 
ton-mile  rect's,  etc.,  *ii5 
train-load,  frt.  and  pass.,  *2i7 
growth  of,  *ioo 
Boston    &  Lowell,  Iocs,  cost  and 
[miles  per  year,  *i59 
p.  c  switching-miles,  *i8i 
Boston  &  Maine,  locos.,  cost  and 
[duty,  *i59 
Boston  &  Prov.,  locos.,  cost  and 
washouts  on,  781     [duty,  *i59 
Bottom    lands   and    high   water, 
[850  & 
Bound  Brook  line,  fuel  tests,  528 
Box  cars,   g.v.,  dimensions,  etc., 
60,000  lb.  st'd,  *4go         [*486-7 
Box  culverts,  g.v.^  wooden,  755 
Brake-gear,  accidents  from,  *246 
Brakes,  automatic,  cost  new,  *i5i 
effect  on  speed.  370 
gain  from,  804  & 
cost  of,  deprec'n,  ^204 
destructive  to  wheels,  377 

extent  of  do.,  *3i8 
efficiency  of,  average,  494 
coeff.  fric.  of,  290 
computing,  336-8,  494 
maximum,  495 
on  caboose,  359 
waste  of  power  by,  691 

examples,  337-343  [371-2 
when  needed  on  grades. 


INDEX. 


955 


Bra-Bui 

Brakes —  Contin  7ied. 

hand,  and  low  speed,  268 

Branches,  ry.,  731,  51 
av.  earnings,  732 
early  building  bad,  764 
for  defence,  718 
pass,  trafif.  of,  734  [732 

reason  for  great  increase  of, 

PROJECTING,    UNIV'l   RULE   for, 
SECOND,  do.,  734  [733 

to  develop  territory,  735 
Brasses,  car,  maint.  of,  *i62  & 
locos.,   q.v.,    wt.,    etc.,  *i5o, 

[*4I2  & 

Breckenridge,  Col.,  loc'n  at,  695  -+• 
Brenner,  ry.  profile,  698-9 
British  ry.  dividends,  *4i 

operating  expenses,  *i78 
{See  Great  Britain,  etc.) 
Bridge-building,  cause  of  prog,  in, 
Bridges,  accidents  from,  *247      [3 
cost  new  per  lb.,  905 

asaff.  by  rolling  Id.,  767  + 
draw,  weight  of,  905 
erecting,  cost,  905 

all  spans  but  one,  68 
floor  of,  900,  904 
heaviest  car-loads,  *49o 
maint.,  cost  of  U.S.,*i2o,  *i28, 
prelim,  ests.  of,  903       [*i72-6 
rerailing-guard  for,  900 
rolling  load,  767  -{-,  490 
types  of,  for  var.  spans,  904 
vibration  of,  447 
weight  of,  903 

as  aff.  by  depth,  *904 
by  rolling  I'd,  *-j6j-^j2 
by  span,  *-j6j-']x 
by  st'l  or  iron,  *-]67-'ji 
double  track,  765 
draw,  905 
formulae  for,  903 
light,  save  little,  765 
onnarrow-g.,  752 
width  of,  904 
Bridge  piers,  prelim,  ests.,  898 

pile,  770 
Bridge  spiral,  g.v.^  678-9,  681 
Bridging,  p.  c.  cost  to  total,  *757 
Broad  St.  station,  Phila., traffic,  69 
'  Broken-back  '  curves,  870 
Brooklyn,    B.   &  C.    I.,  sharpest 
[curve,  325 
Brooks,  rate  of  fall  of,  840  & 
B^-ooks   Loc.  Works.,  loc.  dimen- 
[sions,  etc.,  *407-8 
load  on  drivers  per  sq.  ft. 
[grate,  ^452 
Brunswick  &  Ch.  rd.,  alignment 
[statistics,  *264 
Buffalo,  greatest  yd.  in  world,  822 
inundations  at,  783 
miles  of  sidings  in,  *82i 
Buffalo  Creek  rd.,  side  tracks,  *82i 
Buffalo,  N.  Y.  &  Phila.,  alignment 
[statistics,  *259 
sidings,  Buffalo  yd.,  *82i 

total,  *825 

loco,  perf 'ce,  ^438 

Building,  const'n  of,  and  surveys. 

on  bonds,  30  [856 

virhat  is  built  well,  655  &    [*25 

Buildings  (houses),  U.  S.  value, 

ry.  cost  new,  p.  c.  to  total. *7S7 

maint.  various  rds.,  *i2o, 

[*i7o-6 


Bul-Car 

Bulgaria,  cost  rys.,  etc.,  *45 
Bunching,  curvature,  q.v.^  655 

grades,  g.v.,  587  & 
Burlington,  la.,  brake  tests,  496  & 

slack  tests,  489 

train-res.  tests,  496 
Burlington   &  S.  W.,  alignment 
[statist.,  *262-4 
Burlington,  C.  R.  &N.,  do.,*262-4 
Burr,  J.  D.,  paper  by,  279 
Burnettizing  cross-ties,  q.v.,  i-z^ 

Cable  traction,  merits  of,  686,  944 
modern,  origin  of,  689 
passing  summits  by,  689 
Caboose  brakes  set,  359 

dimensions,  etc.,  *486-7 
Caledonian  ry.  locos.,   cost    and 
[duty,  *i';9 
int'l  rad'n  tests,  472 
California:  area,  pop'n,  sid'g's,  p.c. 
of  op'g  exp.,  earn'gs  p.  mile  and 
head,  *9o;  wealth  per  cap.,  *26 
Calumet  mine  bch.  (8^  gr.),  *7oo 
Camden  &  Atl.  rd.,  wheel-wear 
[on,  *287-8 
Camp  outfit  for  loc'n,  q.v.,  867 
Canada,  Am.  Iocs,  in,  422 

bonds  and  stock  per  m.,  *io7 
earnings  per  m.,  *io7 
growth  rys.,  ^424 
pop'n,  rys.,  wealth,  etc.,  *27 
ry.  subsidies  by  govt.,  *io7 
Canada  Southern  ry.,  align't,  and 
[Huds.  R.,  328 
branches,  money  spent  on,  764 
earn'gs  and  length,  *7i9 

per  mile,  *ioj 
fiucts.  in  stock,  *46 
nature    of    traffic,  local    and 
[through,  214 
train-load  growth,  *ioo 
{See  Michigan  Central.) 
Canadian  Pac.  ry.,  length  of  divs., 
rolling-stock  per  m.,  *47    [169 
Canals,  U.  S.  value,  *25  [*325 

Canarsie  &  Rock'y.sharp't  curve. 
Carbon,  H.  U.  m,  *45o  [dents,  254 
Carelessness,   as   cause    of    acci- 
Cant  (superelev.,  q.v.\  271 
Cape  Government,  roU'g-st'k  p. 
[mile,  *47 
Capital,  floating,  U.  S.,  amt.,  *25 
in  rys.  of  world,  *27,  ^43  & 
made  less  by  bad  loc'n,  60 
return  on  Am.  rys.,  *4i 
English  rys.,  *4i,  ^79 
Capital  acct.,  danger  of  increas- 
[ing,   113,  654 
distrib'n  of,  *j\  & 
Car-Builders'  Dictionary,  491 
Car,  falling,  ex.  of  grav.,  342 
Car-couplers,  aut.,  and  speed,  804 
pass.,   why    easily   intro- 
[duced, 489 
probabilities  as  tofrt.,  488 
types,  two  distinct,  489 
bad,  impede  long  trains,  566 
Car  {q.v.)  mile,  fuel,  P.  R.  R.,  *i4o 
Carpets   falling   over,   accidents, 
Carr's  Rock  disaster,  255  [258 

Cars  and  rail-wear,  122 

capacity  of,  increase,  485,  114, 

effect  on  exp.,  485     [135 

on    car    consti*.     and 

[sp'd,  370 


Car— Car 

Cars — Continued. 

capacity  of,  effect  of  narrow- 
[gauge  on  485,  752 
transition  state  of,  487 
classes  of,  fr't,  486  -j- 
pass.,  491 
side-dump,  774 
cost  of  maintenance,  160-7 
as  affected  by  additions, 
age,  162  [166 

M.  C.  B.  rule,  205 
curvature,  319 

radius  of,  641 
distance,  201-4 
growth  of  traffic,  166 
high  mileage,  162 
local  service,  162 
rise  and  f.,  377 
train  length,  570 
average  cost  of,  160 
per  cent,  details,  full,  frt., 
pass.,  167  [*i6i-4 

bodies  and  trucks  sepa- 
[rate.  *i64 
pass., outside  and  inside, 
[204 
distrib'n  to  causes,  *203 

TO  VARIOUS    PARTS,  167 

Chicago  rds.,  *  174-6 
sections,  U.  S.,  *i70-6 
trunk  lines,  *i72-6 
34  years,  129 
English,  *i48  & 
per  car  per  year,  *i48 
cost  new,  163-4 

box  and  stock,  details,*204 
flat  and  coal  details,  *205 
per  mile  N.  Y.  C,  *7i 
depreciation    of  (see  above), 
[162,  205 
varying  causes  for,  202 
dimensions  of  frt.,  all  classes, 
pass.,  *49i  [486-7 

irreg'ties  in,  487 
European,  520  -|- 

and  Am  cross-sec,  522 
elev'd  ry.,  646 
friction    of,    q.v.     (&     train 
[res.),  501 
European,  *283,  *502 
invention  of  Am.  car,  421 
load  of.  cannot  be  full,  611 
E.  &W.,*6o9-f 
how  to  est.  prob'le,  99 
mileage  of,  cost,  all  parts  U. 
frt.  cars,  161-2   [S.,  *i7o-6 
average,  168 
why  low,  165 
pass.,  168 

sleeping,  168  [*47  & 

number  per  mile,  world,  *43, 

riding  of,  and  curves,  275 

ht.  cent  of  grav.,  271 

ton-miles  per,  U.S.  sects.,  *97 

weight  of  frt.,  486-99        [*49o 

extra    large    and    heavy, 

mat'ls,  separately,  *i63, 

pass.,  491  [567 

WHY    GROW  HEAVIER,   I39 

Car  q.v.  springs,  compres'n  of,  272 
Car-wheels,  accidents  from,  *246 

and  rail,  307,  516  & 

cost  and  depreciation  of,  *204 
failures  on  for'n  rds.,  166 

cracks  and  breaks,  loc'n,  319 

maint.  of,  *i64 


956 


INDEX. 


Car— Cha 

Car-wheels,  maint.  oi—Contini>^. 
causes  of  failure,  *3i7 
p.  c.  due  to  van  causes, 
mileage  life  of,  319    [*203,*377 
as  affected  by  quality,*3i7 
lead'g  and  trail'gwh'ls, 
[*288 
loco,  and  tend'r  trucks, 
[*288 
comparative  pass,  and  ft., 
on  curves,  q.v.^  2S2  [167 

as  pulleys,  302 
flange  wear,  30S 
rotation,  energy  of,  334 
size  and  wt.  of,  '*i63,  av.,  335 
42-in.,  513,  912 
French,  521 
U.  S-.  standard,  ^486 
eiT"t  on  train,  r^  513      [335 
p.  c.  wt.  to~Iotal  of  trains, 
skidded,  fric,  g.v.^  *29o 
tread,  proper  form,  308 
errors  as  to,  307 
Carting,  amt.  of,  and  ry.  traffic,  52 

cost  of,  820 
Castings  in  locos.,  q.v.^  *i5o  & 

prices  Am.  and  Eng.,*4i6,*763 
Cattle,  accidents  from,  ^245,  ^247 
Cattle-guard,  plan  for,  770 
Caucasus  ry.  profile,  698 
Cement,  co.  should  furnish.  903  & 
Census  U.  S.,  defects  in,  =^261 

(Otherwise,  the  many  abstracts 
not  indexed.) 

Centre  of  gravity  of  ctirs,  syi 
of  exchange  traffic,  227 
of  trains  in  sags,  357^0 
of  two  towns,  67  [629  & 

Central  angle  and  curve  comp''n, 
Central  la.,  align't  statist.,  *262 
Central  N.  J.,  fastest  train,  *5a9 
fluct.  in  stock,  *4t3 
loco,  perform.,  *44o 
Central-rail  rv^s..  404 

{See  Rack.) 
Central  Vt.,  alignm't  statist.,  *259 

p.  c.  switching-miles,  *i8i 
Central   Pacif.,  alignm't  statist., 
fluct.  in  stock,  ^46  [^265 

loco.  "  El  Gubernador,"  de- 
[tails,  *4io 
Mastodon    loco.,    details, 
[*4io,  *423 
load  on  drivers  pr.  sq.  ft. 
Mogul,  421       [grate,  ^452 
miles  and  earnmgs,  *7i9 
mountain  grade,  *7oo 
Centrif.  force  on  curves,  q.v.^  269 
common  errar  as  to,  301 
effect  on  curve  resist..  298 
position  wheels.  300 
safety,  300       [eff't.  *273 
limits     of      objectiona.ble 
lbs.  per  ton  var.  curves, 
of  counterwts.,  446    [etc.,*27o 
Ceylon,  long  grades  in,  ^oog 

rolling-stock  per  mile,  *47 
Chain,   with   wheels,   and    curve 
Chains,  metric,  266  [res.,  303 

radii  by,  *266  -)- 
Chairs  for  cross-ties,  English,  125 
Chances,  theory  of,  864  & 
Chanute,  O.,  on   loco,   adhesion, 
loco,  rail  wear,  122  [443 

train  resist'ce,  518,  525      [^264 
Charlotte,  C.  &  A.,  align't  statist,, 


Cha-Chi 

Charlotte,  C.  &  K.— Continued. 
maint.  way  exp.,  128 

Chattahoochee  River  fall,  841 

Cheap  lines,  a  priori  preferable,  18 
when  to  prefer,  583 

Cheat  River,  fall,  841  [=^264 

Chesapeake  &  O.,  align't  statist., 
curve  comp'n  on,  621 
60  ft.  and  6°  comb'n,  656 

Chicago,  distances  to,  240 
grain  rec'ts,  728 
train  speed  to,  650 
rates  to  and  through,  218  & 
terminals,  loc'n  of,  72 
relative  size,  827 

Chicago    roads,    op'g    exp.    and 
[trains  per  day,  *i74 
train-Id.  growth,  *ioi 
rates,  fall  in  20  yrs,  ^726 

Chic.  &  Alt'n,  align't  statist.,  ^262 
fluct.  in  stock,  ^46 
op'g  exo,  £3id  trains  per  day, 
rates,  fall  of,  ^726  [*i74 

train-Id.  growth,  *ioi 

Chic.  &  E.  111.,  align't Fiatist.,  ^262 

Chic.  &  G.  T.,  a4igQ't  statist.,  *262 

Chic.  &  N.  W.  fiucts.  in  stock,  ^45 
furniture  err,  *49o 
miles  and  earnings,  "'719 
cp'g  exp.  and  trains  per  day, 
chart,  of,  etc..  35        [*i74 
rates,  fall  of,  *726 
train-Id.  growth,  *ioi 

Chic,  R.  I.  &  P.,  fluct.  in  stock,*46 
miles  and  earn'gs,  ^719 
op'g  exp.  and  trains  per  day, 
rates,  fall  of,  *726  [*i74 

train-Id.  growth,  *ioi 

Chic.  &  Spr'fd,  align't  statist. ,*262 

Chic,  B.  C.  &  W.,  ahgn't  statist., 
[^262 

Chic.  B.  &  Q.,  align't  statist., *262 
dining-car,  ^491 
dynamom.  tests.  501 
fluct.  in  stock,  *46 
locos,  cost  new,  det'Is,  *i5c>-7 
p.  c.  labor  and  mat'ls,*is2, 
[*4i6 
dimensions,  etc.,  ^407 
Id.  drivers,  per  sq.   ft. 
[grate,  ^452 
performance  of,  ^440 
wt.  and  cost.  det'Is,  *4i6 
tender  capacity,  standard, 
[*378 
miles  and  earnings,  *7i9 
motive-power  expenses,  157 
op'g  exp.  and  trains  per  daj^ 
rates,  fall  of,  *726  [*i74 

traflic,  growth  of,  157 
train  and  brake  tests,  497  -(- 
water-supply  on,  *378 

Chic,  M.  &  St.  Paul,  alignment 
[statistics,  *262-3 
fluctuations  in  stock,  *46 
miles  and  earnings,  ^719 
op'g  exp.  and  trains  per  day, 
rates,  fall  of,  *726  ['''174 

timber  structures  on,  770 
train-load  growth,  loi 

Chief  engineer  should   make  re- 
[connaissance,  23,  832  & 
of  party,  duties,  867 

Child,  sense  of  distance,  844 

Chili,  loco,  performance  in,  *438 
railway  grade  in,  *699 


Chu-Col 

Churches  and  schools,  U.  S.  value^ 

[*25 

Cincinnati,  Erie  business  to,  222 
Cine,  H.  &  D.,  align't  statist.,  *26i 
distance,  value  of,  221 
curve  comp'n  on,  621,  656 
Cine,  N.  O.  &  Tex.  P.,  loco,  tests 
[on, 477 
So.    Ry.,   pedestals  and   via- 
[viaducts.  cost,  etc.,  901 
60  ft.  and  6°  comb'n,  656 
Cine,  N.  O.  &  Tex.  P.  (Cine.  So.), 
[alignment  statistics,  *264 
Cine,  W.   &  Mich.,   align't  stat., 

[*26l 

Cities,  great,  to  nowhere,  731 

and  small,  traffic  of,  70 
Cities  often  in  hollows,  859 
party- wall  laws,  814 
terminal,  q.v.^  655  & 
traffic  of,  q.v.,  heavy  into,  617 

growth,  *7i4 
train  speed  between,  648-50 
Clark,  D.    K.,   on  adhesion   and 
[speed,  435 
tram  resistance,  518,  528 
radiation,  int'l,  472 
wire-drawing,  etc.,  474 
Classification  of  material,  and  con^ 
[tour  maps,  877 
Clearance  spaces,  loco.,  q.v.^  \t2. 
Clearing,  illusive  effect  from,  850 

p.  c,  cost  to  total,  *757 
Cleaning  locos.,  q.v.^  cost,  *i47 
Cleveland,  Erie  business  to.  222 
Cleve'd  &  Mar., align't  statist.*26i 
Clev'd   &   Pitts.,  p.  c.  switching- 
[miles,  *i8i 
Clev'd. ,C.,  C.&  I.,  align't  statist., 
p.  c  switching-m.,  *i8i    [*26i 
rates,  through  and  way,  con- 
[stant  ratio,  224-5 
growth,  traffic,  *2i6  [^214 

p.  e  local  traffic  and  thro', 
p.  e  various  classes,  *2i5 
tons  and  ton-miles,  E.  and 
[W.,  etc.,  *2i6 
train-load  growth,  *ioi 
Clev'd.T.V.  &  W.,  align't  statist., 

[*26l 

Clev'd,  Mt.V.«S:  D., align't  statist., 

[*26l 

Cluster-bent  trestles,  goo 
Coal,  cost  per  ton,  U.  S.,  132 

lbs.  per  car  and  eng.  m.,  139  & 

{See  Fuel.) 
ship'ts  west,  economy  of,  135 
used  at  N.  Y.  terminals,  *8i9 
car,  q.v.,  extra  heavy.  ^490 
trains,  operating,  ^132  & 
Coatepec,  line  at,  937 
Coasting  and  ry.  accidents,  257 
Cocks,  loco.,  cost.  412 
Colburn,  Z.,  loc.  tests,  437 
Collins,  C,  on  ditching,  773 
Collisions,  causes  of,  245 
Colorado:   area,  pop'n,  sidings,  p. 
e  op'g  exp.,  earnings  per  mile 
and  head,  *9o:  wealth  per  cap., 

[*26 

ditches,  ocular  illusions,  847 
elevations,  696-8,  700 
rys.,  cost,  682,  6g6 
example,  694 
gauge  of,  694 
Colo.  Centr.,  align't  statist.,  *2S^. 


INDEX, 


957 


Col-Con 

Columbus,  C.  &  I.  C,  p.  c.  switch- 
[ing-miles.  *i8i 
Combustion,  heat  in  gases,  *456 

loco.,  q.v.,  capacity,  449  + 
Commerce,  triangular  course  of, 
'  Company,'  nature  of,  28-9  &  [615 

rent  their  line,  36 
Compass  lines,  863  — 

(of  transit)  graduating.  888 
Compensation  of  curv.,  q.v.^  620 
Competition,  effect  on  p.  c.  op'g 
[exp. ,  109 
Competitive  rates  and  non-comp., 
{See  Through  and  Local.)  [58 
are  from  door  to  door,  54 
on  very  long  haul.  218 
traffic,  true  classif'n,  212 
effect  distance  on,  215 
Compound  interest,  *8o-83,  *747 
effect  of,  80 
locomotives,  chances  for,  133 
Composition  of  vel.  ex.,  287 
Compression,  loco.,  q.v..  loss  and 
[gain,  470 
Concentrating    resistances,    gain 
[by,  587 
Concord    &   Portsm.,    alignment 
[statistics,  ^259 
Concrete  for  pedestals,  903 
Conde,  Hacienda  del,  loc'n  at.  682 
Condensing  eng's,  cost  and  eff'y, 
gainby,  *46S  [*53i& 

Coning,  effect  on  amt.,  slipping, 
path  of  wheels,  312   [2S8 
probably  injurious,  289 
no  effect  on  position  of  wh'ls, 
soon  disappears,  284  [282 

Connecticut:  area,  pop'n,  sidings, 
p.  c.  op'g  exp.,  earnings  per  m. 
and  head,  ^90  ;  wealth  per  cap., 

*26 

Connections,  short,  desirable,  219 
Connellsville  &  So.   Penn.,  map 
[on, 888 
Consolidation    loco.,  g.v.,  origin 
[of,  278 
most  used   on  heavy  curves, 
on  136  ft.  radius,  279    [148,281 
rel.  cost  reprs.,  *i46 
Construction,  abandoning,  787 
a  priori  basis  of,  18 
'cheap  and  nasty.'  768 
cost  of.  and  accidents,  252  [+ 
and  cable  traction,  688 
curve  limit,  635         [694 
indep't    return     tracks, 
switchbacks,  684,  950  — 
washouts,   783 
bad  lines  cost  most.  926 

CONTRAST  BETWEEN  SPEXD- 
[iNG  TOO    .MUCH  AND  TOO 

[little,  87 
economizing,    safe  direc 
[tions  for,  655,  757 
effect  on  val.  of  distance, 
[211 
danger  of  increasing,  113 
estimating,  834 
by  eye,  833  [849 

ocular    q.v.    illusions, 
in  Colorado,  682.  696 

Mexican  r'y,  031  [*757  & 

p.   c.  cost  various  items, 

to  S.  G.  a  minor  item,  833 

unevenly  distr'd  on  line, 

ECONOMY  OF,  762  [750 


Con— Cul 

Construction — Continued, 

fixed  sum  only  available,  762 
order  of  time  in,  763 
postponing,  86 
similar  st'd  for  all  lines,  737 
temporary,  q.v..  624  & 
Constructive  mileage,  218,  241 
Contour  lines,  nature  and  def.,  873 
errors  in  drawing,  8S4 
maps,  CONCLUSION  as  to,  880 
good  and  bad,  ex.,  888 
Contractors  and  cement,  903 

estimates  by,  834 
Convenience    of  buyer,    consult- 
Corliss  engine  tests,  553      [ing,  52 
Corn,  acres  per  mile  ry.,  *go 
Cornfield,  locating  through,  652-I- 
Corporation,  modern  ry.,  28 
and  grade-crossings,  815 
errors  of,  707  & 
Corpus  Christi,  error  at,  722 
Cortez,  route  in  ilexico,  928 
Cotton-bales,  per  mile  r\'.,  ^90 
cloth  and  transp'n,'manuf're 
[of,  48 
Counterweights,  loco,  wt.,  *4i3  -\- 
centrif.  force  of,  446 
effect  on  bridges,  447 
Coupler,  car,  q.v.^  488 
Couplings,  car,  q.v.,  close,  need- 
forces  acting  at,  303      [ed,  365 
slack,  q.v.,  effect,  358 
strength  of,  and  grades,  328 
three  conditions  for,  362 
when  most  broken,  368 
Courtesy  of  employes,  649 
Country  farmer  and  steep  hill,  656 

inspecting  grades,  662 
Credits,  scap,  loco..  *i46-9 
Crest  of  hill,  contours  of,  885 

eye  fixes  on,  842  -f- 
Creusot,  Corliss  eng.  tests  at,  533 
as  to  steam  pressure,  474 
Cricket  and  ry.  accidents,  258 
Crossings,  grade,   q.v.,  accidents 
[at.  *246 
Cross-sections  plotting,  898,  897 

rods  for,  882 
Cross-ties,  burnettizing,  114,  125 
creosoting,  320 

cost  of,  AVERAGE,    I24 

putting  in  track,  125 
cost  of  maint.  U.  S.  sections, 
[*i28,  *i7o-6 
various  roads.  120,  170-6 
as  affected  by  ballast,  774 
by  rad.  of  curves,  640 
cutting,  125 

economy  and  form  of,  775 
length,  780 
no.  vs.  wt.  rails,  776 
thickness,  778 
life  of,  and  curvature,  320 
seasoning,  124 
preserving,  114 
practice  as  to,  777-81 
size.  U.  S.,  777 
Gr.    Brit,   and   Europe, 
Croton  water,  purity,  *378        [124 
Crown-bars,  loco.,    q.v.,    weight 
[and  cost,  *4i2 
Cuchillo,  spirals  on.  684 
Cul-de-sacs,  def'n,  851 
examples.  852,  855 
Culverts  and  floods.  781 
loc'g  in  deep  fills,  851 


Cul— Cur 

Culverts — Continued. 
prelim,  ests.,  898 
wooden,  755  [statist.,  *26o 

Cumberland     Valley,     alignment 

loc.  performance,  *438-4i 
Current  of  water,  judging,  840 
Curtis,  G.  W.,  on  Mex.  ry.,  932 
Curvature,  242 

accidents  from,  245 

Adams,  C.  F.,  on,  254 
danger  of.  real,  257 
Monte  Carlo  disaster,  252 
on  elevated  rys.,  646 
p.  c.  accidents  due  to,  249 
possible  pay'ts  for,  250 
a  minor  detail,  185 
amount  of.     {See  also  Sharp.) 
as   affected    by  care   and 
[skill,  635  & 
inexperience,  654  & 
radius,  641-2 
smooth  slopes,  843    [656 
time  given  to  surveji-s, 
limits  of  choice,  narrow, 
No.  of,  U.  S.,  249.  259  [188 
on  high  line  to  Leadville, 
[697 
on  Rocky  Mt.  r\'s.,  *265  & 
per  mile,  av.,  628       [*2sq 
States&rys.,U.  S.,  full, 
possible   change  in   loc'n 
[not  great,  251 
use  to  reduce  grades,  ex., 
and  heavy  engines,  27S  [661  -\- 
loco.,  reprs.,  small  effect  on, 
[*i88 
making  time,  268 
smooth  riding  of  cars,  275 
bad  practice  as  to,  ^263 

English,  242 
'broken  back,'  870 

COMPENSATION    FOR,  620 

as  affected  by  speed.  622 
by  length  train,  634 
by  radius,  633 
at  stopping-points.  633 
computing  Irom  cent,  an- 
[gle,  629 

CONCLUSIONS  AS  TO,  632 

effect  diff.  rates,  *63o 
on  pusher  grades,  598 
origin  of.  621 
proper  rate  not  fixed,  627 

EXAMPLE.    628 

virtual  profile  given   by, 
COST  OF,  312  [621 

as  aff.  by  radius,  323 
by  repairs  engs  ,  315 
by  rate  grades,  581 

causes  of.  two  distinct,  312 

^^      CONCLUSIONS  AS  TO.  32I 

effect  on  cross-ties.  320 
p.  c.  on  loc.  and  car  re- 
[pairs,  *203 
per  train-mile,  *322 

degree  of.    MEANING.  258 

distinct  objections  to,  636 
eye  exaggerates.  842  -(- 
max.  and  min.  of  limiting, 
max.  limits  for,  635      [652 
disadvantages  visible,  243 
distribution  irregular,  622  & 
ends  of,  trackmen  flatten,  276 
transition,  $r.z/.,  curves,  276 
entering  and  leaving  worst, 
[275 


958 


INDEX, 


Cur— Cur 

Curvature — Continued. 
forces  acting  on,  281 
loss  of  power  small,  316 
loco.  q.v.  safety  on,  148,  433 
loss  traffic  from,  275 
lost  time  on,  648  & 
moral  effect  of,  276 
prevailing  error  as  to,  244 

LIMITING,  620 

TABLE  OF,  652 

limit  of,  and  bankruptcy,  655 

CONCLUSIONS  AS  TO,  653 

effect  on  construction,  635 
fixing  in  advance  wrong, 
on  light  rys.,  749  [654 

60  ft.  and  6°  comb'n,  656 

TOPOGRAPHICAL   LIMIT,  655 

wrong  mode  of  det'g,  244 
limits  of  object'able  spd.,*273 
metric,  degrees  of,  684 
radius  of,  bankruptcy  never 
[comes  from,  655 
effect  on  compar've  rail 
[wear,  296 
curve  compens'n,  633 
curve  resistance,  con- 
[cLUsiONS,  305 
distance,  642 
speed,  645 

train-load,  650        [292 
flange,  q  z/., press,  unaff'd, 
in  ft.,  ch.,  and  m.,  *267 
-^  inherent  cost,  63B 

length  between  same  T. 
[Ps.,  *644 
limiting  effect,  645 
loss  of  time  by,  647 

cost  of,  648 
various  modes  of  design- 
[ing,  258-66 
rail  wear  on,  ex.,  293 
rel.  importance,  ex.,  395 
sharp  and  zigzag  devel'ts,  678 
examples,    elevated   rys., 
[N.  Y.,  645-7 
high  line   to  Leadville, 
Mexican  ry.,  931        [697 
Peruvian,  679 
sharpest  in  regular  use 
[U.  S..  *325 
U.  S.  Mil.R.R.,326 
.    flange,  q.v..,  wear  on,  292 
gives  choice  more  routes, 
[656,  698 
lengthens  tangts.,  641 
may  save  dist.,  642 
on  pusher  grades,  667 
radii  for,  *266  [266-7 

running  with  short    ch., 
taking  out  on  old  lines,  787 

on  Penna.  rd.,  277 
'  train-degree  '  of.  582 
Curve  protractor,  892 
Curve  resist.^nce,  mechanics  of, 
[281 
amt.   due  to  surf.  fric.  only, 
L291 
as  affected  by  age  of  rails,  295 
form  do.,  295 
centrifu.  force  and  super- 
[elevation,  298 
greasing  flange,  516 
obliquity  of  traction.  301 
six    and    four    wheel 

[truck,   288 
various  types  Ioc.,*279— 


Cur-Den 

Curve  resistance—  Continued. 
as  affected  by  velocity,  911 

CONCLUSIONS   AS   TO,  304 

distinction  force  and    power, 
600°  =  I  mile  dist.,  315        [293 
Curves,  broken  rails  on,  256 

centrif.  force,  q.v.,  on,  269  -\- 
functions  of,  det'g  diffs.,  *644 
inside  and  outs,  rail,  differ, 
[length,  284 
loco.  q.v.  truck,  why  needed, 
offsets  to,  det'g,  872  [426  -(- 
projecting,  892  — 

to  fit  topog'y,  668 
transition  curves  for,  869 
radii  of,  determ'g  diffs.,  644 
sharp,  short    chords    prefer- 
[able,  267 
slipping  of -wheel  on,  cause, 
error  as  to,  287       [284-6 
velocity  of,  289 
transition,  q.v.^  why  needed, 
vertical,  q.v..,  869  [276 

Cushing,  G.  W.,  loc.  tests  by,  553 
Cut-off,  loco.,  q.v.,  av.,  *463-|-- 
and  speed,  477 
theoret.  gain  by,  *467-8 
Cuts(excav.,  q.v.~),  shallow,  snow 
[in,  126 
generally  last  work  done,  893 
Cutting  of  cross-ties,  cause,  125 

trains  in  two,  599 
Cylinders,  non-conduc'g  theoret. 
[eff'y,  *468  & 
loco.,  q.v.,  life  of,  420 

Dakota,    align't    statistics,    *263; 
area,    pop.,    sidings,  p.   c.  op. 
exp.,    earnings    per   mile    and 
head,  *90;  wealth  per  capita,  *26 
Danville  &  S.  W.,  align't  statis- 
[tics,  *262 
Days  per  year,  taken  at  365,  97 
Dayton  &  Mich.,  align't  statistics, 
Dazio,  spirals  at,  673  [*26i 

Dead  weight  and  fuel  consump'n, 
freight  cars,  av.,  610 &      [139 
mineral,  present  ratio,  614 
of  loco.,  all  grades,  *688 
pass,  trains,  491 

why  little  injurious,  139 

WHY  TENDS  TO  INCR.,  567 

Decapod  loco.,  q.v.,  details,  *4io 
Defaults,  railway,  *40  [258 

Degree  of  curve,  q.v.,  measur'g, 
Depreciation,  fr't  cars,  rate,  *204 

M.  C.  B.  rule,  *205 

Delaford,  M.  F.,  expts.  as  to  st'm 

[press.,  474 

Delaware,    area,  pop  n,  sidings, 

p.  c.  opg.  exp.,  earning  per  mile 

and  head,  *9o;  wealth  per  cap., 

[*26 

Delaware,  Lac.  &  West.,  align't 
[statistics,  *26o 
loco,  performance,  *438 
sidings,  total,  *825 
p.  c.  switching-miles.  *i8i 
terminal  exp.,  etc.,  N.  Y.,  *8i9 
track,  Buffalo  yd.,  *82i 
train-load,  growth,  *ioo 
Delaware  &  H.  C.  Co.,  gravity 
[r'y,  692 
Denmark,  rail'ys,  cost,  etc.,  *45 
Denver  &  Rio  G.,  Calumet  Mine 
[bch.,  ♦700 


Den— DJs 

Denver  &  Rio  G.— Continued, 

Consolid'n  engs.  on,  281 

curve  comp'n  on,  621 

effect  n.  gauge,  753 

financial  status,  41 

fluct.  in  stocks,  *46 

long  grades  on,  699 

profile  condensed,  698 
Denver,  So.  P.  &  P., location  map, 
Depots.    {See  Stations.)  [696 

Derailing  switches,  def.,  811 
Derailment  accidents,  q.v.,  245 

and  caboose  brakes,  359 
Desdoint,  M.,loco.  tests,  521 
Detroit  grain  receipts,  728 
Detroit,  G.H.  &  M.,  align't  statis- 
tics, '262  [700,  932  & 
Development,  examples  of,  679  -|-» 

in  flat  country,  661  -|- 

RULE  AS  TO,  694 

spiral,  extreme  ex.,  684 
wrong  practice  as  to,  671 
Diagrams  for  ests.  of  structures, 
[898 
geometric,  exagg'n  in,  387 
Differences  in  receipts  and  exp. 
[to  govern,  17,  62 
of  rev.  make  corps,  rich,  50 
Dining  cars,  competition  with,  73 

dimensions,  etc.,  *49i 
*'  Discounting"  the  future,  24 
Dispatching,  train,  and  improve- 
[ments,  old  lines,  791,  803 
and  ballast  trains,  774 
Disproportion  of  traffic,  q.v.,  608 
effect  on  train-Id  ,  100 
coal  movement  west,  135 
Distance  (Chap.  VII.),  195 
a  minor  detail,  185 
and  breaking  tangts.,  324 
light  railways,  756 
reducing  low  grades,  660-f- 
radius  of  curves,  641  4- 
between    towns,     effect     on 
[earnings,  709 
compar.  value,  great  and  small 
[diffs.,  208,  240,  709,  721 
construction    cost,    allowing 
[for,  2ir 
contradictory  law  as  to,  219 

example  of,  728 
cost  of,  ig8,  207-8 

as  affected  by  amt.  of  ex- 
[tra  dist.,  198 
by  rate  grades,  581 
by  way  rects.,  234 
credit  side  to,  211 

nature  of,  197  [*63i 

developing,  q.v.,  to  gain,  ex., 

to     red.    pusher    grades 

[wrong,  671 

diff.  via  any  curve,  *644 

effect  of,  on  competitive  rects, 

[*229 

on  loco,  and  cars  rep  rs, 

|.*203 
ON  OPG.  EXP.,  198,  207-8 

great  diffs.,  209 
on  receipts, 
on  through  rects.,  228 

LAW  AS  TO,  228 

do.   GREAT  diffs.,  709 

errors  in  values  of,  211 
estimating  by  eye,  845 
across  water,  845 
eye  foreshortens,  842  -|- 


INDEX. 


959 


Dis— Ear 

Distance— Continued, 

estimating  by  time,  illusions, 
loss  often  exagg.,  237  [850 
on  reconnaissance,  838 
GREAT  diffs.  of,  effect,  240,  709, 
[721 
increasing,  discourages  traffic, 
[238 
to  secure  way  bus.,  237 
rule  as  to,  238,  720 

LAW   AS    to    THROUGH    CONNEC- 

example,  728         [tions,  219 
moral  effect  of,  239  [195 

mistaken  views  as  to,  cause, 
passing  towns  to  save,  58 
rel.  importance,  ex.,  395 
why  made  basis  of  rates,  196 
Distributing  side  tracks,  *82i 
Ditching,  importance  of,  773 

oc.  illusions  as  to,  847 
Dividends,  L.  S.  &  M.  S.,  ^99 
p.  c.  of  rev.  sections  tJ.  S., 
[*io8 
rates  of  U.  S.  &  Brit.,  *4i 
sections,  U.  S.,  *89,  *92-94 
Division,  length  of,  effect  on  cost 
[grades,  573 
tendency  to  incr.,  169 
Dome,  loco.,  vvt.  and  cost,  ^414 
Dom  Pedro  II.,  ry.,  loco,  perfce., 
Dorsey,  E.  B.,  paper  by,  529  [*44o 
Double-ender  loco.,  def.,  423 
Double-tracking,  764 
and  gravity  rys.,  693 
obtaining,  by  imp'ts  grade, 806 
Drainage,  mental  map  of,  836 
Draw-bars,  elev'd  r'y,  646 
tension  on,  in  sags,  356 

as  mod.  by  speed.  347,  349 

when  most  broken,  368     [*246 

Drawbridges,      accidents     from, 

weight  of,  905. 
Draw-gear,    frt.,    cost    and    de- 
[prec'n,  *204 
repairs  of,  161 

p.  c.  due  to  various  causes, 

[*203 

Dredge,  J,,  "  Penna  R.,"  error  in, 
[*4i6 
Driving-wheels,  centres,  life,  420 
Id.  on  per  sq.  ft.  grate.  *452 
weight  (see  also  Loco.),  414 
'  Drop  test '  for  tr'n  resist.,  909 
Drummers,  and  minor  details,  192 
Dubuque  &  S.C,  align'tstat.,*262 
Dudley,  P.  H.,  expts.  on  ft.  speed, 
on  train  resistance,  518       [370 
Dudley,  P.  H.,  fuel  tests,  529 
Dudley,  C.  B.,  exp'ts  on  rail-wear, 
Duluth,  grain  rec'ts,  728  [320 

Dump-cars,  774  [222 

Dunkirk,  constructive  mileage  to. 
Duplicate  tracks  for  pusher 
[grades,  691 
Durability,  buying,  in  rails,  739  -f 
Durango,  location  at.  722 
Dynamics  of  train  move't,  331 
Dynamometer  tests  and  vel.,  346, 
and  zero  temp's.  508  [349 

deceptive  effect  of,  435 

Earnings  as  affected  by  dist.,  229 
by  dist.   between   towns, 
[709 
per  mile,  sections  U.S., *73-8i. 

[*S9-94.  *i07 


Ear—Eco 

Earnings,  per  m\\&— Continued. 
distribution  of  do.,  *io8 
elevated  r'ys,  646 
Iowa,  77 
L.  S.  &  M.  S.,  99 
Mass.,  78 
per  head,  pass,  and   fr't,  by 
[sections  U.  S.,  *73-8i,  *92-94 
do.    whole   U.  S.,  *73-85, 
Iowa,  77  [*94 

Mass.,  78 
per  engine.  Am.  &  English, 
sections  U.  S.  *89       [*i59 
{See  Revenue,  Europe,  etc.) 
Earthwork,  computing,  895 
cost  of,  on  narrow  g.,  752 
exec'g  by  train,  773,  806. 
prismoidal  form'a,  895        [511 
Eastern  ry.,  France,  journal-box,  ; 
loc.  tests  on,  466,  533        [*i8i  ; 
Eastern  Rd.,p.c.  switching-miles,  : 
Eastern  States,  fall  rivers  in,  841 
East  Kent'y,  loco,  perfce,  ^438 
East  Tenn.,  V.  &  G.  loco,  perfce, 
loco,  tests  on,  701  [*438 

Easy  country,  errrors  in,  584  «& 
Eating  station,  and  compet.  traf- 

.  [*^C'  73 
Economy  in  construction,  g.v., 
[why  generally  safe,  87 


Edg-Eng 

Edgehill,  sidings  at,  827 
Elasticity,  modulus  of,  def.,  345 
Electricity     as     motor,    possible 
[effect,  328 
Electric  interlocking,  g.v.,  811 
Elevated  r'ys,  cost  per  lb.,  905 
curves,  resist,  on,  297 
sharpest,  *325 
speed  on,  273,  325 
earnings  and  exp.,  646 
growth  traffic  on,  *7i4 
per  inhab't,  *7i4 
handling  of  trains,  *559 
length,  stops,  etc.,  *559 
Elevations,  oc,    q.v.  illusions   as 
[to,  844-h 
Elizabeth,  L.  &  B.  S.,  align't  stat- 
[ist.,  *264 
Elliott,  J.  S.,  &  Jalapa  line,  942 
Ely,  T.  W.,  on  Consolidation  eng., 
Emery,  C.  E.,  paper  by,  *53i  [*i4a 
Employes  and  break  in  twos,  359 
and  heavy  engines,  360 
at  N.  Y.  terminals,  *8i9 
courtesy  in,  649 
no.  on  U.  S.  r'ys,  249     [in,  896 
End-areas,  earthwork,  q.  z/.,  error 
End  platforms,  frt.  cars,  *486 
Energy  and  press.,  confusion  as 
how  used  up,  332  [to,  473 


Engravings,  Index  by  Numbers: 

Fig. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

0 

- 

33 

34 

35 

157 

189 

189 

230 

230 

230 

10 

230 

230 

230 

237 

242 

251 

253 

256 

271 

271 

20 

282 

283 

283 

284 

285 

286 

287 

287 

291 

292 

30 

292 

294 

293 

293 

293 

293 

293 

293 

293 

293 

40 

293 

293 

294 

298 

298 

299 

299 

299 

300 

301 

50 

302 

303 

305 

306 

307 

308 

308 

310 

310 

309 

bo 

311 

312 

339 

339 

343 

344 

345 

345 

347 

348 

70 

350 

351 

352 

355 

3'.6 

360 

361 

362 

362 

363 

80 

363 

366 

366 

369 

371 

377 

38s 

386 

386 

386 

90 

3«7 

3B7 

387 

389 

389 

590 

391 

403 

426 

427 

100 

427 

429 

429 

430 

430 

430 

431 

433 

447 

447 

no 

447 

448 

448 

448 

448 

448 

448 

449 

455 

455 

120 

455 

459 

4bi 

462 

467 

467 

476 

476 

476 

477 

130 

477 

478 

478 

478 

480 

480 

480 

481 

481 

481 

140 

482 

482 

482 

482 

483 

483 

483 

483 

484 

489 

150 

489 

489 

493 

494 

497 

504 

5" 

5" 

511 

5" 

160 

514 

515 

510 

518 

521 

521 

53t> 

537 

552 

170 

■;6i 

S6i 

.,62 

562 



■;87 

S88 

588 

■^88 

604 

180 

621 

623 

624 

624 

62  s 

629 

636 

636 

642 

642-6 

190 

647 

647 

652 

660 

661 

661 

664 

664 

668 

666 

200 

668 

671 

672 

672 

673 

673 

673 

676 

678 

679 

210 

679 

67Q 

680 

681 

682 

684 

684 

684 

68  s 

68  s 

220 

686 

686 

68q 

b8q 

6«^. 

6qi 

693 

694 

695 

6q6 

230 

696 

697 

698 

708 

708* 

710 

711 

711 

712 

723 

240 

727 

728* 

735 

735 

736 

739 

763 

767 

769 

770 

2  so 

775 

775 

783 

791 

7Q6 

799 

801 

801 

802 

260 

802 

803 

805 

80s 

806 

807 

838 

843 

843 

844 

270 

84s 

846 

846 

847 

848 

849 

853 

853 

859 

8SQ 

280 

8sq 

862 

863 

869 

870 

870 

871 

872 

874 

874 

290 

882 

882 

883 

884 

885 

885 

887 

888 

889 

889 

300 

897 

902 

914 

917 

918 

918 

918 

919 

928 

932 

310 

\    934 

945 

946 

947 

234',  I 

3.  708; 

241',  p 

•  734- 

960 

INDEX. 

Engravings 

Engravings 

Engravings 

Engravings,  Index  by  Subject: 

Engravings,  Index  by  Subject: 

Engravings,  Index  by  Subject: 

Abutments,  pile,  770 

Double  track,  uses  of,  693-4 

Jour'1-box,  usual  Am.,  514  [914 
Jour'l  fric,  app'tus  for  test'g, 

Alignment,  possible  devia'ns 

Eastern    ry.,    France,    jour.- 

[small,  189 

[box,  511 

diagrams  of,  515,  917 -f 

Ameca  River  spirals,  etc.,  684 

Elevated  ry.  curves,  646-8 

Lake    Shore    &    M.   S.   train 

Ames  car  coupler,  489 

English  tunnel,  242 

[resist,  tests,  518 

American     line     to    Mexico, 

Estimating,  from  profiles.  897 

Latitudes  and  departures,  dia- 

[maps,  etc.,  932  + 

Falling  bodies,  paths,  339 

[gram  for  comp'g,  889 

Arc,  mental,  striking,  838 

vel.  of,  624                     [887 

Leadville,  high  line  to,  695-7 

Areas,  ft.  lbs.  and  H.  U.,  455 

Field-sheets  for  mapping,  ex., 

Lehigh  Valley  rail  sec'n,  310 

Ball  on  plank,  308 

Flange-pres.,  loc,  on  curves. 

Located  and  prelim,  line,  863 

Better  country  than  it  looks. 

[433 

Location  around  ridge,  668 

Bissell  truck,  426,  429-31     [848 

resultant,  292,  294,  299 

in  flat  country,  66r 

Boiler  power,  adapting,  403 

-wear,  actual,  308 

Locomotives,  asst.  and  grades. 

Brakes,  computing  eff'y?  494 

alleged,  307 

profile  for,  666        [587 

branch  lines,  examps.,  734-6 

Foot-lbs.,  areas  and  H.  U.,  455 

vs.  through  engs.,  604 

Breckenridge,  Col.,  loc'n  at. 

Forces,  triangle  of,  clos'g,  537 

use  over  summits,  689- 

Bridges,  comp.  wt.,  767     [696 

Forney,  M.  N.,  model,  311 

boiler-power  of,  403       [94 

diff.  rolling  I'ds,  769 

Friction,  apparatus  for  test- 

Bissell  truck,  426,  429-31 

vibration  of,  447-8 

[ing,  914 

coal,  unburnt,  lump,  449 

Broken-back  curves,  ex.,  870 

coef.  of,  light  press.,  504 

centre  grav.  of,  271 

Burlington  train-r.    tests.  497 

experiments    as    to,    504, 

comp.  safety  on  curv's,433 

Cable  system, planes  for,689-93 

Gauge,  effect  of,  305      [917-19 

counterweights,  447 

Cars,  centre  grav.  of,  271 

Geometric  diagrams,  exagger- 

indicator  diags.,  476-84  — 

Car-wheels,  compression    of. 

[ations,  387 

power  of,ongrades, 552, 587 

usual  Am.,  514              [562 
Cattle-guard,  C,  M.  &  St.  P., 

Georgetown  spiral,  681 

resist,  of,  prop'nal,  521 

Grade-lines,  possible  devia'ns 

trucks,  429  ± 

[770 

[small,  189 

tests,  461-81 

Centre  of  gravity  in  sags,  360 

Grades  and  uncomp'd  curv.. 

wheel-base  diags.,  426 -[- 

of  rolling-stock,  271 

[625,  629 

wts.,  769         [test,  463 

Chicago,  M.  &  St.  P.  timber 

broken,  sags  and  up'd,  624 

London,  Br.  &  So.   C.  loco. 

[strucs.,  770 

forces  on,  339,  536 

Lubrication,    effect  on    fric. 

N.  W.  grain  receipts,  728 

heavy,  of  world,  698 

[917-9 

Cine,  N.  0.  &  Tex.  P.  loco. 

long,   broken   vs.    cent's, 

Manhat  n  elev.  ry  crves, 646-7 

[tests,  482  4- 

momentum,  344-5  &     [385 

Mapping,  field-sheets  for,  ex.. 

Coal,  lump  of  unburnt,  449 

of  repose  increas'g  speed. 

[887 

Cochituate,  L,,  rainfall,  783 

last  car,  362             [369 

good  and  bad  ex.,  888 

Cone,  contour  map  of,  874 

rate  of,  and  asst.  eng.,  587 

Mexican  Central,    Ameca    r. 

Coning,  model  for  testing,  311 

St.  Gothard  r'y,  672-3 

[spirals,  6S4 

radius  of  path  wheels.  312 

reduc'g  by  devel't,  588,668 

Tepic  to  coast.  676-7 

Contour  lines,  errors  in,  884-5 

saves  no  dist.,  671 

spiral  on,  678 

maps,  finishing,  888 

resistance  of,  536 

National,  Pacific  b'ch,  723 

nature  of,  S74 

sags  and  summits,  623-4 

Mexico- Vera  Cruz,  map,  932 

Counterweights,  loc,  447 

switchback  grades,  947 

Momentum      grades,      344-5, 

Couplers,  automatic,  489 

train-load  on,  552 

[623-5,  703 

Couplings,  forces  at,  301,  303 

unif.  and  pusher,  604 

Monte  Carlo  disaster,  253 

Crossings,  stops  at,  grades, 802 

virtual,  q.v.,  348  -f ,  703 

Mountain  grade,  Jalapa  line, 

Cross-section  rods,  882 

long,  353 

[934  + 

Cross-ties,  theory  of  form,  775 

Grain  rec'is,  N.  W.,  728 

Niagara  cantilev'r  brdg.,  wt.. 

Curvature  and  accidents,  253 

Gravit}^,  action  on  grades,  536 

[etc.,  902 

and  tunnels,  242            [629 

on  diff.  paths  of  desc't,  624 

Northwestern  grain  rects.,  728 

compensating,  effect,  621, 

r'ys,  typ.  profile,  691 

Obliquity  of  traction,  301 

on  low  grades,  652 
radius    of,    5°    and    10°, 

Great  inclines  of  world,  69B 

Ocular  il'lusions,  843  -|-,  665 

Grooved  wheel,  294 

Offsets  appear  too  large,  665 

[636-40 

Gyration,  radius  of,  739      [455 

to  curves,  872 

Curves  and  wheel-bases.  283-i- 

Heat-units  and  temp.,distinc.. 

Oroya    ry.   developm'ts,   679. 

checking  speed  on.  647 

Hemisphere,  contour  map  of, 

Overlap,  views  of,  846-7  [684-6 

comp.  safety  locos,  on,  433 

Hill,  J.  W.,  loc.  test.,  461  [874 

Parabola,  principle  of,  387 

offsets  to,  determ'g,  872 

Hut,  ocul.  illusion  as  to,  846 

Parallelogram  of  forces.  302 

position  truck  on.  256.  282] 

Impact  at  joints,  561 

Pass,  oc.  illusion  as  to,  845 

radius  of,  and  speed,  647 

Inclined  planes,  forces  on,  339 

Peruvian  r'ys,  profile,  698 

rail-wear  on,  293          [646 

vel.  down,  624 

Prelim,  and  located  line,  863 

Curves,  sharp,  elevated  rys., 

types.  689-93 

Prices,  fluct'ns  in,  763 

may  save  dist.,  642 

Indicator  diagrams,  actual  ex- 

Profile  condensed,  ex.  of,  862 

variat'ns  dist.  via,  642 

[amps.,  476-84 

estimating  from,  897 

.     Denver,  So.   P.   &  P.,    map. 

typical,  simplest,  456 

Jalapa  line,  938     _        [853 

[etc.,  695-7 

with  expan.,  467 

of  badly  reconnoit'd  line, 

Development,  effect,  588 

Interlocking  app's  for  switch- 

virtual,  pass.,  348  -f 

examples,  668-686  & 

[backs,  946 

frt.,352  + 

Distance  and  rate  grade,  671 

Interpolating  dist.,  effect  on 

long  grade,  355 

and  sharp  curves,  642 

[rect's,  230 

sags,  356  + 

effect  on  receipts,  230 

Iron,  price  of,  past,  763 

Pulley  and  rope,  302 

oc.  illusions  as  to,  859 

Jalapa  line,  maps,  etc.,  932  -}- 

Radiation,  effect  on  cyls.,  476 

slight  effect  lateral  dev'ns. 

profile,  698 

Rails,  alleged  corner  wear,  307 

total  &  rate  grades, 671  [237 

Janney  car-coupler.  489 

and     wheels,     positions. 

via  various  curves,  642 

Journal-box,E.  r'y,France,sii 

[292-4 

INDEX. 


961 


Engravings 

Engravings,  Index  by  Subject; 
Rails,  bending  of,  493,  775 
compression  of,  516,  562 
price  of,  past,  763 
section,  L.  V.,  310 
sections,  worn,  293 
strength  of,  739 
yielding-  of,  493 
at  joints,  561 
Rainfall,  past  20  yrs.,  783 
Rates,  dec.  in  U.  S.,  727,  33-5 
Reconnaissance,   ex.  of  bad, 

L853 
manner  of  making,  838 
Resultant,  flange  press.,  292 
Ridge,  low,  loc"g  over,  661-4 
Rise  and  fall,  on  grades  and 
[level,  366 
worst  class  of,  371.  377 
Rolling-load,  comp.  effect,  767 

diags.  of,  769 
Sags  and  summits,  363,  623-4 
centre  of  gray,  in,  360 
motion  through,  356  + 
filling  up,  806 
in  long  grade,  625     [672-3 
St.  Gothard  r'y  profiles,  etc., 
Slopes,  oc.  illusions,  843-g 
Speed,  check'g,  on  curves,  647 
increas"g,  virt'l  protile,369 
Sphere  rolling  on  plank,  308 
Spirals,  Ameca  river,  684 

bridge  &  tunnel,  typ'l,  679 
bridge,  Mex.  C.  ry.,  678 
Un.  P.,  G'town,  680-2 
St.  Gothard  ry.,  672-3 
Stations,  grade    st.  801  -f- 
grades  bek  ■»,  791 
on  grades, 801,  S03 
Stops  on  switchback,  947 
Stop-watches,  mounting,  796 
Stroudley,  Wm..  loc.  test,  462 
Summits,  stations  at,  805 

types  of.  689.  693 
Superelevation,  effect,  298 
Surveys,  when  to  make,  exs., 

[859 
Switchbacks,  grades  for,  947 
Peruvian,  685-6 
sketch  of  principle,  945 
switches  for,  946  [455 

Temperature  and  H.U..  dist'n, 
Tepic,  descent  from.  676-7 

spiral,  678     [map,  ex.,  888 
Topography,   good   and    bad 
law  of  dif .  in  slopes,  588 
taking,  883 

errors  in  do.,  884-5 
Towns,  loss  dist.  going  to,  859 
Track,  yielding  of.  493 
Train-load  on  grades,  552 
Train-resistance  tests,  497,518, 
[521 
Traffic,  gr'th  of.  U.  S.. 727.33-5 

law  of  growth  of.  712  — 

Traffic  points,  effect  of  multi- 

[plying.  708  -(- 

Transition  curves,  nature  of, 

use  of,  exs.,  870-2         [869 

Trestles,  iron,  effect  ht..  902 

wood,  C,  M.  &  St.  P.,  770 
Trunk  lines,  Mexican,  72^  [306 
Trucks,  Igth.  of,  effect,2S3.287, 
position  on  curve,  256,  282 
rotation  on  curves,  286 
swing-motion,  429 

61 


Eng-Eur 

Engravings,  Index  by  Subject: 
Tunnels  and  curvature,  242 
ex.  of  avoiding,  668 
spiral,  672-S4 
Union  Pacific  spiral,  681 
Valley  lines,  oc.  illus'ns,  848 
Vertical  curves,  theory,  386  -|- 
examples,  389  -f  [703 

Virtual  grades  and  actual  ex., 
descend"g  grade,  369,  799 
level,  passT,  34S  -(-,  352'4- 
stations,  801-2-5  -f- 
theory  of,  348  _-}- 
Way  traffic,  effect  inc'g,  708  -[- 
Wellington,  fric.  diags.,  917 

train-resist,  diag.,  518 

Wheel-base,  length,  effect,  306 

i  long,  on  curves,  2S3,  2S7 

I  Woodbury, C.  J. H.,  fric.  tests, 

i  [504 

Work  and  stress,  distinct.,  455 

Worse  country  than  it  looks, 

[849 

Entrained  water,  loss  by,  470  + 

Engineer,  The,  on  great  inclines 

[of  world,  *699 

on  train  resist.,  pass.,  527 

Engineering,  cost  per  mile,  N.  Y. 

[C.  &  H.  R.,  *7i 

definition  of.  i  [two,  359 

Engineers  and  am't  of  curvature, 

errors  among,  880  [654 

needless  as  to  grades,  659 

have  first  chance  at  co.  funds, 

locating,  av.  work  of,  583-4  [34 

province  of  the,  17 

untrained    and     half-trained, 

[ests.  by,  834 

Engineman  controls  breaking  in 

,.      .  .    [two,  359 

do.  slipping  drivers,  g.v., 

-^      ■  .,,..,         t359 

Jingine-mile  and  tram-mile,  ratio, 

[*i45 

Engine  wages,    q.v.,    per    train- 

{See  Loco..,  Steam.)    [mile,  *i47 

English  practice  as  to  curvature, 

[242 

designation  of  curves,  266 

r'ys.  growth  of,  =^79 

loco,  and  car  exp's,  *i48 
motive-power    exp.      de- 
[tails,  *i47 
pass,  trains,  on,  96 
ratio  eng.  and  train  miles, 
statistics  of.  ^79  [*i45 

{See  Great  Britain.)       [425 
Equalizing  lever,  loco.,  g.v..  421, 
Equanimity  essen'l  to  success,  840 
Equilibrium,  theory  of,  536 
\  stable,  282  *[R.  *7i 

I  Equipment  cost,  N.  Y.  C.  &  P.  R. 
per    mile  sections   U.  S., 
I  {See  elsewhere.)  [*89 

Equivalent.    (.SV^' Virtual  Grades.) 
I  Erection,  bridges,  cost,  905 
'  Erie.    {See  New  York,  L.  E.  &  W.) 
I  Erosion,  water,  effect  of,  684 

Escandon,  A.  &  Mex.  Ry.,  929  [*4i 
i  Estimate  of  future  r'y'construc, 
'  of  future  traffic,  method,  24,  76 

preliminar)'  895 
j  precision  not  imp't,  895 

!  two  opposite  errors  in,  834 

j  Europe,  cheapest  r'ys  in,  +45 
growth  r'ys,  *42 


Eur— Exp 

Europe — Continued. 

pass,  trains  in.  96  [*43 

pop'n,  rys,  wealth,  etc.,*27, 
rolling-stock,  traffic,  etc.,  *43 
terminals  in,  827 
European  car  resistance,  ^502 

rolling-stock  on  curves.  2S3 
Evans,  W.  W.,  paper  by.  691  [*26i 
Evansville  &  T.H.,  alig'n't  statist., 
Evaporation,  loco.,  q.v.,  av.  rate. 
[449,  456 
as  aff'd  by  rate  combus., 
sources  of  loss,  *456     [450 
per  lb.  coal,  av.,  156  & 
per    sq.    ft.    grate,    rate. 
[*464+ 
H.   U.   from   and   to  various 
[temp.,  *4So 
stationary  q.v.  engines,  *53i 
Excavations,  earth,  893-5 

shallow  rock,  868 
Exhaust,  work  of  piston  on,  473 
Expansion,  period  of,  def.  458 

theoretical  gain  by,  467 
Expenditure  on  const  c'n,  q.v.,  15 
Experience  and   am't  curvature, 
and  grades.  583-4,  659        [654 
Experiments  as  to  adhesion,  443 
air-brakes,  290 
bridge  vibration,  447 
brake  efficiency,  434 

max..  495 
coal  per  F   'P.,*46o  & 
coning,  eh  ct  on  pos'n  wheels, 
Corliss  engine  fric,  533      [282 
curve  resistance,  306  & 
sharp  curves,  297  & 
entrained  water,  470 
falling  bodies,  laws,  332 
friction,  brake,  290 
friction,  laws,  503  -|-,  913  & 
fuel  consump.,  light  Iocs.,  137 
grate-area  efficiency,  484 
greasing  flange,  516 
kindling  fires,  200 
locos,  fuel  combustion,  464 
head  resist.,  ^520 
high  speed,  473 
horse-power,  451,  466  -\- 
p'rf 'm'e,  *46i  -f,  *476-84  & 
relative  resist.,  521,  279  & 
running  light,  137 
tract,  power,  437,  552,  701 
loose  wheels,  306 
narrow-gauge,  306 
path-coned  wheels,  309 
radiation,  313 

internal,  472 
rail-wear,  no,  294,  320,  380 
slide-valve  ix\c',  532 
slip,  imperceptible,  445 
slipping  wheels  on  curves,  285 
speed  of  freight  trains,  370 
steam  press.,  economy  of,  474 
train  resist'n'e.  497  -j-,  909,  913 
elements  of,  517  ■\- 
high  speed,  526  -|- 
trucks  on  curves,  282 
wheel  pressure,  122 
Experiments  by  Abbey,  H.,  445 
Baldwin,  O.  H.,  445 
Boston  &  Albany,  532 
Chanute,  O.,  122,  526  — 
Clark,  D.  K.,  472,  474 
Cloud,  J.  W.,  285 
Colburn,  Z.,  437 


962 


INDEX, 


Exp-Fil 

Experiments  by — Continued. 
Gushing,  G.  W.,552 
Delafield,  M.  F.,  533 
Desdoint,  M.,  521,  528,  535 
Dieudonne,  etc.,  443,  533 
Dripps,  I.,  *279 
Dudley,  C.  B.,  320,  380 
Dudley,  P.  H.,  370,  518 
Emery,  C.  E.,  297 
Forney,  M.  N.,  309  + 
Galton,  D.,  200,  434-5,  495 
Hill,  J.  W.,  *445.  *46i  +,  *526 
Hudson,  C.  H.,  701 
Galileo,  332 

Guebhard,  etc.,  443,  533 
Latrobe,  B.  H.,  297,  443 
Marie,  G.,  464,  470 
Morin,  A..  503 
Rabeauf,  M.,  445 
Regray,  M,,  466 
Rhodes,  G.  W.,497  + 
Ricour,  M..  527 
Robinson,  S.  W.,  447 
Sedgeley,  J.  H.,313 
Smith,  C.  A..  445,  472 
Sprague,  F.  J.,  559 
Stroudley,  W.,  137,  200,  451,* 
[460,  526 
Thurston,  R.  H,,  504  -f ,  917  -f- 
Tower,  B.,  504  +,  917  -f 
Vuillemin,  etc.,  443,  ^33,  535 
Wellington,   A.   M.,  282,  293, 
,,.  ,t^97.  320,  380,  504,  904,  913 
Wells,  R    137,  306        [435,  495 
Westinghouse,    G.,   290,   434, 
Woodbury,  C.  J.  H.,  504  + 

Exploration  line,  860 

Export  traffic,  relative  imp'rt'n'e, 

grows  less,  615  [*io5 

Southern    States,    triangular 

[course,  615 

Exposure,  effect  on  car  and  eng. 
[reps.,*203 

Extra  haul  not  a  burden  on  traffic. 

Extra  freight  trains,  102  [61 

Eye  for  country,  acquiring,   23, 
,      .„     .  [834,  876  & 

ocular  illusions,  842 

Fairlie,  R.  F.,  inv.  narrow-gauge, 

locos.,  def.  and  use,  424      [424 
ex.  of  heavy,  410 
in  Mexico,  932 
Falling  bodies,  laws,  338-g  & 
Falling  down-stairs,  deaths  from, 
False  summits,  836  [257 

False  works,  cost  of,  905 
Farmer,  and  steep  hill,  656 

inspecting  grades,  662 
Farms,  U.  S.,  value,  *2s 

machinery  on  do.,  value,  *2$ 
Far  West  States,  area,  pop.,  earn- 
ings per  mile  and  head,  etc.,  *9i 

gen.  r'y  statistics,  *88.  *9o 

maint.  way  exp.  details,  *i28 
Feat,  sci.  skill,  marvellous,  932 
Fell  system,  fric.  r'y.  690 
Fences,  cost  U.  S.  sections,  *i28 

maint.  Chicago  lines.  *i74-6 
sections,  U.  S.,  *i7o-6 
trunk  lines.  *i72-6 

p.  c,  cost  to  total,  *757 
Field-sheets,  mapping,  g.v.^  886 
Field-work  of  surveys,  g.v.,  860 
Fills,  and  cuts,  balanc'g,  895 

locat'g  culverts  in,  851 


Fil-Fra 

Fills  and  cuxs— Continued. 

min.  height  for,  893 

nature  makes  in  valleys,  850 

prove  deeper  than  expected, 

should  exceed  cuts,  893      [851 
Finland,  cheap  r'ys  in,  *45 

Iocs.,  no.  and  work  of,  *i6o 
Fire,  accidents  from,  *247 

and  r'y  accidents,  258 
Fire-box,  loco.,  g.v.,  life,  *4i^-20 

radiation  q.v.  from,  313 

sheets,  fractures,  *42o 

size,  *407-4io 
Fisher  rail-joint,  123     [miles,  *i8i 
Fitchburg    r'd,   p.   c.    switching- 
Fittings,   loco.,  cost  new,  det'ls-, 
[* I 50-1-2-4-5 

wt.  and  cost.  *4i3  -j- 
Fixed  charges,  def'n,  33 

nature  of,  106 

rel.  amt.  of,  ^3-4-5  & 
Flag  for  trains,  how  carried,  102 
Flange,  best  form  of,  307  -|- 

FRICTION,  291 

greasing,  effect,  516 
independent  of  rad.,  291 
pressure,  291 

and  centrif.  force,  269 

CONCLUSIONS  AS  TO,  304 

effect  of,  294 
independent  of  rad.,  293 
resultant  of,  292 
sharp,  proportion  of,  *3i7 
wear,  erron.  views  as  to,  307 
Flat  cars,  dimens.,  etc.,  *486-7 
Flint  &  P.  M.,  loco,  perf'ce,  *438 
Floating  capital,  U.  S.,  value,  +25 
Floods,  accidents  from,  *247 

in  valleys,  g.z'.,  783  [*304 

Floor,  frt.  car,  cost  and  deprec'n, 
Florida :  area,  popu.,  sidings,  p.  c. 
opg.  e.xp.,  earnings  per  mile  and 
head,  *9o  ;  wealth  per  cap.,  *26 
Fly-wheel,  energy  of,  334 
Fog,  as  cause  of  accidents,  254 
Foot-pounds,  expPn  of,  338 
of  work,  and  grades,  329 
Foot  travel,  illusions  from,  850  -\- 
Forces.  triangle  of,  536 
Foreclosed   lines    pass  far    from 
Foreclosures,  r'y,  39        [towns,  68 
Foreign  countries,  pay'ts  per  head 
[to  r'ys,  *io5  & 
Foreign  haul,  effect  on  value  of 
[dist.,  229 
rys.,  gen.  stat.,  +27,  *42-4 
Foreshortening,  oc.  g.v.  ill'n,  8424- 
Forgings,  prices.  Am.  &  Eng.,*4i6 
Forney  loco.,  g.v.^  def.  and  merits, 
[423 
Forney,  M.N., Catechism  of  Loco., 
on  rail-sections,  307  [422 

record  wt.  loco,  parts,  *4i4 
Fortress,ancient.in  Mex.,943  [*26i 
Fort  W'ne,  M.  &  C,  align't  stat.. 
Fractional  sta'ns  and  prelim,  ests,, 

h  rames,  loco.,  g.v.^  cost  new,  etc., 
weight,  414    [*i5o-i-2-4-5 
France,  exp'ts  on  adhesion,  443 
journalrboxes  in,  510,  515     [45 
popu..  r'ys,  wealth,  etc.,  27.  43, 
loco,  drivers,  size,  535        [445 
imperceptible  slip  exp'ts, 
no.  and  work  of,  *i6o 
repr.  details,  *i45 


Fra— Fue 

France — Continued. 

loco.drivers,tests  of,  521,533  -f- 
railway  manage't  in,  *575 
safety  in,  258 
system,  growth  of,  44 
rec'ts  per  inhabt.   pass,   and; 
[frt.,  *io5 
rolling-stock,  traffic,  etc.,  43 

details,  521 
train-loads  in,  and  Am.,  575 
train-resist,  tests,  521,  528 
Francis,  Chas.,  diagram  by,  889 
Free    omnibuses    and    errors    of 
[location,  54. 
Freight    and    pass,    locos.,    q.v., 
[tire  reps.  *i49 
Freight  cars  q.v.  per  mile,  sects. 
[U.  S.  *89, 
world,  43 
earnings,  y.z'.,  thro' and  local,^ 
[sect'ns  U.  S.,  *23r 
per  head,  do.,  92-4 
tons  of,  world,  *43   [U.S.,*i8i 
traffic,  q.v.,  p.  c.  of,  sections,^ 
trains,  q.v.,  no.,  load  and  haul, 
[U.  S.  sections,  *97 
growth  of  load,  98-100 
Fremont  pass.,  *7oo 
Freshets  and  structures,  781 
Freycinet,  est.  by,  loco,  rail-wear,. 
[122: 
Friction  and  heat,  journals,  314 
app's  for  test'g  in  lathe,  914 
as  affected  by  area,  295 
by  lub'n,  509,  917-9 
by  press.,  504-5,  917-9 
by  temp're,  *505 
by  coef.  fric,  time,  *29o 
by  velocity.  289,  913 
bath  lub'n,  509, 918 
brakes,  q.v.,  av.,  494 
brake-shoes  and  wheels,  *29o. 
car-wheels,  289 
driving-wheels,  435 
loco.,  q.v..  *529  -}-  & 
Morin's  exp'ts,  503 
of  rest,  920 

rotative,  wheel  on  rail,  291 
skidded  wheels,  *29o 
slide-valve,  532 
starting,  q.v.,  919 
stationary  eng..  *53i 
Friction-grip  r'y,  origin,  etc.,  691 
Frogs,  accidents  from,  *246 

and    switches,    cost,    various 

[roads,  *i20' 

Frost  and  broken  rails,  256     [*409 

Fry,  Howard,  and  W.  S.  engines, 

on  English  coal  consump.,  133 

Fuel,  consumption  of,  132 

as    affected     by   comp'd 
[eng.,  133 
train-length,  *i36 
due  to  head  resist.,  530  — 
English    and   Am.,    why 
[diff.,  134 
per  mile,  *5i9 
cost  of,  132 

as  affected  by  curv.,  313 
distance.  199 
radius  of  curve,  639 
rise  and  fall,  375 
temperature,  314 
wt.  of  engine,  563 
wt.  trains,  568 
work  done  by  eng.,  376 


i 


INDEX. 


963 


Fue— Gra 

Fuel,  cost  oi— Continued. 

causes  of  variation,  158 
C,  B.  &  Q.,  tendency  on, 
per  ton-mile,  *i47         [157 
Chicago  rds.,  *  174-6 
sections.  U.  S.,  *i70-6 
trunk  lines,  *i72-6 
ejected  from  smoke-stack,  449 
heat  units  in,  *45o 
high  and  low  speeds,  529 
per  car-mile,  P.  R.  R..  *i4o 
H.  P.,  actual,  *46o 
stationary  engines,  531 
theoretical,  *i,6o 
train-mile    P.  R.  R.  lbs., 
cost,  *i4o  1*140 

rate  of  combustion,  449 
terminal  wastage  of,  200 
■wastage  of,  by  blast,  449 
wood  as,  139 

amt.  burned  P.  &  R.,  *2oo 

Furniture,  U.  S.  value,  *25 

Furniture  car,  C.  &  N.  W,,  *49o 

Future    growth,  q.v.,  of    traffic, 

[est'g,  24 

not  to  be  est'd  far  ahead, 79 

g,  value  of,  332 

Galton,  D..  exp'ts  on  brakes,  290, 
Gauge,  def'n,  284  [434-5,  495 

and  curve  resist,  305 

[751 

narrow,  q.v.,  pros  and  cons, 

tight,  effect  on  wheels,  283 

General  and  sta'n  expenses,  118, 

[178 

as  affected  by  distance,  206 

considerable  diff's,  210 
no.  trains,  568 
of  car  repairs,  160 
of  loc.  repairs,  *i45-7 
General  officers  and  clerks,  cost, 
[Chicago  r'ds,  *i74-6 
sections,  U.  S.,  *i7o-6 
trunk  lines,  *z-j2-6   [lence.  832 
Geometric  and   commerc'l  excel- 

diagrams,  exagg'd,  387 
Georgetown,  spiral  at,  680  -f- 
Georgia,     align't     statist.,    *264; 
area,   pop'n,  sidings,  p.c.   opg. 
exp.,    earnings    per    mile    and 
head.  *9o;  wealth  per  cap,  *26 
Georgia  r'y,  align't  statist.,  *264 
miles  and  earnings,  *7i9 
pile-driver  car,  *49o 
Germany,  align't  statist.,  *z6s 
axle-boxes  in,  515 
coal  consumption  perm.,  135 
growth  r'y  system,  44 
locos.,  life  of.  *4i9 

no.  and  work  of,  *i6o 
high  steam-press.,  *5i9 
popul'n    r'ys,    wealth,    etc., 
,,.  ,  ^27,  *43.  *45 

rollmg-stock,  traffic,  etc.,  *43 
Giovi  r'y  grade,  *699 
Gondola  cars,  dimens.,  etc.,  *486-7 
'  Good  times  '  and  r'y  constr., 
[763  & 
Gothard  r'y,  condensed  profile, 
[698-9 
Governing  points  for  grade-lines, 

n     ^-  ,     t^75 

Urading,  p.  c.  cost  to  total,  *7';7, 
filling  by  train,  773,  806  [*833 
cost  of,  vs.  rail-sections,  749 


Grades 

Grade-contour,  def.,  874 

examples,  678,  684,  888 

horiz'l  approx.  to,  error, 

[877 

use  in  projecting,  890 

Grade  crossings  and  curve  limits, 

[655 

AND      INTERLOCKING,     790, 

old  lines,  802-3      [809 
laws  as  to,  812 
Grades,  accidents  on,  949 
and  fluctuating  vel.,  346 
and  rise  and  f.,  distinct.,  327-9 
asst.   eng.,  g.v.,    laying  out, 
[596,  600 
bad  not  always  cheapest,  583 
balance  of,  for  asst.  engs.,  591 
for  unequal  traffic,  608 
diff.  for  each  class  traff., 
example,  617  [617 

errors  in  computing,  611 
practical  consid'ns,  611 
table    for     all    con- 
[ditions,  612 
breaks  of,  measure  cost  rise 
[and  f.,  384 
bunched, 585 -f,  618 

{See  Asst.  Engines.) 
changes  in,  comp.  effect  with 
[diff.  locos.,  555 
choice  of,  659 

GENERAL  RULE  FOR,  66o 

comparison    of    pusher    and 

[uniform,  604  -|- 

cost  of,  560 

as  aff'd  by  I'gth  division,  573 

cheap  pass,  traffic,  580 

conclusions  as  to,  573 

diff.  for  through  and  pusher 

[pr.,  ex.,  674- 

due  to  work  NOT  done,  589 

interest  charge  on  new  Iocs. , 

[570 
per  daily  train  and  ton-m., 
[compar'n,  *574 
French  est.,  *576 
German  est.,  576 

VALUE      OF     AVOIDING     IN- 

[CREASE, 574 

de  facto,  def'n,  543,  515 
descending,      when      brakes 
[needed, 371 
disadvantages  not  visible,  242 
effect  on  loc.  and  car  repairs, 

[*203 

on  net  traia-ld.,   diag., 

[552 
on  train-load,  536 

estimating  by  eye,  844  -\- 

fixing  rates  of,  893 

and  inundations,  783 

high,  causes  favoring,  671 
expedients  for  red'g.  675 
great  inclines  of  world, 
[*698-9,  *7oo 
handling  trains  on,  diff'y, 
p.  c.  wt.  eng.  on,  669 
rel.  train-l'ds  on,  *66g 
speed  on,  369 

how  expressed,  537 
in  England,  538 

humps  in,  dangerous,  367 

hydraulic  grade  line,  625 

improving,  and  more  traffic, 
[comp.  value,  112 
double  track,  806 


Grades 

Grades — Continued. 

improving,  loco.   g.v.   design 
[an  obstacle,  478  — 
oh  old  lines,  788 
inherent  objections  to,  328 
irregular,  effect  on  pass,  tr'ns, 

1.     r     ^  1^577 

length  of,  effect  on  virt.  pro- 

[file,  704 

per  sta.,  horiz.  and  along 

[slope,  *34i 

level,  hardly  exist,  551 

limit'g  eff't,'  and  rail-wear,  379 

locating,  field-work  for,  865  -{- 

selecting  rate,  675 
long,  errors  as  to,  329 

longest  in  the  world,  925 
switchbacks  for,  943 
loss  of  wt.  on,  539 
low,  adapting  to  topog'y,  665 
compens'g  for  curves,  620, 
projecting,  660  [652 

reducing,  665 
wrong  use  of,  671 
momentum,  def.  and  ex.,  344 
motion  of  trains  on,  342  -1- 
objections  to.  two  distinct,  327 
of  repose,  def.,  341 
table,  *358 
French,  *522 
pass.,  all  speeds,  *579 
last  car  in  sags,  362 
one  p.c,  effect,  changes  in,  on 
[loco,  mileage,  *557 
pass,  locos,  aff'd  little,  479 

PER    CENT    CHANGE    NET     LOAD 
[due   to  CHANGES,  554-7 

projecting,  890 

descent  ag'st  valley  slope, 
[682 

GENERAL  RULE  FOR,  66o 

lifting  bodily,  892 
long  g's  dangerous,  893 
over  streams.  893 
selecting  rate,  675 
shallow  cuts  bad,  126,  893 
prop'n  traffic  affected  by,  576 
rate  of.  as  aff'd  by  care,  659 
and  light  rys.,  758 
effect  on  cost,  minor  de- 
[tails,  581 
fitting  to  ground,  ex.,  670 
improving  old  lines,  785 
order  of  importance,  768 
projecting,  893 
p.  c.  wt.  eng.  to  train,  all 
[grades,  669 

PER    MILE    AND    P.      C, 

n    •        ^  ■t^^^  + 

small  imp  ce  with 

[pushers,  *587 

REDUCING,  BY  LOWER  PASS. 
[SPEED,  579 

by  more  care,  ex.,  667  & 
relative  imp'ce,  ex.,  395 
net  load  on,  *574 
train-load  for  all,  +669 
resistance  of,  536-40 

effect  on  gross  load,  540 

on  net  load, 541 
formulae  for,  540 
gain  by  concentrat'g,  *s87 
how  determined,  339 
rolling  frict.  adds  to,  343 
rising  above  and  below,  diff.. 
[367 


964 


INDEX. 


Grades 

Grades — Continued. 

ruling,  AND  LIMITS  OF  cunvA- 

[ture,  652 
effect  on  pass,  trains,  577 
devices  for  reducing,  659 

NATURE  OF  EXPENSE  FROM, 
[587  + 

pusher  vs.  through,  667 
rule  for  reducing,  665 
60  ft.  and  6°  comb'n.  656 
speed,  slow,  effect,  622 
stations  on.  788  + 
starting,  to  elim.  extra  fric, 
station,  gr-z/.,  788+  [512 

and  pass,  trains,  491 
statistics  of,  U.  S.,  States,  etc., 

stops,  g.v.,  on,  *5i2 

importance  of  (elev.  rys.), 
[*558-9 
switchback,  947  + 
train-load  on  all,  for  all 
[locs.,*S43  + 
(small  table),  *593  _ 
undulating,    q.  v.^     and    im- 
[proving  old  roads,  799 
eliminated  by  speed,  348 
error  as  to,  329 
little  efE't  on  pass,  t'ns,  592 
on  light  railways,  755 
safe  limits,  356 
uniform,  hard  to  secure,  586  & 
virtual,  q.v.^  and  actual,  dif¥., 
[543,  551 
length  makes  no  diff.,  799 
starting,    ex.   of    compu- 
[tation,  *559 
Grading,  abandoning  old,  cost,  787 
Grain,  bushels  of,  per  mile  r'y,  *9o 

Northwest  receipts,  728 

Grand  Central  sta.,  N.  Y.,cost,  70 

Grand  Trunk,  cap'l  and  earnings, 

[*io7 

competitive  disadv's,  240 

Grate  area,  loco.,^!'.?/.,  act'I,*407-io 

H.  P.  p  sq.  ft.,  expt.,  484 

limits  for,  451-3 
wt.  on  drivers,  p.  sq.  ft.,  452 
Gravity,  acceleration  of,  333 

action  on  incl'd  planes,  339,  536 
railways,  nature  of,  and  ex., 
rail-wear  on,  122  [691 

tests  of  train  res.,  497  [124 

Great  Britain,  cross-tie  practice, 
curves,  mode  of  design'g,  266 
curves  not  compens'd,  621 
fastest  trams,  and  Am.,  *529 
fuel    q.v.    consump.   in,   and 
[U.  S.,  131-3 
cause  of  dift.,  134 
expenses  per  mile  road,  116 
grades,  modes  of  expr'g,  538 
growth  traffic,  q.v..,  131-2 
iocos.,  q.v.,  comp.   safety  on 
[curves,  434 
duty  of,  comp.  with  Am., 
life  of  parts,  *4i9    [*i59  & 
maint.  per  year  per  eng., 
[and  Am.,  *i59 
p.  c.  labor  and  mater'l, 

[*I52  & 

no.  and  work  of,  *i59-6o 
scrap  value,  420 
type  of  wheel-base.  428 
wt.   and    cost,   and   Am., 
error  as  to,  *4i6  [*4ii-i- 


Gre-Hau 

Great  Britain — Continued. 
no  grade  crossings,  810 
op'g  exp.,  cts.  and  p.  c,  *i78 
pass,  speed,  why  higher,  +530 
p.  c.  op'g  exp.,  *iio,  *i78 

recent  tendency,  116  [*io5 
rects.  p.  inhab.  pass,  and  fgt., 
switching-mileage  prop'n,  135 
terminals,  g^.z/.jand  term,  exp., 
[827  & 
train-mile  cost,  etc.,  *ii6 

Vignoles  on,  1S7 
wages  in  and  Am.,  *i5i 
Great  Eastern  r'y.  locos.,  cost  and 
[miles  per  yr.,  *i59 
traffic  and  fuel  consump.,  *i3i 
Great  inclines  of  world,  *698-9 
Great  North,  ry.,  fastest  trains, 
[*529 
locos.,  cost  and  miles  per  yr., 
repr.  details,  *i45       [*iS9 
Great  So.  &  W.  ry. 

locos.,  cost  new  details,  155 
per  ton,  details,  *4ii 
repairs  in  detail,  *i44-s 
and  renewals,  146 
many  small  details.  149 
p.c.  labor  and  mat'ls,  ^152 
wt.  and  cost  in  det'l,  *4i6 
motive-power  exp.,  *i33 

details,  *i47 
wages  in  shop,  *i5i 
Great  system  of  r'y,  tJ.  S.,  *7i9 
Great  Western  r'y,  fastest  trains, 

.      .,  t*529 

locos.,  cost  and  miles  per  yr., 

„    [*i55,  *i59 
p.  ton,  det  Is,  *i55,  *4ii 
repr.  details,  ^145 
motive  -  power   exp.,   details, 
[*i33,  *i47 
traffic  and  fuel  consump.,  *i3i 
Green  river,  fall,  841  [533 

Grossman,  J.,  on  lubrication,  516, 
Growth  of  r'y  system,  world,  *43 
traffic,  q.v.^  irregular,  85 
how  to  estimate,  87 
ratio  to  rate  interest,  85 

TO      BE     CONSIDERED    ONLY 
[for  3  TO  5  VRS.,  80,  85 

in  no.  engs.,  Engl.,  *i45 
of  train-load,  q.v..,  *97-ioi 
Guadalajara,  Mex.  Nat.  loc'n  to, 
Guessing,  effect  of,  658  &         [723 
Gulf  States:  area,  pop'n,  earn'gs, 
[p.  m.  and  head,  etc.,  *g\ 
fall  rivers  in,  811 
gen.  r'y  statistics.  *88 
pass,  and  frt.  haul  and  train- 
[I'd,  etc.,  *97 
{See  South.) 
Gyration,  radius  q.v.  of,  739 

Hachures,  use,  873 
Hackmen  profit  by  bad  locaiion, 
Hammer  blow,  447  [60,  62,  63 

Hand-level,  use  of,  8^3,  847  [+264 
Hannibal  &  St.  J.  align't  stati.=.t, 
Harlan  &  Hoi.  Co.  pass.  car.  *49i 
Haul,  extra,  not  a  burden  on 
[traffic,  61 

pass,  and  freight  C,  C,  C.  & 
[I.,  12  yrs.,  224-5 

U.  S.  and    States,    *97,   *ii5, 

[*2I7  & 

L.  S.  &  M.  S.  do.,  *98 


Hau-III 

Haupt,  H.,  on  asst.  engines,  585 

on  inclined  planes,  944 
Head  resistance  table,  522 

effect  on  fuel,  530  — 
Headway  of  trains,  def.  and  elev. 
[r'ys,  646 
Heat  from  journal-fric,  q.v.^  314 
Heating  surface,  various  locos., 
[*407-io 
Heat-units  and   temperature  dis- 
in  fuels,  ^450      [tinction,*454 
in  steam,  various  press.,    ^454 
Heavy  construct'n,  q.v..,  error  in, 
[20  & 
Highways,  errors  resulting  from, 
[835,  850 
examples,  667,  853,  936 
grades  of,  illusions,  844 
old  Mexican  road,  941 
Higley  roller  journals,  923 
Hill,  A.  F.,  loco,  test  by,  445 
Hills,  propinq'ty  of,  oc.  illu'n.  846 
Holland,  align't  statist.,  *s65   [*45 
pop'n,  r'ys,  wealth,  etc., 1*27, 
Hopper  cars,  dimens.,  etc.,  *486-7 
Horizon,  best  line  lies  bej'ond,  837 
Horse-cars  benefit  by  bad  loco., 
[60,  62,  68 
traffic  of  N.  Y.,  *7i4 
per  inhab't,  *7i4 
Horse-power,  cost  of,  stationary 
definition,  338,  403  [eng.,  *53i 
effective  and  indic'd,  464 
increases  as  z'^,  *522 
lbs.  steam  per,  loco.,  456  -j- 
stat'n'y  eng.,  *53i 
theoret'l,  all  press.,  *4e>, 
min.,  fuel  per,  469 
per  sq.  ft.  grate,  451,  484. 
to  utilize  full  adhesion,  ^455 
Horse  r'y,  longest  in  world,  030 
Houses,  U.  S.,  value,  25 

and  r'y  accidents,  25S         \(P\ 
Huayacan,  Cuchillode,  spirals  at, 
Hudson,  C.  H.,  loco,  tests  by,  701 
Hudson  river,  fall,  841 
ocular  illus'n  on.  84S 
water  of,  purity,  ^378 
Huds.  R.  Rd'.,  align:nent  statist., 
level  grades  of,  327  [^259 

{See  New  York  C.  &  H.  R.) 
Hut,  ocular  illus'n  as  to,  847 
Hydraulic  grade-line  and  sags,  q. 
Hyperbola,  locus  of,  404     [z'.,  625 

Ice  and  snow,  cost  due  to,  126 
I5aho  :  area,  popu.,  sidings,  p.  c. 
opg.  exp.,  earnings  per  mile  and 
head,  *9o  ;  wealth  per  cap..  *26 
Illegitimate  r'y  enterprises,  14 
Illinois  :  alignment  statist.,  *262  ; 
area,  popu.,  sidings,  p.  c.  opg. 
exp.,    earnings    per   mile    and 
head, *9o 
interlocking  law,  814 
water  in,  quality,  *378 
wealth  per  cap.,  26 
Illinois  Cent.,  align't  statist,  *262 
flucts.  in  stock,  *46 
loco,  old,  wt.  in  det'l,  *4i4 
maint.  way  exp.  by  items,  *i2o 
miles  and  earn'gs,  *7i9 
opg.  exp.  and  trains  per  day, 
rates  on,  fall  of,  *726         [*i74 
train-Id.  growth,  *ioi 
Illusions,  ocular,  q.v..,  842 


INDEX. 


965 


Imp— Jac 

Impacts,  law  of,  561 
Imperceptible  slip,  q.v.,  445     [785 
Improvement  of  old   lines,   g.v.^ 
Inception  of  r'y  projects  (ch.  i.),  13 
Inclined  plane,  theory  of,  536 
lifting'  car  up  by  vel.,  343 
Inclined  planes,  gravity  on,  339 
law  of  motion  on,  339 
passing  summits  by,  689 
pros  and  cons,  686  [*378 

Incrustation,  loco..  ^.z/.,amt.  daily. 
Indeterminate  problems,  bad  so- 
[lutions  of,  7 
India:  locos., no.  and  work  of,*iS9; 
p.  c.   of  operating  exp's,  *iio  ; 
railway  equipt.,  etc.,  *43  ;  roll- 
ing-stock per  mile,  *47 
Indiana  :  alignment  statist.  in,*26i 
area,  popu.,  sidings,  p.  c.  opg. 
exp.,    earnings    per   mile    and 
head,  *9o 

interlocking  law,  813 
wealth,  per  cap.,  26  [*26i 

Indian.,  D.  &  S.,  align't  statist., 
Indicator  diags.,  exs.,  all  cond'ns, 
theory  of,  459,  467  -\-  [*476 
Individuals,  each  a  traffic  unit,  715 
Intiernillos,  location  at,  685 
Ingenio  river,  location  in,  675 
Initial  friction,  q.v.^  919  & 
Inspection  of  steel  rails,  q.v.,  neg- 
[lected,  119 
Insurance    cost,     Chicago     r'ds, 
sections.  U.  S.,  *i7o-6  [*i74-6 
trunk  lines,  *i72-6 
Interchange  of  frt.  cars,  rates  and 
[conditions,  164 
Intercolonial,  rolling-stock  per  m., 
Interest  charge,  nature  of,  106  [*47 
compound,  tables,  *8o-83 
how  affects  location,  17 
on  add'l  locos.,  570,  604 
on  bonds,  p.  c.  of  rev.,  sections 
[U.  S.,  *io8 
Interlocking,  amt.  used,  England 
and  asst.  eng.,  601  [&  U.  S.,  809 
easy  curves,  655 
grade-crossings,  790,  802, 
switchbacks,  946  [S09 

cabins  for,  size,  809 
cost  of,  810-11 
Inundations  of  r'y  lines,  783 
Invention  and  engineering,  i 
Iowa:  align't  statistics,  *262;  area, 
population,  etc.,  90 
fall  rivers  in,  841 
growth  r'ys,  popu.,  earnings, 
[etc.,  *77 
r'y  earnings  per  head,  etc.,*77, 
[*90 
sidings,  p.  c.  opg.  exp.,  etc.,  90 
wealth  per  cap.,  *26 
Iquique  r'y,  Peru,  Fairlie  loc.,*4io 
Irrigating  ditches,  oc.  illus'ns  as 
[to,  847 
Italy,  adhesion  in,  assumed,  443 
locos.,  no.  and  work  of,  *i6o 
popu.,  r'ys,  wealth,  etc.,  *27, 
[*43,  *45 
rolling-stock,  traffic,  etc.,  *43 
p.  c.  opg.  exp..  *iio 
rects.  perinhabt.pass.andfrt., 
Ixtaccihuatl,  mt'n,  927  [*io5 

Jackson,  L.  &  S.,  align't  statistics, 

[*262 


Jal-Lak 

Jalapa,  highway  via,  928 
horse  r'y  to,  930 
line,  description,  932 

low  grades  needed  for,  670 
map,  928 

Mexican  rep't  on,  930 
profile,  condensed,  698,  701 
zigzag  devel't  on,  678 
Janney  car-coupler,  489 
Jeans,  J.  S.,  table  from,  *i59-6o 
Jervis,  J.  B.,  invented  loco,  truck, 
[421 
Journal,  effect,  size  of,  513,  912 
M.  C.  B.  st'd,  499 
max.  I'ds  on,  513       [tion,  *204 
bearing,  cost,   and  deprecia- 
roller,  912, 923 
weight  of,  *i63 
box,  defects  of  ord'y,  510  -}- 

improved,  511 
friction,  509,  913 

as  affected  by  I'd,  503,  611 
expts.  as  to,  913 
app's  for,  914 
normal  am't,  *509 
starting,  512  [24  & 

''Judgment,"  danger  of  trusting. 
Junction  points  for  fr't  cars,  166 
Justifiable  expend,  for  future  Si, 
to  save  $1  per  y'r,  *83        [*82 
Jura  r'y,  profile,  69S 

Kansas:   area.popu.,  sidings,  p.c. 
opg.  exp.,  earnings  per  mile  and 
head,  ^go;  wealth   per  cap.,  *26 
Kansas  Pac,  loco,  perf'ce,  *439 
Kentucky,  align't    statist.,   *264; 
area,  popu,,  sidings,  p.  c.  opg. 
exp.,    earnings    per    mile    and 
head,  *go;  wealth  per  cap,  *26 
Kentucky  river  bridge,  wt.,  901 
Kindling  fires.  Ph.  &  R.  cost,  *20o 
Kingwood  tunnel,    temp'y    line, 
[*7oo 
Labor,    wages,  g.v.,  Amer.  and 
[Eng.,*4i7 
and  mat'l,  cars,  q.v..,  *i6i-4 
locos.,  q.v..,  details, *i33, 
Eng.,  *i33    [*i45,*i5i 
French,  *i47  [19 

Laborer,  useless  work  no  gain  to, 
Lagging  loco.,  g^.z'.,  effect  of,  508 

wt.  and  cost,  *4i3  -f- 
Lake  Erie  &  W.,  align't  stat..*26i 
Lake  Shore  &  M.S., align't  statist., 
ditching  on,  773  [*26i 

chart  of  financial  record,  33 
exp'ts  on  frt.  speed,  370 
flucts.  in  stock,  ^46 
freight  car,  reprs.  on,  162 

renewals  separately,*i65 
fuel  tests,  529 
loco,  boiler,  life,  ^419 

water  supply,  *42o 
miles  and  earn'gs,  *7i9 
motive-power,  exp,  det'ls,*i47 
radiation  tests,  313 
rates,  through  and  way,  E,  & 
[W.  b'd,  226,  IIS 
fall  in,  *726 
sidings,  total,  etc.,  *825 
statistics  frt.  traff.,  *98 

pass,  traff.,  *98 
ton-mile  rects.,  etc.,  *iis 
track  Buffalo  yd.,  *82i 
train-resist,  tests  of,  518,  909 


Lan— Loc 

Lancashire  &  Y.  loco.  repr.  det'ls, 
[*i45 
Landscape  gardening  and  maint. 
[way,  124 
Landslides,  accidents  from,  *247 
Lap,  def'n  of,  470  [122 

Launhardt,  est.  by.  loc.  rail  wear, 
Latimer  rerailing'guard,  900 
Latitudes  and  departures, 

use  of,  886  [comput'g,  8S9 

Latrobe,  B.  H.,  expts.  on  adh's'n, 

[temp'y  lines  by,  445,  700 

Lava,  basaltic,  character,  684  [443 

river  of,  928-32 
La  Veta  Pass,  ^698-9 
Lead,  loco.,  470 

of  freight,  etc.   {See  Haul.) 
Leadville,  high  line  to,  695  -|- 
Legal  exp's,  various  rds.  and  sec- 
[tions  U.  S.,  *i7o-6 
Lehigh  &  Susq.  loc.  perform.,  ^440 

sharpest  curve,  *325 
Lehigh  Valley  align't  statist.,  *26o 

•Consolidation     loc.    invented 
[on,  278,  423 

loc.  performance,  *438-4o 
Mastodon,  details,  ^410 
Id,  on  drivers  per  sq.  ft. 
[grate,  *452 

pass,  car,  st  d,  *49i 

rail-sect'n  and  wh'l  tread,  310 

track  Buffalo  y'd,  *82- 
Level,  hand,  use  of,  838,  S47 

line,  guessing  at,  838 

party,  organiz'n,  861,  867 

slope,  882 
Levelling  on  preliminar's,  861.  865 
Lewisb'g  &  Tyrone  align't  statist. , 
[*26o 
Lighters,  no.,  N.Y,  term'Is,  ^Sig" 
Light  lines  in  difficult  c'try,  20  & 
Light  rails,  q.v.,  and  I't  r'ys,  737 
Light  railways,  737 

and  curvature,  749 

and  dist.  (choosing  route),  722- 

and  value  low  grades,  576,  75S 

CONCLUSIONS  AS  TO,  761 

expedient  economies,  748 
rel.  value  of  more  traff.  to,*7i3 
total  cost,  758  & 
why  do  not  multiply,  737 
Lignite,  H.  U.  in,  *45o  [on.  679-I- 
Lima  &  Oroya  ry.,  developments 

profile,  698-9 
Limiting  curvature,  q.v.,  620 

grades,  q-v.,  536 
Line,  always  easy  to  get  a,  832, 840 
best,  lies  beyond  horizon,  837 
may  survey  a,  but  notrecon., 
no.  of,  to  survey,  q.v.,%2,^  [835 
worst  errors  in  wrong  selec'n, 
[832 
(See  Route,   Location,  Topogra- 
phy.) 
Line  cars,  def'n,  168 
mileage  of,  168 
relative  cost  reprs.,  *i6i 
Link,  coupling,  q.v.,  forces  act- 
[ing  at,  303 
Link-motion,  invention,  etc.,  458 
Liverpool,  sidings  at,  827 

station  exp.  at,  828 
Live-stock,  U.  S.  value,  *25 
Local  freight,  sidings  for,  *82i  -j- 
Local  rates,  q.v,,  constant  ratio 
[to  through,  224-6 


966 


INDEX. 


Loca— Loco 

Local  traffic, ^f.z/., true  classifi.,  211 
effect  distance  on,  213 

Locating  engineer,  q.v.^  altitude 

[of  mind,  21,  831  +>  840,  855  & 

end  of,  2  \Xq.v.'),  684 

Location  and  transition  curves, 
aptitude  for,  and  topog'y,  880 
art  of,  lies  in  choice  of  route, 
av.  practice  in,  4,  583  [840 

bad,  reasons  for,  4  -j- 
care  in,  and  amt.  curv.,  656  & 

CHOICE  OF  ROUTE  WHEN  CLOSE, 
[583 

freer  with  sharp  curves, 

CONDUCT   OF,  831  [656 

correct'g  by  trans'n  curv..  870 
curve  limit  and  topog'y,  655 
difficulty    of  good  prac.    in, 
[2  +,  926 
effect  on  rev.,  48 
■errors  in,  &  cont'r  maps,  876 
how  originate,  658 
worst  in  recon'sance,832 

CENERAL   RULES   FOR,  66o,  694 
LINE   ALWAYS    EXISTS,  832,  840 

marvellous  feat  sci.  skill,  932 
office  chair  loc'n,  880  —      [787 
old  lines,  common  errors  in, 
over  prairie  ridge,  661  + 
paper,  q.v.,  868  + 
party  for,  867  [328 

possible  effect  of  electricity, 
project'g  {q.v.)  and  mapping, 
[886,  890 
rule  for,  in  moderate 
[country,  694 
running  in  the,  867  [698 

sharp  curves  give  new  routes, 
Western  States,  errors  in,  6, 
[21,  *263,  330,  588,  660 
Loch  Katrine  water,  purity,  *378 
Locomotive  engine,  399 
adhesion  of,  434 
AMT.  OF,  435  -|- 
computing  from  I'ds,  444 
defic'y,  how  shown,  405 
effect  of  changes  in,  *44o 
exp'ts  as  to,  434  -f- 
extreme  resorts  to  incr. , 
maximum,  440  [424 

per  sq.  ft.  grate,  *452 

RATIOS   OF,  437 

Am.  and  for'n,  443 
resistances  which  tax,  492 
safe  limits  for,  441 
sand,  effect,  437 
slipping,     q.v.,      drivers, 
[laws,  435  & 
imperceptible,  445 
speed  does  not  affect,  435 
winter  and  summer,  443 
American,  advantages  of,  422 
decreasing  use,  114 
dimensions,  etc.,  407 
invention  of,  421     [*407-|- 
wt.    various    parts,    *4oo, 
and  curvature,  q.v.^  278  & 

stationary  q.v.  engs.,  492 
assistant,  q.v.^  585 
boiler-power,  449 

and  tractive  p.,  *453 
blast-nozzle,  sizes,  *409 
combust'n  and  evap'n,45o 

max.  rate,  449 
deficiency  in  power,  how 
[shown,  405 


Locomotive 

Locomotive — Continued. 

boiler    power,    diagram    of 
[403 
dimensions  of  b.,  407-11 

various  parts,  changes, 
efficiency  high,  457    [*409 
energy  stored  in,  *454 
evap'g     boilerful,      time 
[for,  456 
evap'n,  average  rate,  449 
explosions,  *247 
fire-box,  life,  *4i9 
as  aff.  by  water,  *42o 
fractures,  *42o 
size,  *407-4io 
grate  area  and  load    on 
[drivers,  *452 
H.  P.  per  sq.  ft.  grate,  484 
incrustation,   amt.    daily, 
[*378 
incrusting  solids  in  water, 
^  [*378 
lbs.  coal  per  h.  p.,  *46i 
life  of  boiler,  *4i9 
loss  of  heat  in,  av.,  *456 
low  water,  gain  by,  455 
pass,     and     fr't     service 
[same  b.,  403 
p.  c.  efficiency,  457      [402 
power  measured  in  ft.  lbs., 
radiation,  q.v.^  winter  and 
[sum.,  508 
shell,  thickness,  *42o 
steam,    lbs.  per  h.p.,  av., 
[451 
pressure,  *409-io 
boiler  and  effec,  *479 
cutting    down,    eff't, 
[405 
higher,  effect,  408,  468 
high,  Ger.  and  Swiss, 
*5i9 
reserve  of,  453-4 
steam-chest     and     b. 
[press.,  473 
tendency  to  incr'se  b.,  408 
tubes,  life  of,  *42o 
no.  and  size,  *409-io 
wt.  and  cost  *4i2  4- 
washing  out,  *42o 
water  supply.quality,  *378 
weight  of  ,*407-ii,*4i5-6 
w'ts,  q.v.,    all  parts   and 
[mat'ls,  *4oo,  *4i2  -(- 
to  incr'se  boiler  power 
[10  p.  c,  400 
water  and   steam,  *407- 
[11.  *454 
coal  burned  per  mile,  *i29 
English,  *i3i-2 
Penn.  R.  pass.,  ^134 
compound,  chances,  133 
Consolidation  1.,    q.v.,    def'n 
[and  origin,  423 
cyl.  q.v.  tract,  power,  553 
change  in,  Penna.  R.,*409 
increased  use  of,  114 
most  used  on  heavy 

[curves,  281 

wts.  of  diff.  sizes,  701,  769 

various  parts,  *4oo     [*564 

cost  new,  all  types  and  wts.. 

Am.   and   Eng.    per  ton, 

[det'ls,  *4ii 

as  affected    by  wt.,  etc., 

[*4ii,  *564 


Locomotive 

Locomotive — Continued. 

cost,  builders'  approx.  rules, 
[*565 
details,  150-1-2-4-5 
narrow-gauge,  *564 

disadvantages,  565 
per  ton,  all  types,  *564 
cost  of  operating,  121  -f 

as  aff'd  by  wt.  eng.,  560 
as  pushers,  601  -f- 
cost    of    double    no.   for 
[same  train,  *568,  *57i 
double  wt.  for  same  train, 
[*567 
gain  by  fully  loading,*587 
intermittent  service,  eff't, 
[603 
mat'l  and  labor.  Am.  and 
[foreign,  *4ii  & 
per  year,  *i48  & 
shop  and  gen'l  exp.,  *4ii, 

[*4i7 
standing  still,  cost,  602 
cylinder  power,  457 

all  cyls.  and  drivers,  *479 
and  slipping  drivers,  406 
back  pressure,  amt..  472 
compared     with    adhes., 
[diag.,  552 
cut-off,    no    tendency    to 
[early,  *467 
deficiency,    how   shown, 
[405 
falls  with  speed,  457 
expansion,  theoret.,  gain 
[by,  467 
practical  losses,  470 
indicator  diags.,  *476  -|- 
limits  of,  ex..  703 
losses  of  eff'y,  chief,  470 
of  frt.  eng.  and  speed,  474 
often  too  little,  406 
ratio  to  wt.    on    drivers. 
[*4o8 
reciproc  g  parts,  loss  by, 
[473 
speed,  effect  of  reduc'g, 
[476  + 
varied  easily,  400 
wt.  to  increase   cyl.  p.   10 
[p.  c.  401 
why  should  be  in  excess, 
[400 
cylinders,  cold  or  hot,   eff't, 
[476 
clearance  space,  eff't,  472 
common  error  of   design 
[in,  474 
disadvan.  of  too  large,  402 
entrained  water  in,  470 
large     cyls.     disadvanta- 
[geous,  406 
lead  and  lap.,  def.,  470 
loss  of  press,  in,  *4to 
radiation,    external,    315, 
[377,  471 
internal,  nature,  315,  471 
locos.,  376 

size  of,  why  used  to  de 
[scribe  engines,  402 
steam  cap'y  of,  ^459 
design  of,  402  -f- 

limits  for  same  boiler,  40^ 
logical  order,  402 
narrow-gauge,  7^1     [*i4q 
p.  c.  standard,  P.  R.  R., 


INDEX. 


967 


Locomotive 

Locomotive — Continued. 

dimensions  of  boiler,  *407-4io 
chimney,  *409-io 
drivers,  French,  535 
frt.,  Gt.  East.  Ry.,  *i32 
most  powerful  in  world, 
[*4io,  *42i 
pass,  eng  ,  477 
Tables     of     all    types, 

P407-IO,  *42I 

various  eng.,  *279 
earnings  per  year.  Am.  and 

sections,  U.  S.,  *89 
Pairlie,  def.  and  use,  424 

in  Mexico,  932 
frame,    wt.   and     cost,    *4oo, 

.  .    t*^^3  + 
frt.  Iocs.,  op'g  conditions,  478 
friction  resist.,  q.v.,  of,  530 
fuel  q.v.  consump,  light,  315 
future      improv'ts,     possible 
[effect,  328 
handling  locos.,  breaking  in 
[two,  359 
cut-off,  usual,  469 
drawing  fires,    fuel    lost, 
first  in  first  out,  141      [199 
heavy  engines  and  break- 
[ages,  360 
running  backward,  950 
starting  of,  how  done,  797 
switching    Iocs.,    use    as 
[pushers,  792 
using    heavier  vs.   more, 
[560 
height  cent,  of  grav.,  271 
horse-power       in      practice, 
[*46i  + 
computing  do.,  338 
interest    charge    on,    due    to 
[grades,  570,  604 
limitations  of,  399  + 
and  grades,  327 
and  boiler,  406 
limits  to  work  of,  399 
mileage  of.  Am.  and  Europ'n, 
[*i43,  *  1 59-60 
as  affected  by  age,  *4i8 
C,  B.  &  Q.,  20  years,  157 
exaggerations  in  statist., 
life,  q.v.,  *i43         [103,  142 
pass.  max.  N.  Y.  C,  ^143 
Penna.R.R.  pass,  and  fr't. 
[i886,*5i-84,  *i4o,  *4i8 
U.  S.  sections,  *g7 
run  in  general  office,  142 
special  performances,  *4i9 
switching,     q.v..     prop'n 
[mileage,  135 
life  of,  *i43,  *4i8-9.  *438 

various  parts,  ^419 
machinery,  breakages  of,  *247 
cost  new,  *4i2  + 
essential  elements  of,  457 
link-motion.  458 
repairs,  *i43 
slide-valve,  fric.  of,  532 
valve-gear,  458 
weights  of,  *4oo,  *4i2  & 
Mastodon  loco.,  423  [553 

cyl.  and  adh.  tract,  power, 
dimensions,  etc.,  *4io 
increased  use  of,  114 
Mogul  loco.,  def'n,  422 
dimensions,  etc.,  *4o8 


Locomotive 

Locomotive— (7tf«^r«M^^. 

Mogul  loco.,  max.  w't,  769 
motive-power   record,    Penn. 
[R.R.,  1851-S4.  *i4o 
number  of,  various  countries, 
[*i6o 
English,  *i48 
per  mile  all  countries.*43. 
[*47,  *i48,  *i6o 
sections  U.  S.,  ^89 
No.  of  separate  pieces  in,  *4i5 
passenger  1. ,  coal  consumption 
[light,  132 
grades  affect  little,  479 
need  much  tract  pT,  407 
power  limited   by  boiler, 
[406 
performance      of     American 
[iocs,  (long  tablej,  *438 
Mastodon  loco.,  *4io 
rail-wear,  q.v..,  due  to,  122  & 
repairs,  cost  of,  139 

as  affected  by  align't,  *i88 
class  of  engine,  *i46-8 
curvature,  315 

radius  of,  641 
distance,  201 
grade-crossings,  202 
length  of  trains,  570 
rise  and  fall,  377 
w't  of  engine,  144,  563 
av.  Chicago  r'ds,  *i74-6 
sections  U.  S.,  *i7o-6 
trunk  lines,  *i72-6 
cleaning,  147 
details  by  items,  *i43-9 
deterioration,    causes  for 
[and  rates,  202-3 
distribution  to  causes, *203 

TO  LOCO,  PARTS,  153 

effect  growth  q.v.   traffic 
[on,  153  & 
English,  *i33 
and  American,  422 
details,  *i44 


fittings. 


[153 


gen'l  exp.  often  notinc'd, 

K.See  Motive  Power.) 
gen.  rep'rs,  freq'cy,  420 
labor  and   mat'al.  Amer. 

[and  foreign,  *  143-5  & 
Mass.,  etc.,  142 
minor  details  (many),*i49 
painting,  ^143 
pass,  and  fr't,  *i48 
jjast  history  of,  C.  B.  & 
[Q..  158 

Penna.  R.,  35  y  rs,  140 
p.   c.   in  shop,   P.   R.  R., 

p.c.  renewals,  *i46-7,*563 

p.  c.   round-house   rep'rs, 

[*i45-6,  *i49 

per  year  per  engine.  Am. 

[and  Eng!,  *i59 

running  gear,  *i43 

shop,   tools,  and  general 

\_q.v.  exp.,  153 

tenders,  q.v.,  *i43-6-7 

trucks,  q.v.,  *i43         [*i29 

trunk-line  exp.,    34    y'rs, 

resistance  of,  av'ge,  *465,  ^530 

experim'ts,  q.v.,  as  to,  279 

accurate,  diffic't,  533 
coupled     drivers,     extra 
[for,  534-5 


Locomotive 

Locomotive — Conti7iued. 

resistance     of,    in     practice, 

[*463+ 

head,  at  high  speed,  *522 

error  by  neglecting,  533 

internal,  no    tax  on    ad- 

[hesion.  532 

mach'y  separately,  534-5 

PROBABLE    AMT.,  53I  4" 

slide-valve  fric,  532 
true  test  for  determining, 
running  gear,  421  [492 

Am.,    distinctive    peculi- 
[arities,  421-5 
comparative     safety     on 
[curves,  diag.,  433 
coupled     drivers,     extra 
[fric,  434-5 
driving-wheel  base,  rota- 
[tion  of,  427 
foreign,  hard  on  track,  425 
hammer-blow,  447 
H.  P.  transmissible,  452 
journals,  sizes,  ^409 
load   on   driv.    per  sq.  ft. 
[grate,  =^452 
slipping  drivers,  285,  406, 
[797 
tires,  cost  q.v.  maint.,  316 
truck,   mechanics  of,   426 

[+,433 
weight  and  cost,  *4i3  -|-, 
*400 
wheel-base  lengths, 

[*407-io 
wheel- wear,  C.  &  A.  r'y, 
[*288 
runs,  tendency  to  incr'se,  169 
starting  q.v.  power  of,  352  & 
slack,  effect  of,  490  [424 

switching,  q.v.,  def.  and  use, 
no  iC  y.  terminals,  *8i9 
per  cent  of,  sect'ns  U.  S., 
[*i8i 
tank  Iocs,  as  asst.  engs.,  592 
why  advantag's,  551,  554 
ten-wheel,  def'n,  *423 

dimensions,  etc.,  *4o8 
theoretical  defect,  most  seri- 
three  forces  of,  399      [ous,  329 
deficienc}^,  how  shown, 
[405 

TRACTIVE    POWER,  q.V.,  434 

average  between  stations, 

532 

compared    with    single 

[tests.  551 

all  cyls.  and  drivers,  *479 

as  modified  by  speed,  346 

by  type  of  eng.,  280 

causes  of  fiuct'ns  in,  ^440 

comparative,  cylinder  and 

[adh.,  552 

compared      with      boiler 

[power,  452-3 

with  weight,  all  grades, 

[*6S8 

deficiency,    how    shown, 

[405 

economy    of      fully    em- 

[ploying,  587 

effect    low   boiler  press., 

French    practice     as    to, 

t.      .        .  ..       f^*S75 

head  resistance,  *52o-2i 


968 


INDEX. 


Loc— Los 

Locomotive — Continued. 

tractive  power,  high  speed, 
horse-powrer,  ^sig  *si9 
imperceptible  slip,  445 
increases  faster  than  fuel 
[burned, 133 
loss  at  speed,  nature  of, 
[473 

ON    AI.L    GRADES   IN     DAILY 
[service,  *544  + 

tass.    and    freight   Iocs., 

[diff.,  478 
pass.,  needs  much,  407 

P.C.  CHANGE,  FROM  CHANGE 
[in  any    GRADE,  554-7 

p.  c.  wt.  train  to  wt.  eng., 
[all  grades,  669 
ratio  to  total  wt.  loc.,*542 
weight  train,  all  grades, 
[-  *544  4--  *593 
Speed  reduces,  474 
starting  needs  most,  474 
tank  locos..  551 
testing  by  fiuct'ns  of  vel., 
[792 
■why  great  in  Am.,  422 
wire-draw'g  reduces,  474 
wt.,   to   increase  10  p.  c, 
trimfnings,  wt.  of,  ^400      [401 
TYPES  OF,  defs.,  422 

change  in  most  used,  114 
compar.  cost,  new,  ^565 
effect  grades  on,  555-7 
weight  of,  all  parts  and  m't'ls, 
[*40o,  *4i2  -}-,  *4i6 

ALL  TYPES,  '^407-424,  *279 

as  affected  by  low  grades, 
[566 
by  steel  rails,  561 
by  volume  traffic,  597  & 
boiler,  water  and  steam, 
[*454 
cost  of  doubling  to  haul 
[same  train,  =^567 
details  (full),  ^412-4-6 
effect  on  cost,  new,  ^565 
on  operat'g  exp.,  ^560 
empty    and    in    service, 
P407-8 
fast  pass.,  wt.,  etc.,  421 
French  practice,  *576 
increase  in  recent  years, 
[* 407-10,  *466 
P.  R.  R.  since  1852,  *i4i 
explanation  of,  408 
of  parts,  constancy  in 

[ratio,  *4oo 
on  drivers  compared  with 
[cyl.  p.,  *4o8 
p.   c.   to    train-load,   all 

[grades,  ^669,  *688 
p.   c.  various  materials, 

[Am.  and  Eng.,  *4i6 
ratio  to  trac.  power,  *542 
various  engs.,*279,*4.o7-24 
extra  heavy  eng.,  *42i 
parts  of  eng.,  400 
roads,  ^438 
Long  chords,  diffs.  length,  det'g, 
[*644 
Long  tangents,  q.v.,  bad  practice 
[as  to,  324 
Long  Isl.  r'y..  loco,  perf'ce,  *439 
Loop,  679        {See  Spiral.) 
Loss  and  damage,  cost,  r'ds  and 
[sections,  U.  S.,  ^170-6 


Los— Mai 

Loss  of  time  by  reduc'g  speed, 

Vq.v.,  *594-5 

Low  grades,  g.v.^  and  asst.  eng., 

London  terminals,  cost,  827     [659 

expenses  at,  827-8 

location  of,  72  [*S29 

London,  B.  &  S.  C,  fastest  train, 

kindling  fires,  exp'ce,  *2oo 

locos.,  cost  &  ms.  per  yr.,  ^159 

tests,  *462 

traffic  and  fuel  consump.,  *i3i 

London,  Chat.  &  D.,  fastest  train, 

[*529 

London  &  N.  W.,  am't  sid'gs,  827 

fastest  trains,  ^529  [*i59 

Iocs.,  cost  and  miles  per  yr., 

rep'r  details,  ^145 
interlocking  app's  on,  809 
terminals,  cost,  827 
Louisiana:    area,  pop'n,  sidings, 
p.   c.   op'g    exp.,  earnings  per 
mile  and  head,  ^90 ;  wealth  per 
cap.,  *26 
Louisville,  fall  at,  841 
Louisville  &  N.,  align't  stat.,  ^264 
fluct.  in  stock,  ^46 
maint.  way  exp.  by  items,  *i2o 


miles  and  earn's 


^719 


op'g  exp.  and  tr'ns  pr  day,*i72 

train-l'd,  growth,  *ioi 

Louisville.  C.    &    L.,   miles    and 

[earn'gs,  ^719 

Lubricat'n  as  affect'd  by  temp. ,506 

bath,  efi'y,  509,  91S 

minute  dilJs.,  effect,  509 

Luchmanier  pass,  grades  at,  *7oo 

Lunch  counters  and  curvat.,  649 

Luxemburg  locos.,  no.  and  work 

[of,  *i6o 

Luxury   in    cars,  why  tends    to 

[incr.,  139,  567 

McAlpine,  C.  L.,  on  sharp  curve, 

[326 

Machinery,  loco.,  g.v..,  cost  new, 

[details,  *i5o-5 

reprs.   p.  c.   due  various 

[causes,  *203 

minor  details  of,small, 

shop,  maint.  of,  154  [*i49 

Macon  &  Br.,  align't  statist.,  *264 

loco,  perform..  ^438    {jj.v.^  732 

Mahoning    bch.,  N.  Y.  P.,  &  O., 

handling  trains  on.  791 
Making  time  and  curvature,  268  & 
Malicious  obstructions,  derailm'ts 

from,  245 
Maine:  area,  popu.,  sidings,  p.  c. 
op'g    ex.,    earnings    per    mile 
!      and  head,  *90;  wealth  per  cap., 
*26  [miles,  *i8i 

Maine    Central,  p.  c.   switching- 
Main  (trunk,  q.v.),  lines  and  bchs., 
[707  + 
ex.  of  error  m.  928  & 
Maintenance  of  way,  118 
anomalies  in,  127 
as  affected  by  distance,  199 
gauge,  753 
minor  details,  191 
no.  of  trains,  127,  569 
pushing  eng.,  602 
exps.,  details,   U.  S.  sec- 
[tions,  etc.,  *i28,  *i7o-6 
general  tendency,  117 
iron  rail  era,  items,  "=120 
trunk  lines, 34  years, *i29 


Mai— Mas 

Maintenance  of  Way — Continued, 
exps.,  ratio  to  maint.  cars,  etc., 

[*i3i 

ratios  of  ,to  each  other, 

[*i27-3i 

why  constant  pr.  train- 

[mile,  127.  569 

Manchester,  stat'n  exp.  at,  828 

Manhattan      (elev'd,     q.v.)      ry., 

[length,  stops,  etc.,  *559 

operating  details,  speed,  etc., 

[*559 
Stations  on,  and  power  used, 
speed  on  curves,  273  [*3oi 

Mann  sleeping-cars,  *4gi 
Manufacture  of  rails,  121 

of  transportation.  48,  106 

Manufacturing    regions,    burden 

[traffic  into,  618 

heavy  traffic  of,  63 

Mapping  and  project'g  loc'n,  886 

contours  yq.v.)^  pro  and  con 

[874  + 

GOOD  AND  BAD,  eX..  888 

large  scales,  best,  884 
loose  sheets  always  best,  886 
Maps,  making  mental,  835,  S49 
ex.  of  need  for,  852 
ocular  illusion,  q.v.^  on,  665 
right  use  of,  836-7 
small  scale,  making,  889 

need  for,  665 
use  in  reconnais.  ex.,  934 
Mari^,  G.,  loco,  tests.  464,  470 
Marine  engines,comp'd,  and  loco., 
coal  per  H.  P.,  ^460  [133 

utmost  economy  of,  469 
Marriotte's  la\v,  467  [*262 

Marquette  H.  &  O., align't  statist.. 
Marsh,  Sylvester,  invented  rack 
Marshall  pass.,  *6g8-9  [r'y,  690 
Marvellous  feat,  sci.  skill,  932 
Maryland:  area,  popu.,  sidings,  p. 
c.  op'g  exp..  earnings  per  mile 
and  head,  *9o;  wealth  per  cap., 

[*26 

Mason  loco.,  Am.,  dimens.,  etc., 
[*407 
Id.  on  drivers  persq.  ft. 
[grate,  *452 
Masonry  and  floods,  781 
cost  of,  752 
dry,  bad,  898 
estimating,  898 
Mexican,  929 

p.  c.  cost  to  total,  *757,  *833 
Massachusetts:  align't  statist.,  259; 
area,  popu.,  sidings,  p.  c.  op'g 
exp.,    earnings,    per    mile    and 
[head,  *9o 
classification  of  through  and 
[local  traffic,  211 
cost  per  year   per  eng.   and 
fuel,  cost  of,  136         [car,  *i48 
interlocking  law,  812 
loco,  reprs.,  cost,  142 
maint.  way  exp.  by  items,  *i2o 
motive-power  exp.,  det'ls,*i47 
ry.  earnings  per  head,  etc.,  *78 
wealth  per  cap.,  26 
Master  Car-B'ders  Ass'n,  assumed 
[action  on  rail-heads,  307 
Comm.  rep't  on  heavy  eng., 
[279 
on  interchange  rules,  166 
rule  for  deprec'n  cars,  *2os 


INDEX. 


969 


Mas— Mid 

Master  Car-B'ders  Ass'n— C^;zV. 
stand'd  axle,  w't  ^486 
journal,  *499,  *5i3 
60,000    lb.    box-car,   *ii4, 
[*49o 
Mastodon  loco.,  q.v.,  def.,  423 
introduction  of,  114 
Material,  borin^f  to  test,  868 

cars,  prop'n  to  labor,  *i6i-4 
loco.,   q.v.^  rep'rs,    prop,   of, 
[*i47  + 
prices  of.  Am.  &  Eng.,  *4i6 
w't  and  cost  in  locos.,  *4i2-6 
Mauch  Chunk,  grav.  r'y  at,  692, 
[945 
Mauritius,  roirg-stock  per  m,,  *47 
Maximum  and  min.  limits  of  ests., 
[24  & 
Mechanics  of  curve  resist.,  281 
of  train  move't,  331 
tools,  U.  S.  value,  *25 
Memphis  &  Ch.  align't  stat.,  *264 
Mental  perspective,  i 
Merrimack  river,  fall,  841 
Metric  curves,  radii,  *267 

stationing,  266 
Mexican  Cent.  R'y,  descent  from 
[Tepee,  670  + 
into  Ameca  Valley,  682 
general  route  of,  721 
long  grade  on,  *7oo 
Pacific  b'ch  of,  736,  670  + 
Reventon  tunnel,  668 
spirals  on,  678,  682  [721 

Mexican  Nat.  r'y.  gen.  route  of, 
location,  problems  on,  722 
long  grades  on,*70o 
Mexican  R'y^  curves  on,  326 

error  in  not  going  to  Puebla. 
Fairlie  engines  on,  424        [928 
history  and  descrip'n,  929 
long  grade  of,  ^699 
profile,  698 

{See  Jalapa  line.)  [65 

Mexican  towns,  ex   of  stations  at, 
Mexico,  Am.  line  to  city  of,  925 
Am.  locos,  in.  422 
plateau  of.  927 

rects.  per  inhab't  pass.  &  frt., 
rolling  slopes  in.  844  [105 

trunk  lines  in,  720 

{See  Jalapa,  etc.) 
triangular  course  traff.,  616 
Michigan,  align't  statistics,  *262 
area,  pop'n,  sidings,  p.c.  exp., 
[earn'gper  m.  and  h'd,  *9o 
interlocking  law,  13 
'  rough  country "  of,  840 
wealth  per  cap.,  *26 
Michigan  Air-L.  align't  stat.,*262 
Mich.  Cent,  r'd,  chart  of  financial 
fall  of  rates  on,  *726  [record,  34 
fluct's  in  stock,  *46 
miles  and  earnings,  *7i9 
traffic,  local  and  through,  214 
train-load,    fuel     burned, 
growth  of,  *ioo    [*i36 
{See  Canada  Southern.) 
Michigan,  Lake,  water  of.  *378 
Middle  States :  area,  pop'n,  sid- 
ings,   earnings     per     mile 
and  head,  etc.,  *9i 
bonds  and  stocks  perm.,  *io7 
curve  and  grade  statist.,  259 
earnings  per  mile,  *io7 
distribution  of,  *io8 


Mid-Mit 

Middle  States — Contimied, 

frt.  earn.,  thro'  and  local,  *23i 
gen.  r'y  statist.,  88-90 
growth  r'y  system,  44 
main  results,  oper'n.  *24 
maint.  way  details,  *i28 
op'g  exp.  and  traffic  details, 
[*i7o-6 
pass,  and  fr't  haul  and  train- 
[load,etc.,  *97,  ^217 
p.c.  op'g  expenses.  91 

pass,  and  lr"t  traffic.  *i8i 
switching  mileage,  181 
rect's  per  inhab.,  pass  and  fr't, 
rolling-st'k  per  m.,  47    [*io4-5 
switching  mileage,  181 
ton-mile,  rec'ts  and  haul,  *ii5 
train-l'd   and    haul,    fr't    and 
[pass.,  *97,  *2i7 
wealth  per  cap.,  26 
Midland  r'y,  fastest  train,  *529 
locos.,  cost  and  miles  per  y'r, 
reprs.  details,  *i45      [*i59 
motive-power,  exp.,  det'ls, 
[*i33,  *i47 
traffic  and  fuel  consump.,  *i3i 
Milan  r'y,  profile,  698 
Mileage,  constructive,  218        [103 
loco.,    exaggerations    in, 
rale  for  fr't  cars,  164 
Milwaukee  grain  receipts,  728 
Mineral  traffic,  q.v.^  and  balance 
[grades,  614 
dead  wt.  of,  610 
changes  in, 609 
Mines,  U.  S.,  value,  *25 
Mining    regions,   burden    traffic 
[toward,  63,  618 
Minnesota:   align't   statist.,  *263; 
area,  popu.,  sidings,  p.c.   op'g 
exp  ,    earnings    per    mile    and 
head,  *9o;  wealth  per  cap.,  *26 
Minor  details  of  align't,  183 

and  drumming  business, 

[192 

cost  of,  as  aff'd  by  ruling 

[grades,  581 

effect  on  amt.  of  surveys, 

[858 

nature    and    importance, 

■     ■      t^^5  + 
possible     variations      in, 
[slight,  189 
relative  imp'ce  ex.,  395 
Mississippi:  area,  popu.,  sidings, 
p.c.    op'g    exp.,    earnings    per 
mile  and  head,  *9o;  wealth  per 
cap.,  *26  [841 

Mississippi  river,  fall,  and  tribs., 
'points,'  rates  to,  218 
steam-engines  on,  *46o 
water,  purity,  *378 
Mississippi   valley,  bad  location, 
\_q.v.^  in,  656  & 
Missouri:     align't    statist.,    *264; 
area,  ,popu.,  sidings,  p.c.  op'g 
exp.,    earnings   per    mile    and 
head,  *9o;  wealth  per  cap.,  26 
Missouri,  K.&  T.  loco.  perfce,*439 
Missouri  Pacific,  miles  and  earn- 
[ings,  *7i9 
Missouri  river,  fall,  841 

'points,'  rates  to,  218 
Mistakes,  narrow  margin  for,  28 
Mitchell,    A.,    invented    Consol. 
[eng.,  278,  423 


Mix-Neb 

Mixed  trains,  when  used,  93 
Mobile  &  O.,  align't  statist.,  *264 
"Moderate"  grades,  q.v.,  330 
Modern  r'y  corporation,  the,  28 
Modulus  of  elasticity,  def.,  345 
Mogul  loco.,  q.v.,  dimens.,   etc., 
rel.  cost  reprs.,  146      [408 
Momentum  and  curve  comp"n,62i 
def'n  as  used,  632 
grades  (virtual,  ^.w.),  def.  and 
[ex     344,  701 
Monarch  sleeping  cars,  ===491 
Monopoly  powers   of  r"ys,  effect 
[of.  32 
Montana:    area,   popu.,    sidings, 
p.  c.   op'g    exp..    earnings   per 
mile  and  head,  *9o;  wealth  per 
cap..  *26 
Mont  Cenis  r'y  fric.  grip,  690 
loco,  tests,  464 
profile.  698 
Monte  Carlo  disaster,  252        [753 
Mountainous  regions  and  gauge, 
curve  limit  in,  655 
valleys  q.v.  penetrate 
[into,  586 
Mountains,  slopes  of,  why  eye  ex- 
[aggerates,  845 
propin'q'ty  of,  oc.  illu'n,  846 
Mount  St.  Elias,  ht.,  927 
Mount  Washington  r'y,  first  rack 
[r.,  690 
Moon,  why  large  on  horizon,  845 
Moral  effect  of  curvature,  276 
of  distance,  239 
of  good  maint.  way,  124 
of  large  traffic,  55-7 
Mordecai,  G.,  table  by,  818      [503 
Morin,   A.,   expts.   on   fric,  q.v., 
Morris  &  Essex,  align't  statist., 
[*26o 
Morse,  J.   R.,  table  from  paper, 

[*47 

Mortgage  interest  builds  rds.,  36 

Motion,  accel'd  and  retard.,  laws, 

[331  & 

Motive-power,  cost,  U.S.  r'ds  and 

[sects.,  *i7o-6 

by  items,  *i47 

English,  *i48 

general  exp.  for  {see  Loco.), 


*378      [*27 


Mud  and  incrustation, 
Mulhall,  Diet.  Statis..  table  from", 
Murders  and  r'y  accidents,  257 
Narrow-gauge.  751 
and  cross-ties,  779 
curves  q.v.  on,  326 
curve  resist,  on,  305-6 
in  Colorado.  604 
in  mountainous  regions,  753 
locos.,  comp.  cost,*564-5 

Consolid.  engs.,  281 
origin  of.  424 

useful  effect  on  car  construc- 

[tion,  485 

Nashua  &  Lowell,  p.c.  swiiching- 

[miles,  *i8i 

Nashville,  Chat.  &  St.  L.,   miles 

and  earnings,  *7i9 

'Natural  gift'  for  location,  q.v.. 

Nature,  working  with,  589  [22 

Nebraska:  area,  popu.,    sidings, 

p.    c.  op'g   exp..  earnings    per 

mile  and  head,  *9o;  wealth  per 

cap.,  *26 


970 


INDEX. 


Nee— New 

Necessary  traffic,  q.v.^  very  little, 

[52 

Nesquehoning     valley,      svvitch- 

[back,  945 

Netherlands,  locos.,  no.  and  work 

[of.  *i6o 

Net  revenue,  q.v.,  sections,  U.  S., 

*92-4  & 

Nevada:  area,  popu.,  sidings,  p.  c. 

op'g  exp.,   earnings   per    mile 

and  head,  ^go  ;  wealth  per  cap., 

Newton,  first  law  of  motion.  341 
r'y  train,  best  ex..  342 
Kew  England   States,  alignment 
[statistics,  *259 
bonds  and  stock  per  mile,  ^107 
earnings  per  mile,  *i07 

distribution  of,  *io8 
frt.,  through  and  local,  ^231 
general  r'3-  statistics,  *88,  *9o 
haul,  train-load,  etc.,  *97 
growth  r'y  sj-stem,  *44 
main  results  op'n,  ^92 
maint.  way  exp.,  details,  *i28 
op'g  exp.   and   trafific  details, 
[*i70-6 
p.  c.  pass,  and  frt.  traffic.  *i8i 
p.  c.  switching  mileage,  *i8i 
rec'ts   per    inhab.    pass,    and 
[frt.,*  1 04-5 
rolling-stock  per  mile.  47 
ton-mile  rec'ts  and  haul,  *ii5 
train-load  and    haul,  frt.  and 
wealth  per  cap.,  26  [pass.,  ^217 
New  Hamp'shire,  wealth  per  cap., 

[*26 

New  Jersey:  align't  statist.,  ^259  ; 
area,  popu.,  sidings,  p.  c. 
op'g  exp.,  earnings  per  mile 
and  head,  *9o;  wealth  per  cap., 

*26 

'  rough  country  '  of,  S40 

New  Mexico:  area,  popu.,  sidings, 

p.   c.    op'g    exp.,  earnings  per 

mile   and  head,  *9o;  wealth  per 

cap.,  *26  [408 

New  So.  Wales,  Am.  loco,  in,  422, 

rolling-stock  per  mile,  *47 
New  York  City,  cost  frt.  cartage, 
[820 
elevated  q,v.  rys.,  curves  on, 

[645-7 
Gd.  Cent.  Sta.,  cost,  70    [^714 
internal  pass,  traffic,  growth, 
points  near,  rates  to,  219 
pop"n,  growth  of,  ^714 
-Smithville  traffic,  718 
terminal  facilities,  cost,  70,  818 

rates  at,  219 
train  speeds  from,  648-50 
New  York  State,  align't  statistics, 
*259;  area,  popu.,  sidings,  p.  c. 
op'g  exp.,  earnings  per  mile  and 
head. *9o 

curvature  in,  259 
interlocking  law,  813         [*i2o 
maint.   way,    exp.   by  items, 
switching  engines  in,  156 
wealth  per  cap.,  26 
New  York  &  Harlem,  alignment 
[statist.,  *259 
N.  Y.  &  New  Eng.,    alignment 
[statist..  *259 
New  York  Cent.  &  H.  R.,  align't 
[statist.,  *259 


New  York 

New  York  Cent  &  H.  ^.—Cond.  • 
an  ex.  of  long  line  prospering, 
[240 
asst.  engs.  on  Hudson  R.,  591 
construction  acct.,  items,  *7i 
cars,  box,  wt.  of,  det'ls,  *i63 
distance  and    through  traffic 
[of,  240 
negative  val.  on,  234 
fastest  trains,  *529 

loss  by  stops  to,  595 
fiucts.  in  stock,  ^46 
formation  unforeseen,  707  [724 

HISTORY   AND    SUCCESS    OF,  707, 

level  grades  on,  H.  R.,  327 
Iocs,    cost   and  miles  per  yr.. 

reprs.  by  items,  ^143  [*i59 
p.c.  labor  and  mat'l,*i52 
maint.    way    and    roll,   stock 
[exp.  comp.  34yrs.,  ^129 
miles  and  earnings,  =^719  [*i72 
op'g  e.xp.  and  trains  per  day. 
p.  c.  of,  why  high,  no, 
and  rates.  220  [725 

op"g  pushers,  H.  R.  div.,  792 
pass,  trains,  longest,  596 
rail  section,  307 
rail-wear  on.  pass,  and  frt.,  561 
rates  on.  fall  of,  *726 

and  Mex.  r'y,  923  [220 

effect  on  p.  c.  op'g  exp., 
sharpest  curve  on,  326 
sidings,  total,  ^825 

Buffalo  y'd,82i 
terminal  exp.,  etc.,  N.  Y.,*8i9 
train-Id.,  frt.  and  pass.,  *2i7 

growth  of,  *ioo 
train-mile  cost,  *ii6 
train-resist,  tests,  518 
New  York,  Chic.  &  St.  L., 

sidings,  Buffalo  yard,  *82i 

elsewhere.  825 
New  York,  L.  Erie  &  W.,  align't 
[statist.,  *259 
Carr's  Rock  disaster,  255 
connections,    relations    with, 
[221,  729 
curve  compens'n  on,  621 
distance,  value  of,  to,  221 
dynamom.  tests,  501 
financial  status,  41,  729 
fiucts.  in  stock,  *46 
freight  time-table  on.  102 
grades,  balance  of,  618 

60  ft.  and  6°  comb'n,  656 
inundations  on,  783 
location  of  heavy  grades,  585 
locos,  cost  and  miles  per  yr., 

tests  of  (Z.  C),  *437  [*i59 
loss  traffic  from  curves.  275 
maint.  way  and  rolling-stock 
[exp.  34  y'rs,  *i29 
miles  and  earnings.  ^719 
op'g  exp.  and  traffic  det'ls,*i72 

p.  c.  of,  comparison,  no 
pass,  pushers  on.  595 
rates,  fall  of,  *726 
rates  on  and  Mex.  r'y,  923 

and  N.  Y.,  P.  &  O.,  221 
sharp  curves  on,  278.  326 
sidings,  total,  etc..  *82S 
term'l  exp.,  etc.,  N.  Y.,  *8i9 
tires,  cost  m'nt'g,  316 
ton-mile  rec'ts,  etc.,  *ii5 
track,  Buffalo  y'd,  *82i 
train-load,  frt.  and  pass.,  *2i7 


New— Nor 

New  York,  L.  Erie  &  ^.—Cori'd. 
train-load,  growth  of,  *ioo 
train-mile,  cost,  *ii6 
wheel-wear,  statistics,  ^317 
why  has  poor  connect'ns.  730 
New  York,  N.  H.  &  H.,  fastest 
[train,  =^529 
fiucts.  in  stock,  *46 
locos,  cost  and  duty,  *i^9 
sharpest  curve,  *325  [*2i7 
train-load,  frt.  and   pass., 
New  York,   Ont.    &    W.,    term'l 
[exp.,  etc.,  N.  Y..  *8i9 
New  York,  Penna.   &  O.,  align't 
[statist.,  *26i 
bad  location  of,  223 
bridge  vibration  tests,  447 
handling  trains  on,  791 
locat'n  at  Springf'd,0.,  56 
Mahoning  I3'ch,  732 
op'g  exp.  and   trains   per 
[day,  *i72 
p.  c.  switching-mile's.  *i8i 
rail-wear  tests  on,  294 
strategic  disadvantage  of, 
[222 
train-load,  frt.  and  pass., 

[*2I7 

why  a  bad  property,  223 

New  York-Phila.,     etc.,     traffic, 

[and  dist.,  239,  709  -\- 

New  Zealand,   rolling-stock    per 

[mile.  *47 

Niagara  cantil.  bridge,  w't,  etc., 

[902 

Niagara  river,  discharge,  841 

fall,  841  [695-6 

Nigger-hill,      develop't     around. 
Non-competitive  traffic  and  good 
[facilities,  58 
and  restaurants,  74 
comparative  rates,  58 
effect  distance  on,  213 
true  classifications  of  .212 
Norfolk  &  Wn.,Consol.  loco,  tests, 
[etc.,  431 
North  British  r'y,  locos.,  cost  and 
[miles  per  yr.,  ^159 
North  Carolina:    align't  statists., 
^263  ;   area,  popu.,  sidings,  p.  c. 
op'g  exp.,  earnings  per  mile  and 
head,  ^go;  wealth  per  cap.,  *26 
North   Central  States:  alignment 
statist.,  ^262;  area,  popu.,  earn- 
ings   per  mile  and  head,  etc., 
♦91  [*259 

curve  and  grade  statist., 
fall  rivers  in,  841 
freight  earn.,    thro'    and 
[local,  *23i 
gen.  r'y  statist.,  88,  91 
haul  and  train-l'd,  etc.,  *97 
no.  pass,  trains,  96 
op'g  exp.  and  traffic  det'ls, 
[*i7o-6 
p.c.  pass,  and  frt.  traffic, 
[*i8i 
switching-mileage,  *i8i 
ton-mile  rec'ts  and  haul, 
[*ii5 
train-load  and    haul,    frt. 
[and  pass.,  *2i7 
North-Eastern  r'y,  locos,  cost  and 
[miles  per  y'r,  *i59 
Northern    Pacific    r'y,    fiucts.  in 
[stock, *46 


INDEX. 


971 


Nor— Ope 

Northern  Pacific  r'y— Continued. 
heavy  cars  on,  485 
loco,  dimens.,  etc.,  553, 407 

tests  on,  552 
long  grades.  *joo 
Northern  r'y  (France),  impercept. 
[slip  tests,  445 
Northwestern  grain  receipts,  728 
Northwestern  States:    area,  pop- 
ulation, earnings  per  mile  and 
head,  etc.,  *9i;  general  r'y  stat- 
ist., *88  [*i28 
maint.   way  exp.  details, 
pass,    and   frt.,  haul    and 
[train -load,  etc.,  ^97 
{See  Western.) 
Norway,  align' t  statist.,  *z6s 
locos,  no.  and  work  of,  *i6o 

performance  of,  *439 
popu.,   r'ys,  wealth,  etc.,  *27, 
rolling-stock,  ^43  [^43,  ^45 

Notch,  loco.,  q.z'.,  def  n,  797 

O  =  %«  "^D,  872 
Obelisk,  ex.  of  natural,  684 
Obliquity  of  traction  and    curve 
[resist.,  301  4- 
Obstructions,  accidents  from,*247 
Ocular  illusions,  842 
as  to  quantities,  849 
broken  back  curves,  871 
chief  danger  from,  852 
distance  on  maps.  665,  859 
examples  of,  680,  846  & 
grades  in  flat  country,  661 
sharp  ridges,  668 
steep  slopes,  ex.,  684 
Odometer,  use  of,  838 
Office  location,  evils  of,  880  — 
Offsets,  eye  exaggerates,  842  + 
for  transition    g.v.    curves, 
869  +,  684 
Ohio:  alignment   statist,  in,  *26i; 
area,  popu.,  sidings,  p.  c.  op'g 
exp.,    earnings    per    mile    and 
head, ^90 
interlocking  law,  813 
'  rough  country'  of,  840 
wealth  per  cap.,  26 
Ohio  &  M.,  aiign't  statist.,  *26i  + 

train-ld..  growth.  *ioi 
Ohio  river,  &  tribs.,  fall,  841 
Oil  and  waste,  cost,  *i47,  *i7o-9 
Oil  excitement  and  rys.,  30 
Old  Colony,  locos.,  cost  and  miles 
[per  year.  *i59 
p.  c.  switching-miles,  *i8i 
washouts  on,  7B2 
Old  lines  and  oper'g  rules,  791 
improvement  of,  785 

CONCLUSIONS  AS  TO,  8o8 

gaining    double    track, 

[806 
possibilities  as  to,  787 
pushers  on,  788 
sags,  taking  out,  806 
virtual  profile,  798 
usual  errors  in,  787 
origin  of,  789 
Open    road    (the    part    between 
stations),    improving    grades 
on,  *8o3 
Operating  ballast  trains.  773 
Operating  Expenses  (Ch.V,),  106 
and  bad  bridge  eng.,  3 
as  affected  by  curvature,  313 


Ope— Pap 

Operating  'Ex^cns&s— Continued. 
as  affected  by  distance,  *207-8 
no  trains,  568 
radius  of  curves,  638 
rise  and  fall,  375 
train-Id.,  560 
average  amt,,  108 -(- 

ESTIMATKn    AVERAGE,  180  — 

grand  divisions  in,  117 
great  change  in,  107 
p.  c.  Chicago  roads,  *i74-6 
Enghsh,  *79,  *i88         [*88 
sees.,  U.  S.,*io8-io,*i7o-6, 
trunk  lines,  *i72-6 
p.  c.  to  exp.,  no  criterion  of 
[management,  109 
trunk    lines,    q.v..,    cause 
[incr.,  725 
per  mile  road,  English,  *79 

U.  S.,  *i7o-9,  *99  & 
per  ton-mile,  *ii5  & 
per    train-mile,    English, 

^  [*79,*i78 

U.  b.,  *i70-9 
Operating    heavy     grades,    q.v., 
[d iff 'y,  596  + 
Operating  rules  and  ballast  trains, 
[773 
and  impr'told  lines,  791.  803 
Operation,  lines  in.  6"^^  Old  Lines, 
Optimism  proper  in  loc'n.  832 
Oregon-  area,  popu.,  sidings,  p.  c. 
op'g  exp.,  earnings  per  mile  and 
head,  *9o;  wealth  per  cap.,  *26 
Orizaba,  peak  of,  927 
Oroya  r'y,  develooments,  679-!- 
sharpest  curve,  *325 
profile,  698-9 
train,  g.v.,  911 
Oscillatory  train   q.v.  resist,  517, 
Overlaps,  848,  836  [911 

ex.  of,  852,  854 
Overloading  cars,  accidents  from, 
[*246 

Pacific  States  :  area,  pop'n,  earn- 
[ings  p.  m.  and  head,  etc.,  *9i 
bonds  and  stock  p.  m.,  *io7 
earnings  per  mile,  *ioj 

distribution  of,  *io8 
fuel,  cost  of,  136 
frt.  earnings,  thro'  and  local, 
general  r'y  statis.,  88-90  [*23i 
growth  r'y  system,  *44 
haul  and  train  Id.,  etc.,  pass, 
[and  frt..  *g7,  *2i7 
main  results,  op'n.  *94 
maint.  way  exp.,  details,  *i28 
op'g  exp.  and  traffic  details, 
[*i7o-6 
p.  c.  pass,  and  frt.  traffic.  *i8i 

switching  mileage,  *i8i 
rolling  slopes  in.  844 
rolling-stock  per  mile,  *47 
sidings,  ^gi 

train-l'd  and  haul,  freight  and 
[pass.,  *97,  *2i7 
ton-mile  rects.  and  haul,  *ii5 
wealth  per  cap.,  *26 
Painting,  car,  *i62-4,  *204 
locos.,  *i46,  "'149-55,  *4i3 
English,  144-6 
Palace-car,  inspection  from,  2 
Pan  Handle,  tunnel  on,  240 

{See  Pittsb.,  C.  &  St.  L.) 
Paper  location,  890 


Pap-Pen 

Paper  location — Continued. 

best  hard  to  secure,  880 
deficiencies  of,  877 
from  office  chair.  878-81 
take  off  by  bearings,  892 
use  of.  868 
Parabola,  cubic,  869 
law  of,  387 

not  suitable  for  r'y  curves,  276 
properties  of,  390 
Parallelogram  of  forces,  302 
Parallel  rules,  best,  887  [*i55,  *4i6 
Paris  &  Orl.,  cost  locos.,  details, 
per  ton,  details,  *4ii 
repairs,  details,  *i45-7 
p.  c.  labor  and  mat'ls, 

[*I52 

wt,  and  cost  in  detail, 

[*4i6 

Paris,  Lyons  &  M.  r'y  locos.,  repr., 

[details,  *i45 

tests,  464 

Parlor-cars,  dimens.,  etc.,  491 

why  so  freely  used,  567 
Party-wall  laws,  814 
Pass,  lowest  usually  best,  858 

ocular  illusions  as  to,  846  & 
Passaic,  sharp  curve  at,  326 
Passenger  and  freight  locos.,  q.v., 
[tire  reprs.,  *i49 
cars,  q.v.,  no.  perm.,  world, 

[*43 
per  train,  q.7K,  '''134  & 
-mile  rates,    q.v..  Am.    and 

[Eng.,  *i59 

revenue,  q.v.,  per  head,  U.  S., 

[sections,  *92-4,  103  & 

traffic,  q.v.,  pushers,  ex,,  607, 

and  speed,  645  [616 

irregular  eff.  of  grades, 577 

low       speed        reduces 

[grades,  578  -|- 

luxury  in,  why  increas'g, 

[567  & 

no.  of  pass.,  world,  43 

on  branches,  734 

p.  c.  of,  sects.,  U.  S.,  *i8i 

third   class,   likely  to  in- 

[crease,  580 

train-load,  U.  S.,  sects.,  *97 

trains  and  grades,  576,  616  — 

gain  on  grades  by  speed, 

[592 

length  for  diff.  speeds,  592 

longest,  592,  596 
manufacture  pass,  trips,  50 
no.  load  and  haul,  U.  S., 
[sects.,  *97,  *i7o-9 
probable  no.  of,  est'g,  95 
trip,  av.  U.  S.  sections,  *97 
Passes,  travel  on,  249 
Payments  per  head  to  r'ys,  U,  S,, 
[*g2-4,  *io3  & 
Pedestals,  concrete  for,  903 

design  and  est'g,  901 
Peekskill,  ocular  illusion  at,  848 
Pegram,  G.  H.,  bridge  formulae, 
trestle  formula,  901      [766,  903 
Pennsylvania,  aiign't  statist.,  *259 
area,   pop'n,  sid'gs,   p.   c.  op'g 
exp.,  earn'gs  p.m.  &  h"d,  *9o 
curves  on  coal  roads,  278 
gravity  r'ys  in,  692 
wealth  per  capita,  *26 
Penna.  &  N.  Y.  Canal  rd.,  aiign't 
[statist.,  *26o 


972 


INDEX. 


Pennsylvania 

Penna.  Coal  Co.,  gravity  r'y,  692 

Penna.  Co.,  freight  car,  dimens., 

[etc.,  once  and  now,  *486 

Pennsylvania  Rd.,  align't  statist., 

bal.  of  traffic  on,  *6o9        [*26o 

capital  account,  items,  *7i 

stock  of  control,  lines,  *7i 
cars,  frt.,  dimens.,  etc.,  once 
[and  now,  *486 
pass,  dimens.,  etc.,  ^491 
load,  average,  *6io 

changes  in,  485 
movement  of  I'd,  *6o9 
condensed  profile,  698 
curvature,  taking  out,  on,  277 
distances,  N.Y.  to  Pittsb. 5*609 
dynamometer  tests,  501 
expt.  as  to  curve  slipping,  285 
fastest  trains,  =^529 
flucts.  in  stock,  ^46 
frt.   move't.   thro,   and  local, 
[E.  &  W.,  35  yrs.,  *232 
fuel  burned,  freight,  *i35 

pass.,  134 
f^ood  condition,  value  of,  276 
grades,  balance  of,  618 

location  for  pushers,  585 
Tyr.  &  CI.  branch,  *7oo 
hist,  and  cause  of  success,  725 
inundations  on,  783 
local  traffic,  large  prop'n,  235 
locos.,  breakages  in  starting, 
[*4i9 
Consol'n,  experience,  *i48 
cost,  new,  details, *i5i-2-4 

per  ton,  details,  *4ir 
fast  pass.,  weight,  etc.,  421 
loads  hauled,   Tyr.  br'h, 
mileage  of,  140  [*44o 

all  ages,  *4i8 
running,  first  in  first 
[out,  *i4o,  *4i9 
repairs,  cost  of,  140  & 
per  year  per  eng.,  *is9 
by  divs.,  *i88 
general     repairs    on, 
[frequency,  420 
p.  c.  labor  and  mate- 
[rials,  *i52 
statists,  loco,  op'n, 1851-84, 
[*i4o 
wt.  and  cost,  det'ls,  *4i2-6 
Consol.  eng.,  ^409 
various  parts,  *4oo 
tank,  wt.,  etc.,  421 
wt.  on  drivers  per  sq.  ft. 
[grate,  *452 
maint.  way  exp.  on,   123,  128, 
[130 
and  roll. -stock,  34  yrs., 

1*129-30 
by  items,  *i2o 
policy  as  to,  123  & 
miles  and  earnings,  *7i9 
motive-power     exp.,    details, 
[*i47 
Statistics,  1851-84,  ^140 
op'g  exp.,  and  trains  per  day, 
[*i7a 
p.  c.  of,  why  low,  no,  725 
why  increasing,  725 
planes  on  old  line,  944 

pres't  line  plan'd  for,  944 
pass,  pushers  on,  595 
rail- wear  tests,   119,  295,  320, 
[380,  562 


Pen-Pit 

Pennsylvania  Rd, — Contint^ed. 
rates  and  p.  c.  opg.  exp. ,  220  & 
fall  in,  726 

ton-mile  rects.,  etc.,  *ii5 
sharpest  curves  on,  *325-B 
term'l  exp.  etc.,  N.  Y.,  *8i9 
tires,  cost  m'nt'g,  316 
track,  best  in  world,  277 -f- 
traffic,    disprop'n   E.    &   W., 
[etc.,  *6o9 
train-Id.,  firt.  and  pass.,  *2i7 
growth  of,  100  -|- 
pass.,   no.  cars  and  fuel, 
[*i34,  *595-6 
train-mile  cost,  *ii6 
wages  on,  loc.  shops,  *i5i 
wheel-record  and  brakes,  377 
why  many  branches,  729 
Peoria  grain  rec'ts,  728 
Per-diem  rate  for  frt.  cars,  165 
Perkiomen  r'y,  align't  statist.,*26o 
Perote,  Cofre  de,  ht.,  etc,  927 
Perspective,  mental,  i 
Peruvian  ry's,  profiles  of,  698-9  & 
Petersburg,  sharp  curve  at,  326 
Petroleum,  H.  U.  in,  *45o 
Philadelphia-N.  Y.  trafi.,  loss  by 
[dist.,  709 
terminals,  loc'n,  etc.,  of,  68 
train-speed  to,  648-50 
Phila.      &     Atl.      City,      align't 
[statist.,  *26o 
Phila.  «&  Erie,  align't  statist.,  *26o 
expts.  as  to  loc.  resist.,  *279 
loco,  performance,  *44o 
rep'rs  by  divs.,  *i88 
trains  and  fuel  consump.,  *i38 
Phila.  &  Rdg.  coal  car,   heavy, 
[*49o 
coal  consump.  pass.,  134 
fastest  train,  ^529 
fuel  tests,  var.  speeds,  528 
kindling  fires  on,  *2oo 
locos.,  cost  new,  ^152 

fast  pass.,  wt.,  etc.,  *42i 
fr't,  heavy,  *42i 
rep'r  details,  *i4S 

and  renewals,  *i45 
tests  of  fast,  473 
maint.    way  and    roll. -stock 
[exp.,  34  yrs.,  *i29 
by  items,  *i2o 
pushing  serv.,  cost,  601 
Piedmont,  yard  at.,  618 
Piers,  area,  etc.,  N.Y.  term's,  *8i9 

bridge,  estimating,  898 
Pig-iron,  past  prices  of,  763 
Pile-driver  car,  Ga.C,  det'ls,  *490 
Piles,  driving  by  vel.  of  car,  ex., 
[345 
Pile  structures,  770  [473 

Piston,  loco.,  q.v.,  loss  energy  by, 
Pittsburg  &  Conn.,  align't  statist., 
[*26o 
Pittsburg,  C.   &   St.    L.,  align't 
[statist.,  *26i 
train-Id.  growth,  *ioo 
tunnel  on,  saving  dist.,  240 
Pittsburg    &    Ft.  W.,  flucts.    in 
[stock,  *46 
opg.  exp.  and  trains  per  day, 

[*I72 

sharpest  curve,  *325 
ton-mile  rates,  etc.,  *iis 

fall  in,  on,  *726 
train-Id.,  growth,  *ioo 


Pla— Pru 

Planimeter,  use  of,  897 
Plateau  of  Mexico,  descr.,  616 
Platte  Canon,  697 
Plotting  cross-sections,  868,  897 
mapping,   q.v.,    proper 
[methods,  886 
Plates.     {See  Engravings.) 
Political  economy  of  cheap  con- 
[struction,  18,  27 
of  distance,  197 
Pony  truck,    q.v.,  mechanics  of, 
Poor,  H.  v.,  table  by,  *726       [431 
Popocatepetl,  mtn.,  927         [*92-4 
Population,  sections  U.  S.,  73-81, 
growth  of  la.,  *77 
Mass.,  *78 

U.  S.  *88-9o  [227 

does  not  help  poor  lines, 

large    and   small,   traffic    per 

[head, *7i3 

law  of  addition  to  traf- 

[fic,  708 

per  mile  road,  la.,  *77 

Mass.,  *78 

sections  U.  S.,  *88-9o 
world,  *43 
law  as  to,  720 
per  sq.  m.  &  m.  r'y,  U.  S.,  *88 
pay'ts  per  head  to  r'ys,  *92, 
[*io4  & 
r'y  capital  per  head  U.  S.,  *88 
Portable  engines,  cost  &  eff 'y,  *53i 
Port  Jervis,  grades  at,  619  [*27,  ^45 
Portugal,  pop'n,  r'ys,  wealth,  etc.. 
Postal-cars,  dimens.,  etc.,  *49i 
Power,  static,  and  dyn.,  292  & 
Practice    does    not    make    loc'g 
[eng'r,  22  & 
Prairie  ridges,  loc'g  over,  661  -j- 
Prairie  States,  bad  loc'n  in,  6,  21  & 
Preliminary  line,  q.v.,  861-2 

and  contour  maps.  876 
Prepossessions,  abandon'g,  835  & 
Present  worth  of  future  $1,  *82 

of  future  Si  per  year,  *83 
Pressure,  loco.,  q.v.,  steam,  q.v., 
[effec.  cyl.  in  pract.,  *46i  4- 
Prismoidal  form'a,  use  and  abuse, 
[895 
Probabilities,  theory  of,  864,  896 
Profile,  balancing  quantities  of, 
[895 
errors  in  laying  grades  on,  329 
estimates  from,  895 
paper  and  actual,  868,  880 
putting  grades  on,  893 
small  scale,  861-2 
need  for,  665 
Profit  from  r'ys,  conditions  for, 
14-16 
Profit  traffic,  importance  of,  62 
Progress  of  r'y  cons.,  q.v.,  world, 
U.S.,*44  [*42-3 

Projectiles  and  air  resist.,  517 
Projecting    asst.      eng.     grades, 
low,  (ltd        [high,  669 
grade-lines,  675 
location,  q.v.,  8qo 
Propellers,  no.  N.  Y.  term'ls,  *8i9 
Protractor,  best,  886 
Providence  &Worc'er,  p.c.  switch- 
[ing-miles,  *i8i 
Provision  cars,  dimens.,  etc.,  ♦487 
Prussia,  cost  r'ys.  etc.,  *45 
loco.  repr.  details,  *i45 
p.  c.  op  g  exp.,  *iio 


INDEX, 


973 


Pul-Rai 

Pulley,  transmiss.  of  power  ar'd, 
[302 
Pusher  (asst.  q.v.  engine)  grades, 
[projecting,  666 
Puebla,  error  in  line  to,  928 
Puente  Nacional,  929 
Pulque  district,  Mexico.  928 
Pusterhal  r'y  profile,  698 
Pyramid,  of  traffic,  712,  731 

Quantities,  balance  of,  not  exact, 
estimating  {q.v.').  895  [895 

Quarries,  U.  S.,  value,  *25 
Queensland,  roU'g-st'k  perm.,  *47 
Quincy,  Mass.,   double-truck  car 
[at,  421 

Rack  rys,  history,  etc.,  6go,  943 

reason  for,  404 
Radiation  and  fr"t  speed,  370 
external,  313,  456,  471,  508 
boiler    and  cylin.,  comp, 
in  yards,  315    [imp'ce,  471 
winter  and  summer,  508 
internal,  315,  471 
Radius  of  curv.,  q.v.,  cost,  etc., 
designation,  258-66      [635 
gyration  of  car-wheels,  334 
rails,  739 
Radius-bar,  loco.,  def'n,  etc.,  426 
Rail  joints,  accidents  from,  *246 
best  form  of,  123 
wear  of  rail  from,  123 
yielding  at,  561 
Rails,  and  cross-ties,  775  -}- 
foreign  locos.,  425 
speed,  268, 274 
track  labor,  758 
average  life,  119  [256 

broken,  accidents  from,  246, 
condition  in  winter  and  sum- 
[mer,  315 
cost  of,  best  IS  cheapest,  748 
durability,  *745 
stiffness,  *74i 
strength,  *742 
elastic  reaction  of,  516 
form  of,  307-8,  738 

and  flange  wear,  317,  639 
hard  and  soft,  121 
inspection  of,  121  [*i2o 

iron,  cost  of,  various  roads, 
formerly,  119,  763 
vs.  steel,  119,  268,  561 
light,  and  I't  ry's,  737 
past  prices  of,  763 
renewals  of,  cost,  U.  S.  sec- 
[tions,  etc.,  *i28,  *i7o-9 
spread,  acc'd'ts  from,  *246 
steel,  effect  on  op'g  exp.,  *i3o 
revolutionized  mt.  of  way. 
why  better,  119  [118 

wear  of,  as  affected  by  age  of 
[rails,  296 
curvature.  297-319 

radius  of,  639 
grades,  380 
quality,  320 
rise  and  fall,  379 
sand, 380 
speed,  561 
front  and  back  wheels,  287 
loco,  and  car,  122,  561-2 
nature  of  wear,  308 
of  pass  and  frt.  trains,  562 
on  curves,  q.v.^  293,  319 


Rai— Rec 

Rails — Continued. 

wear,  as  aff.  by  age  and  form, 

CONCLUSIONS,  304  [296 

diff.   European  &  Am. 

•  [exp.,  283 

wt.  of,  and  grading,  749  [744 
comp.  durability,  est'g, 
buying,  strength,  etc.,  739 
choice  of  wt.,  738  [*747 
interest  charge  on,  extra, 
vs.  cross  ties,  776  [13  & 
Railway  projects,  inception  of, 
Railways,  acres  in  crops  per  mile, 

all  legitimate  enterpr.,  14  [*9o 

capital,  p.  c.  to  total,  *27 
of  world,  *27 

construction,  est.  of  future, *4i 
past  progress  of,  *44  -j- 

COSt,  *27,  *43,  *45 

of  world,  progress,  *42 
value,  *25,  *27,  *45 

cost  per  head,  world,  *27 
total,  world,  *45 
per  mile  English,  *7o 

U.S.,  etc,  *25-7,'*43-5 

earnings,  q.v.,  per  mile,  *77, 

«         -1  •  •    t*^^*^ 

financial  errors  in  projects.  707 

foreclosures,  *4o  [186 

good  lines  for,  popular  error, 

indirect  wealth  from,  *27 

light,  737 

miles  of,  sections  U.  S.,  *92-4 

world,  *25,  27,  *43-45 

per  head,  world,  ^43 

per  sq.  mile,  ^43 

must  go  to  traffic,  53 

profit  on,  conditions  for,  16 

Rainfall,  amt.  of,  783 

fiuct'ns  in,  783 

and  floods,  784  [759 

Raising  and  surfacing  track,  q.v., 

Rankine,Prof.,  on  steam  exp'n,469 

Rates,  fixing  of,  195  +  & 

as  affected  by  diffs.  dist.,  709 

cartage,  820 

distance,  194  -f,  723  -}- 

strategic      advantages, 

competitive,  212      [218,  723  -f- 

sum  of  two,  218 

division  of,  217 

fractional  per  cents,  227 

E.  «&  W.-bound  C,  C,  C.  &  I., 

L.  S.  &  M.  S.,  226        [225 

how  fixed  on  through  traffic, 

Mex.r'y  and  N.Y.  C.,Q32  [217 

on  regular  and  occas'l  traffic, 

\<].v.,  diff.,  235 

per  pass.-mile.  Am.  &  Eng., 

[*i59 

per    ton-mile,    q.v..    Am.    & 

[Eng.  *i59 

recent  fall  of.  726  ± 

through,  division  of,  219 

LAW   AS    TO    DISTANCE   RE- 
[SULTING  FROM,  219 

and  local,   q.v.,  constant 
[ratio  of,  224-6 
why  based  on  distance,  196 
Receipts    per  head    by  sections, 
[*io3-5,  *ii5  & 
Reconnaissance,  art  of,  831,  21 
conditions  of  success,  22 
maps,  nse  of,  836-7,  934 
rule  for  choosing  grades,  675 
descend 'g  into  valleys,683 


Rec-Ris 

Reconnaissance — Continued. 
to  be  of  line,  not  area,  835 
worst  errors  orig'te  in,  832 
Refrigerator  cars,  dimens.,  etc., 
[*487 
Renewals,  p.c.  of,  etc.,  frt.  cars, 
\_q.v.,  *i65  & 
loco.,  q.v.,  *i45-7  &  [*255i 

Rensselaer  &  Sarat.,  align't  stat.. 
Rental,  pd.  by  fixed  charges,  106 
Repose,    grade    q.v.    of,     def'n, 

T,         .  ■     •  ,  1^341  & 

Rest,  friction  q.v.  of,  920 
Restaurant  and  compet.  traffic,  73 
Retaining  walls,  Colorado,  697 

and  improving  old  lines, 
[802 
indic'g  on  profile  934 
Return  grades,  q.v.,  for  I't  trains, 
[612 -H 
Return  tracks,  indep't,  693-4 
Reventon  tunnel,  etc.,  668 
Revenue  and  minor  details,  rel. 
[imp'ce,  397 
effect  of  location  on,  48      [=^64 
moving    stations   on, 
more  dist.  on,  *229 
from  through  traffic,  q.v.,6\- 
[vision  of,  218 
increase  of,  effect  on  profits 
[111& 
more    important    than 
[low  exp..  Ill 
pass,  and  frt.,  sections,  U.  S., 
[etc.,  *92-94 
per  head  by  States,  *9o,  *io4 
sections,  U.  S.,  etc.,  *89 
law  as  to,  716-7 
per  mile  road,  sees  U.  S.,  *89 

States,  U.  S.,  *9o 
small  p.c.  decisive  to  proper- 
[ty,  62,  72 
theory  of  growth  of,  708 
Revenue  train -mile,  av.  cost,  *i79 
difficulty  of  est'g,  103 
Revere  disaster,  254  [*4i4 

Reverse-lever,  loco.,    q.  v.,    wt., 
Reynolds,  Lieut.,  ascent  to  Ori- 
[zaba,  927 
Rhigi  r'y  and  Mt.  Wash.,  690 
Rhode  Island:  area,   popu.,  sid- 
ings,  p   c.  opg.  exp.,  earnings 
per  mile  and  head,  *9o;  wealth 
per  cap.,  *26 
Rhode  Island  Loco.  Works,  incr. 
[wt.  eng.  15  yrs.,  *466 
Richardson  bal.  slide-valve,  532 
Richelieu  River  disaster,  254 
Richmond    &    Danville,    align't 
[statist.,  *264 
Richmond,  F.  «&  P.,  align'tstatist., 

[*264 

Ricour,  M.,  est.   value   reducing 
[grades,  *576 
train-resist,  tests,  527 
Ridge  and  valley  lines,  836  & 

low,  loc'g  over,  ex.,  661  -f 
Ridge  line,  eye  fixes  on,  842  -\- 
Right  of  way,  folly  of  economiz- 
[ing,  16,  53 
cost,  N.Y.C.  and  Penna.  rds.. 
Rip-rap,  natural,  850  [*7i 

Rise  and  Fall  (Chap.  IX.),  327 
a  minor  detail,  185 
and  ruling  grades,  distinct., 
[327 


974 


INDEX. 


Ris-Rol 

Rise  and  Fall — Continued. 
as  modified  by  speed,  347 
amount  of,  est'g,  366,  374 
limits  of  choice   narrow, 

measured  by  no.  breaks, 
[3S4 
r'ys   and    States,   U.    S., 
[*259  + 
classes  of,  defs.,  330,  374 
cost  of,  375  [injur's,  385 

concentrated  r.  and  f.  less 
CONCLUSIONS,  382-3 
as  aff'd  by  rate  grades,  581 
iron  and  steel  rails.  380 
loco,  reprs.,  small  effect 
[on,  *i88 
*  foot '  of,  defined,  374 
limits  of  classes,  366,  356 
class  A,  365  + 
class B,  368 

class  C,  369  [grade, 375-7 
incl's  whole  Tgth 
under     various- 
conditions,  *372 
most  imp't  to  frt.,  354  -f- 
relative  importance,  185.  395+ 
sags  and  summits,   different 
[effect,  363  & 
speed  in,  *367 
'train-foot '  of,  582 
what  constitutes,  366    [of,  682 
Rivers,   descending  into  valleys 
est'g  fall  of,  840 
grade-lines  over,  893 
Road  and  equipt.,  cost,  U.  S..*io7 
Road-bed  and   track,  cost,  U.  S. 
[sections,  *i28,  ^71 
cost  as  aff'd  by  rad.  of  curves, 
rise  and  fall,  381    [639 
proper  w^idth  of,  772 
rel.  cost,  833 
Robinson,  S.  W.,  expts.  on  bridge 
[vibration,  447 
Rochester  &Pitts'g,  sidings,  total, 
Buffalo  yd.,  821  [*825 

Rochester  &  St.  L.,  align't  statist.. 
Rock,  estimating,  897  [*259 

indic'g  on  profile,  934 
testing  for,  893 
Rock  cuts,  needless,  867,  868 
shallow,  881 
on  contour  maps,  877 
Rocky  Mountains  &  rough  coun- 
align't  in,  2,  265  [try,  840 

Rocky  points,  decept.  effect,  836, 
[842  -1-,  848 
Rod,  extended  by  vel.  of  car,  ex., 
[345 
Rogers  Loco.  W'ks,    catalogue, 
[422 
Roller  jour,  bearings,  value,  912, 
[923 
Rolling  country,  illusions  as  to, 
locating  in,  661        [849-50 
Rolling-friction,    q.v..,  def'n,  493, 
[515  + 
as    affected    by   coupled 
[wheels,  534-5 
computing  from  I'ds 

[hauled,  444 
constit.  elements,  505 
effect  like  a  grade,  343 

on  pusher  grades,  597  — 
higher  in  winter,  314 
{See  Train  Resistance.) 


Rol-Sax 

Rolling-load,  diags.  of,  769 

effect  on  wt.  bridges,  767 
Rolling-stock,  485  {See  Car,  Loco.) 
per  mile  U.  S.,  *47 

foreign,  *43  * 

rel.  cost,  833,  71 
trunk  line,  maint.  exp.  34 
[years,  *i29 
Rome,  W,  &  Ogd.  align't  statist., 

[*259 
Roof,  car,  cost,  etc.,  *i63,  *204 
Rough  country  and  grade  con- 
[tours,  877 
a  relative  term,  840 
errors  in,  843  &        [849-54 
for  foot-travel,    illusions, 
two  prelims,  in,  865 
Roumania,  locos.,  no.  and  work 
[of,  *i6o 
Round-house  reprs.  p.  c,  *i45-6, 
[*i49 
Route,  choice  of,  favored  by  sharp 
[curves,  656 

ONE    GENERAL     RULE    FOR, 
[660  & 

easier  with  sharp  curves, 
[698 
to  be  studied  as  a  whole,  665 
Ruling  grades,  q.v.,  and  minor 
[det'ls,  185 
'  Running  '  at  grades,  804  & 
{See  Virtual  Profile.) 
Running-gear,  cars,  rel,  cost  of, 
[*i6i-4 
p.  c.  due  var's  caus.,  *203 
loco.,  q.v.^  cost  new,  details, 
[* I 50-1-2-4-5 
repairs,  *i44-9 
p.  c.  due  various  causes, 
[203 
Russia,  locos.,  no.  &  work  of,  *i6o 
pop'n,  r'ys,  wealth,  etc.,  *27, 
*435  *45 
rolling-stock,  traffic,  etc.,  *43 

Safety,  as  affec.  by  centrif.  force, 
[etc.,  300 

{See  Curvature,  Grades.) 
Safety-guard  for  bridges,  900 
Sags  and  hydr.  grade-line,  625 

and  summits,  diff.,  367 

vert,  curves  on,  363 

extreme  example  of,  625 

increase  speed.  366-7,  623 

on  grades  and  levels,  366 

safe,  limits  of,  356 

taking  out  on  old  lines,  806 

TO  OBVIATE  ALL  DANGER  FROM. 

why  admissible,  623  [363 

example,  623 

{See  Rise  and  Fall.) 
St.  Gothard  r'y,  location  of,  671 

and  prairie  lines,  est'g  betw'n, 

St.  Louis  grain  rec'ts,  728        [858 

terminals  at,  70 

train  speed  to,  6qo  ['''264 

St.  Louis  &  S.  E.  align't  statist., 

St.  Louis  &S.F.,  loco,  perform'ce, 

[*438 

St.  Paul,  Minn.  &  Man.,  financial 

[hist'yi  *37-38 

Sand,  effect  on  adhesion,  q.v.,  437 

use  of,  and  rail-wear,  380 
Saving  per  year,  aggregating  $1 
[at  given  dates,  *82 
Saxony,  cost  r'ys,  etc.,  *45 


Sca-Slo 

Scales  of  maps  should  be  large,  884 

small  scales,  use  of,  665  & 
Scenery,  ex.  of  imp't'ce,  678  & 
Schools  and  churches,  U.  S., value. 
Science  and  Art,  831  [*25 

Scientific  skill,  marvellous  feat  of,. 
[932 
Scott,  Gen.,  route  of,  in  Mex.,  92S 
Scrap  credits,  loc,  amt.  of,  *i46-9,. 
cars,  details,  *204        [*4i2 
value  of  rails,  allow'g  for,  122 
Searles,  W.  H.,  train-r.  formula, 
[517 
Section  hands,  limit  to  reduc'n,  199 
Sections,  length  of,  126 

as  affected  by  curvat're,  321 
Selling  price  of  commodities,  how 
I  Selling  transp'n,  48  -|-     [fixed,  196 
I  and  whims  of  buyer,  52 

i  Semmering  ry.  profile,  698 
Sharpsville  ry.,  loco,  perf'ce,  *438 
Shinn,  W.  P.,  paper  by,  *7i9 
;  Shipping,  U.  S.,  value,  *25 
"  Shoo-fly"  line,  860 
Shop  and  gen'l  charges,  loco.  q.v. 
[maint.,  *i45,  *i5+ 
English,  133 
Short-haul  traffic,  q.v.,  and  conve- 
[nient  depots,  57 
Short  line,  moral  effect  of,  239 
trunk  line,  value  of,  728 
law  as  to,  219 
{See  Distance.) 
Side-hills,  illusions  as  to,  850  & 
Side-hill  lines,  culverts  on,  851 

prelim,  ests.  of,  897 
Sidings,  amt.  at  Boston,  *823 
Buffalo,  *82i 
New  York,  *8i9 
and  trunk  lines,  law  as  to,  825 
classes  of,  *82i 
for  pusher  grades,  599 
p.  c.  of,  sections  U.  S,,  *88 
Side-track,  taking,  and  imp't  old 
[lines,  791 
Signal  cabins,  interlocking,  q.v.., 
[sizes,  809 
Silver,  in  world,  etc.,  929 
Silver  Plume,  spiral  at,  680  -f 
Sixth  Ave.  Elev.  ry.  curves,  646 
Skill,  marvellous  feat  of,  932   [359 
Slack  in  couplings,  q.v..,  amt.  of, 
Burlington  tests  of,  490 
effect  of,  359 

import'ce  of  eliminat'g,  487  & 
Sleeping-cars,  dimens.,  etc.,  *49i 
English,  *49i 
why  so  freely  used,  567 
sections  in,  *49i 
Slide-valve,  balanced,  532 
description  of,  457 
friction  of,  532 

life  of,  420  C^.i'.,  284-6 

Slipping  of  car-wheels  on  curves, 

amt.  due  to  flange  press., 

error  as  to,  287  [294 

vel.  of,  on  curves,  *289 

of  drivers,  446,  797 

and  skill  of  eng'r,  406 
coeffs.  of  fric,  435 
if  begun,  continues,  285 
must  not  be  too  easy,  406 
no  fault  in  fgt.  eng.,  406 
Slope-level,  use  of,  882  [842  & 

Slopes,  rate  of,  eye  exaggerates, 
smooth,  meaning  of,  843 


J 


INDEX. 


975 


Smi-Spa 

Smith.  C.  A  ,  ioc.  expis.  by,  445 

tables  from,  468 
Smiihville-N.  Y.  traffic,  718,  729 

-Jonesburg-,  etc..  729 
Snow  and  ice,  accid'is  irom,  *247 
cost  due  to,  126 
storms,  as  cause  of  accid't,  255 
Soft-steel   rails,  q.v.^  error  as  to, 
[121 
Soil,  layer  of,  and  rough  country, 
[840 
South  America,  Am.  Iocs,  in,  422 

rollinsj  slopes  in,  844 

South  Australia,  rolling-stock  per 

[mile,  *47 

South  Carolina,  alignm't  statist., 

♦263;   area,  popu.,  sidings,  p.c. 

of  op'g  exp.,  earnings  per  mile 

and  head,  *9o;  wealth  per  cap., 

*26 

Southern  Pacific,  accident  on,  949 
align't  statist.,  *26s 
long  grade  on,  ^700 
miles  and  earnings,  *7i9 
Southern    States,  align't  statist., 
[*263 
area,  popu.,  sidings,  p.c.  opg. 
exp.,  earnings  per  mile  and 
head,  etc.,  *9i 
bonds  and  stock  per  mile,*io7 
curvature,  etc.,  in,  263 
earnings  per  mile,  etc.,  *io7-8 
fall  rivers  in,  841 
fr't.  earn.,  thro.  &  local,  *23i 
gen'l  ry.  statistics,  *89-9o 
grow^th  ry.  system,  *44 
haul    and    train-load,    etc., 

,      ^    [*97.  217 
main  results  op  n,  *93 
maint.  viray  exp.,  details,  *i28 
mineral  devel't,  effect,  616 
opg.  exp.   and  traffic  details, 
[*89-93,  *  1 70-6 
p.    c,   pass,   and   fr't!    traffic, 
[*i8i 
switching-mileage,  *i8i 
rects.  per  inht.,  pass,  and  fr't, 
[* 104-5 
rolling-stock  per  mile,  ^47 
ton-mile  rects.   and  haul,  *ii5 
train-Id.   and   haul,    fr't    and 
[pass.,  *97,  *2i7 
triangular  course  of  traffic, 615 
wealth  per  cap.,  *26 
South-western  States:  area,  popu,, 
sidings,  earnings  per  mile  and 
head,  etc.,*9i 
freight  earnings,  through  and 
[local,  *23i 
general  r'y  statist.,  88 
haul   and    train-Id.,  etc.,  *97, 
main  results  op'n,  ^93        [^217 
maint.  way  exp.,   details.  *i28 
op'g  exp.   and   traffic    det'ls. 
[*i70-6 
p.  c.  pass,  and  fr't  traffic,  *i8i 

switching-mileage,  *i8i 

rects.  per  inhabt.,   pass,  and 

[fr't,  *io4-5 

ton-mile  rects.  and  haul,  *ii5 

train-Id.  and  haul,     fr't    and 

[pass.  *97,  *2i7 

Spain,  p.  c.  op'g  expenses,  *iio 

popu.,  r'ys,  wealth,  etc.,  *27, 

,  ^       [*43,  *45 

rolling-stock,  traffic,  etc.,  *43 


Spa-Sta 

Spalding,  E.   C,   on  car    rep'rs, 
[161 
Specie  U.  S.,  value,  *25 
Speculative  interest,  nature  of,  29 
Speed  and  adhesion,  435 

and  centr'f  force,  *27o 
and  curvature,  268 

difif.  much  or  little, 648 
very  sharp,  326 
and  curve  resist.,  305 
and  fr't  Ioc.  cyls.,  474 
and  heavy  grades,  369 
and  pass,  traffic,  645 
corresp'g  to  time  over  293', 

elevated  r  y  sp.,  648 

effect  on  locos.,  *476  •\-      [579 

TO  REDUCE  PASS.  GRADES, 

to  reduce  grades,  limit, 

[592 
extreme  examp.  of,  625 
fluctuations    of,   in    practice, 

testing  locos,  by,  792 
freight,    and    improving    old 
[lines,  804-7 
English,  *i32 
maximum,  368 
safe  assump'sas  to,  371 
tendency  to  high,  369,  488, 
[804 
high,  economy  of,  488 

has  caused  large  boilers. 
[408 
highest,  Engl.  &  Am.,*529 
tendency  to   use   higher, 
[488,  804 
increased  by  sags,  q.v.,  366-7 
limits  of  objectionable,  *27i-3 
lowest,  at  summits,  353 
loss  of,  from  stop,  274 
on  max.  grades  slow,  622 
pass,  and  fr't  (also  above),  268 
vel.-head  due  to,  *335 
why  higher  in  Engl'd,  *53o 
Speed-gauge,  injurious  effects  of 
[370 
Sphere,    rolling    of,  and    flange- 
[wear,  308 
Spirals,  classes  of,  679 

def.,  and  advantages,  681 
examples  of,  682-4-6 
St.  Gothard  r'y,  671 
series  of.  684 
typical,  679 
Split  stringers,  etc.,  900 
Sprague,  F.  J.,  tests  on   elev.  r'y, 

[559 
Springfield,  O.,  loc'n  N.  Y.,  P.  & 
[O.  at,  56 
Springs,  car,  compression  of,  272 
by  vel.  of  car,  ex..  345 
loco.  wt.  and  cost,  ^413  -f- 
Stable  equilibrium  on  truck,  282 
Stage-coach  measures    necessary 
[trav.,  52 
Starting,  effect  slack  on,  490 

effect  to  cut  down  trains,  442 
fric,  q.z'.,  journal,  512 
grades  for,  needed, 512 
greatest  trac'n  req'd  for,  474 
locos.,  how  done,  797 

loco,  breakages  from,  *4i9 
on  elevated  r'y,  *559 
on  switchback,  947 
pass,  trains,  406 


Sta-Sti 

Starting — Contimied. 

resist,  of,  910. 
{See  Stations,  Stop,  Virtual   Pro- 
file.) 
State  r'ys,  projecting,  20 
Station  (100  ft.),  length  on  slopes, 

r-      .  1^*341 

Stationary  engines,  comp.  econo- 

[my  for  planes,  688 

cost  and  eff'y.  *53i 

loco,  an  equiv't  for,  492 

Stationery  and  printing,  cost,  U. 

[S.  r'ds  and  sects.,  *i7o-9 

Station,  etc., expenses,  abstract  of, 

as  affected  by  dist.,  206      [118 

no.  trains,  568 
English,  828 
Stations,  area,  etc.,  N.  Y.,  ^819 
asst.  engs.  at,  599 
correcting  grades  at,  790.S01-2 
cost,  N.  Y.  C.  &  H.  R.,  *7i 
curve  compens'n  at,  633 
diffic'ties  in  moving,  786 
elevated  r'y,  *5S9 
effect  on  grade  resist.,  347 
est'd    effect    removing    from 
grades  at,  512  [towns,  *64 

and  loco,  design,  475 
and  pass,  tr'ns,  491 
growth  of  towns  to,  71 
large,  switch-eng.  as  pushers 
neatness  of,  649  [at,  792 

on  grades,  moving,  803 
on  summits,  and  virt'l   prof., 
[805,  807 

RULE  FOR   LOCATING,  63,  791  -j- 

virtual  grades  at,  704  791  -|- 

Station  supplies,   cost,   ids.    and 

[sects.,  U.  S..  *x7o-9 

Stay-bolts,   wt.,   etc.,   in   boilers, 

[*4i2 

Steam,    expansive    energy    only 

[used,  457 

lbs.  per  H.  P.,  av.  Ioc,  451 

theoretical,  *46o  [*454 

wt.  and   heat,  various   press, 
wt.  in  loco.  q.v.  boiler,  *454 
Steam-boats,  full  stroke  eng.  for, 
[*46o 
Steam-chest  and  boiler  press,  473 
Steam-engines, cost  and  eff 'cy,*53i 
lead  and  lap.  defin.,470 
perfect,  eff'cy  of,  *46o 
Miss'pi  river.  *46o  [457 

uses   expansive   energy  only, 
working  full  stroke,  *458 
{See  Stationary',  Loco.) 
Steam-pipe,  loco.,  size.  *409 

wt.  and  cost,  *4i2  + 
Steam-ports,  losses  by,  470  -}- 
Steam-press,  boiler  and  effective, 
English,  *i32  ['''479 

H.  U.  due  to  various,  *45o 
little  effect  on  economy,  473 
theoret.  gain  by  higher,  *468 
Steam-shovel,  working  with,  cost, 

^      ,      .,  [etc.,  773 

Steel-rail,  q.v.^  per  cent  of.   sec- 

[tions  U.  S.,  *S8 

Stephenson,  G.,  and   link-motion, 

[458 

Steubenville,  O.,  tunnel  at,  240 

Stevens,    A.    J.,   inv.    Mastodon 

Ioc,  423 

Stiffness,  cost  of  and  wt.   rails, 

[739.  *74i 


9;6 


INDEX, 


Sto-Sur 

Stock  and  bonds  p.  mile,  sections, 

[U.  S.,  *I07 
fluctuations  in  price,  *46 
nature  of,  29 

per  mile  r'y  and  head,  U.  S., 
watering,  nature  of,  32      [*88 

Stock  cars,  dimens.,  etc.,  *486-7 

Stopping  and  starting,  $)'.7/.,acci- 

[dents  from,  *246 

at  grade-crossings,  q.v.^  810  & 

loss  by,  810-12  [*203 

effect  on  car  and  eng.  reps., 

fuel  burned  for,  200 

Stops,  cost  of,  810 

heavy  trains,  600 
effect  on  grade  resist.,  346 

virtual  profile,  q.v.,  350-2 
no.  of,  Mich.  C.  R.  R.,  136  & 
on  max.  grades,  effect,  623 
on  pusher  grades,  596 
power  lost  by,  200,  *335 
time  lost  by,  201,  274,  595 

Stop-watch  and  loco,  tests,  794 
cost,  etc.,  796 

Storage  sidings,  q.v.,  *82i 

Stores,  loco.,  q.v.,  cost,  ^147  & 

Storms  and  structures,  781 
great  ones,  local,  782 

Strategic  advantages,  effect    on 
[rates,  218,  241  & 

Streams,  est'g  fall  of,  840 
grade  lines  over,  893 
mental  map  of,  836  & 

Street  accidents  and  r'y,  257 

Street  r'ys,  cable,  690 
traffic  of,  N.  Y.,  *7i4 

per  inhab't,  ^714  [*73g-42 

Strength,   cost  of    and  wt.  rails, 

Stroudley,  Wm.,  loc.  tests  by,  451, 

Success,  conditions  of,  i,  8,  840  — 
Summits,  false,  836 

gravity  r'y  seeks,  692 
high,  ascending  to,  925,  943 
may  cost  little,  590 
often  wise  to  go  to,  590 
lowest  safe  speed  at,  353 
normal  types.  689 
leading,  of  world,  *698-9 

of  Colorado,  696  -\- 

not    always    control  grades, 

[675- 

not  always  governing  point, 

[670 

passing,  by  cable  tract'n,  889 

RULE    FOR    PASSING,   66o 

Store  power  in  train,  692 
station,  q.v.,  on,  and  virtual 
[profile,  q.v.,  805,  807 
Sun,  why  larger  on  horizon,  845 
Sundavs    disappearing   from  r'y 
[serv.,  97 
train-work  on,  169 
Superelevation,  298  + 

common  error  as  to,  301 
effect  of,  271 

on  curve  resist.,  298 
on  position  wheels,  300 
on  safety,  300 
lateral  force  from,  298 
on  tang.,  possible  effect,  911 
Surfacing.     {See  Track.)         [4-5 
Surplus,  fluctuations  in,  etc.,  33- 
Surveys,   care  q.v.   in,  and  amt. 
[curv.,  q.v,,  656  & 
compass  lines,  863 


Sur-Tax 

Surveys — Continued. 
field-work  of,  860 
location  line,  866 
no.  successive  lines,  834,  860 
organization  of  party,  867 
paradox  as  to  time  on,  856 
saving  needless  work,  871-2 
should  start  with  no  curve- 
[limit,  654 
when  to  make,  856 

how  to  determine,  857 
Susquehanna,  grades  at,  619 

river,  fall,  841 
Sweden,  popu.,  r'ys,  wealth,  etc., 
[*27,  *43,  *45 
rolling-stock  and  traffic,  *43 
Swing-motion  truck,  q.v.,  def'n, 
objection  to,  428  [426 

Switchbacks,  684,  943 

aut.  switches  for,  946 
best  for  great  inclines,  943 
germ  of  true  plan,  945 
good  loc'n  for,  ex.,  682 
grades  for,  947 
Peruvian,  685-6,  699 
vs.  spirals,  682-4-6 


Swi— Ten 

Switches,  deraiUng,  811 

misplaced,  derail'ts  from,  245 
Switching,  accidents  in,  *246 
slipping  drivers  in,  446,   797 
terminal  charges  for,  156  & 
Switching  engines,  descrip.   and 
as  pushers,  600  [use,  424 

est'd  av.  prop'n  of,  156,  182 
mileage  allowance  for,  156 
Switchmen,  at  stations,  791 
Switching  mileage,  how  exagg'd, 
[103 
prop'n  of  English,  135 
sections,  U.  S. 
Switzerland  locos.,  no.  and  work 
high  loc.  press.,  *5i9  [of,  *i6o 
pop'n,  r'ys,  wealth,  etc.,  *27, 
[*45 
Syracuse,  B.  «&  N.  Y.,  alignment 
[statist.,  *255 
Syracuse,  Gen.,    etc.,    alignment 
[statist.,  *259 
'  Syst^me  Richenbach,'  690 
Systems  of  r'ys,  all  lines,  parts  of^ 

[51 
great,  of  U.  S.,  *7i9 


Tables— Index  by  Number: 


No. 

" 

' 

2 

3 

4 

5 

6 

7 

8 

9 

0 

- 

25 

26 

27 

38 

40 

41 

42 

43 

44 

10 

45 

46 

47 

64 

71-7* 

78 

79 

80 

82 

82 

20 
30 

as 
98 

88 
98 

90 
99 

92 
100 

92 
104 

93 
107 

■S 

94 
no 

94 
115 

116 

40 

120 

128 

129 

130 

131 

131 

133 

— 

134 

135 

50 

130 

140 

143 

144 

145 

146 

147 

147 

148 

149 

60 

149 

149 

150 

151 

152 

152 

154 

155 

159 

160 

iS 

161 
179 

162 
180 

163 
181 

164 
188 

165 
200 

170 

203 

172 
203 

174 
204 

176 
207 

178 
208 

90 

215 

216 

217 

224 

225 

226 

229 

231 

232 

246 

100 

248 

259 

261 

264 

265 

267 

270 

273 

279 

286 

no 
120 
130 

288 
358 
410 

289 
367 
411 

290 
373 
412 

290 
378 
414 

317 

383 
416 

322 

388 
418 

325 
400 
419 

333 
407 
421 

335 
408 
438 

341 
409 

443 

140 

150 

450 
468 

452 
479 

453 
482 

454 

483 

454 
486 

456 
487 

462 
490 

465 
491 

466 
495^ 

468 

49S 

160 

500 

502 

505 

507 

519 

522 

524 

529 

531-^ 

54^ 

170 
180 

544 
579 

587 

557 

593 

559 
595 

ti 

567 
612 

571 
630 

572 
644 

574 
652 

576 
688 

190 

099 

713 

714 

719 

726 

741 

742 

745 

747 

757 

200 

771 

^  795 

819 

821 

825 

*i 

4^,  p. 

77  *i6E 

J,  p.  5 

39 

[Tables  are  indexed  by  subject  by  prefixing  a  *  to  the  page  refer- 
ence.]   


Tabor  grade,  ^699 
Talcott,  A.  H.,  &  Mex.  Ry.,  929 
Tangent,  breaking  sixty-mile,  663 
desirable  length,  324  [330 

long,  bad  practice  as  to,  324, 
sharp  curves,  q.v.,  lengthen. 
Tank  engines,  424  [641 

as  assist,  eng.,  592 
comparative    power     on 
[grades,  *557-8 
why  advantageous,  554 
{See  Tender.) 
Taunton  Loco.  W'ks,  increase  wt. 
[engs.,  35  y'rs,  *466 
Taxes,  cost  of,  sections  and  r'ds, 
[U.  S.,  *i70-9 
as  affected  by  dist.,  206 


Tehachapi  accident,  949 
Tenders  (builders'   rule  for  total 
[weight,  20  lbs.  per  gall,  water.) 
cost  of,  new,  ^564-5 

details,  *i5o-i-2-4-s 
and  weights,  *4i2-4-6 
cost  repr's  of,  det's,  *i43-9 
English,  144-6 
French,  147 

p.  c.  cost  of  eng.  r.,  144 
cost  renewals,  146  & 
due  various  causes,  *203 
for  switching-engs.,  424 
life  of,  *4i9 

tires,  cost  of,  *i49  [* 407-16 
WTs.  AND  cap'y,  all  cng., 
wheel-base,  all  eng.,  *407-io 


INDEX. 


977 


Tel-Tir 

Telegraph.cost  of,  r'ds  and  sect'ns 
[U.  S.,  *i70-9 
of  U.  S.,  value,  *25 
offices,     and     improv'g    old 
[lines,  803 
stations  and  asst.  eng.,  601 
Temperature  and  H.  U.,distinc'n, 
and  radiation,  314  1*454 

changes  of,  in  cylinders,  g.v., 
[376 
effect  on  coeff.  fric,  *so5 
fuel  consump.,  136-7 
train  resistance,  506 
summer  and  winter,  314 
Temporary  lines,  advantages  of, 
[16,  86,  766 
B.  &  O.,  *7oo 
ex.  of  proper  use,  277,  654 
for  light  r'ys,  750 
sags,  q.v.,  in,  624-5 
examp.,  625-6 
Tennessee:    align't  statist.,  *264; 
area,   popu.,  sidings,  p.  c.  op'g 
exp.,     earnings    per    mile    and 
head,  *9o;  wealth  per  cap.,  *26 
Tennessee  pass,  Col.,  *-joo 
Tepetate,  def'n,  683 
Tepic,  location  at,  67.';  -\- 
Terminals  (Chap.  XXVI.),  818 
allowances     on     rates,    g.v., 
and  curvature,  655  [156  & 

expenses,  N.  Y.,  etc.,  *8i9 

European,  827 

for  light  r'ys,  749 

good,  imp'ce  of,  768,  68 

locat'n   and  cost  of,  various 

[cities,  68-70,  818-27 

must  be  near  largest  cities,  727 

rel.  no.  of,  on  trunk  lines,  729 

Terre  Haute  &  Ind.  loco,  perf'ce, 

[*438 

Terre  H.  &  S.  E.  align't  stat.,  *26i 

Texas:  area,  pop'n,  sidings,  p.  c. 

opg.  exp.,  earnings  per  mile  and 

head,  *9o;  wealth  per  cap.,  *26 

Texas  Cent'l,  align't  statist. ,*265 

Theis  r'y,  Austria,  est.  for  rates 

[on,  198 

Thompson,  J.  E.,  on  incl.  planes, 

[944 

Throttle,  loco.,  g.v. ,  effect  of  clos- 

[ing,  473  & 

'Through  '  traff.,  g.v.,  true  clas- 

effect  dist.  on,  215     [sif'n,  211 

rates,  g.v.,    constant  ratio  to 

[local,  224-6 

Thurston,  R.  H.,  fric.  tests  by,  504, 

[918  + 

Time  in  seconds  and  speed  trains, 

[*795 

Time,  effect  on  car  and  eng.  reps., 

[*203 

loss  of  by  reduc'g  sp'd,  595 
est'g  import'ce  of,  649 
on  curves,  *647  -|- 
round  trip  per  day  limit, 
[649 
of  descent  on  grades,  theory 
[of,  624 
Time-tables,  fr't,  how  arranged, 
Tires,  accidents  from,  *a47      [102 
life  of,  420 
maint.  of,  *i49  + 
mileage  of,  *i49  -\- 
price,  Am.  and  Eng.,  *4i6 
w'tand  cost,  *4i3  + 
62 


Tod— Tra 

Todhunter's  math'l  series,  331 
Toledo  grain  rec'ts,  728 
Ton  (in  this  vol.  2000  lbs.  or  '  net,' 
[unless  otherwise  stated.) 
Ton-mile,  cost  increasing  grades, 
[gv    per,  +574 
rates,  g.v..  Am.  &  Eng.,  *i59 
E.   &  W.,    through    and 
[local,  *2i6  & 
through  and  local,  12  y'rs, 
[C,  C,  C.  &  I.,  *224-5 
15  years,  L.  S.  &  M.  S., 

[*226 

rec'ts,  exp.,  etc.,  large  table, 
[*ii5& 

varying  cost  of,  est  g,  198 
Topographer,  frequent  errors  of, 

needs  practice,  885  [884 

outfit  of,  882  [867 

Topographical    party,   organiz'n, 
Topography  (mapping),  873 

colored,  873 

CONCLUSION  AS  TO,  88o 

contours,  g.v.,  873 

dangers  of,  ex.,  881 

double  use  of,  876 

field-sheets  for,  886 

inking  in,  888 

large  scales  best,  884 

plotting,  883 

sh'd  be  taken  in  field,  882 

taking  topog.,  881 

over  areas,  684  & 
use  and  abuse  of,  873 
"  (physical    geography),   adapt'g 
[low  grades  to,  665 
and  bal.  of  grades,  614 
and  curve  compens'n,  628 
and  transition  curves,  869 
curvature  bunched,  622 
curve  limit  may  be  easy,  655 
effect  insuffic't  study  of,  583 
effect  on  use  of  curves,  635 
fitting  curve  comp'n  to,  *63o 

GENERAL  LAW  AS  TO,  586 

law  of,  as  to  changes  of  level, 
in  easy  country,  660   [*588 
mountain  foot-hills,  937 
no  country  difficult,  832,  840 
often  favors  low  grades,  670 
Peruvian,  679  -(- 
rough,  light  Unes  in,  832  & 
Tourist    travel,    ex.    of    imp'ce, 
[678  & 
Tower,  B.,  fric.  tests  by,  504  -\-, 
[918 
Towns,  effect  not  running  to,  on 
[rec'ts,  49 
effect    of    removing    station 
[from,  64 
growth  of,  to  stations,  g.v.,  71 
location  of  stations  at,  *64 
moving  to  r'ys,  66 
often  hard  to  approach,  859 
passing  lines  between  two,  67 
passing,  to  save  dist.,  g.v.,  58 
should  be  entered,  16 

RULE  AS  TO,  63 

Track,  accidents  from,  *246 

cost  of,  U.  S.  sections,  *28,i 
labor,  cost  of,  123  [*i7o-6 

relation  to  traffic,  123 
as  aff'd  by  curvature,  321 
min.  limit  to,  199 
not  exactly  as  dist.,  199 
reduction  difficult,  126 


Traffic 

Track  \3.hor— Continued. 

requirements    for    emer- 

[gencies,  126 

vs.  heavy  rails,  758 

maint'ce,  cost  of,  U.  S.   rds. 

[and  sects.,* 1 20,* 1 70-6 

as  aff'd  by  no.  of   trains, 

..        .  ^569 

radius  of  curves,  639 
rise  and  fall,  381 
wt.  locos.,  561 
relatively  to  other  items, 
[833 
Trackmen  flatten  P.  C.'s,  275 
Track-walking,  cost,  126 
Traction,  stores  force  in  train,  342 
Traction-increaser,  404 
Tractive  force  and  energy,  con- 
[fusion  as  to,  473 
and  H.  P.,  403 
Trade,  universal  law  of,  55      [733 
Traffic,  additional,  relative  cost, 
anthracite  west,  609 
disproportion  of,  608 

TABLE    OF    GRADES   FOR, 
[612 

daily  fluctuations,  611 
effect  on  curve  limits,  652 
effect     to     change    cost 
[transp'n,  198 
into  cities,  heavy,  617 
P.   R.    R.,  35  ye'ars,  etc., 

[*232,  *2l6  & 

ratio  of  E,   &  W.  trunk 

[lines,  609 

variable    on    same    road, 

[609 -f 

estimating,  95-99 

exchanging,  and    narrow-g., 

,    .     ,     ,[753 

export,  grows  relatively  less, 

[615 

GEOMETRIC  EFFECT  OF  INCREAS- 
[ING,  708 

getting  all  there  is,  53 
growth  of,  depends  on  facili- 
[ties,  715 
does  not  help  poor  lines, 
[227 
effect  on  car  rep'rs,  166 
loc.  exp.,  158 
maint.  way,  123-7 
effect  to  reduce  exp.,  114, 

ti53 
law  of  growth,  75 
statistics  of  C.,B.  &Q..iS7 
C,  C,  C.  &  I.,  216 

C.  &  N.  W.,3S 

English,  *79,  *i3i-2 

Iowa,  *77 

L.  S.  &  M.  S.,  *98 

Mass.,  78 

New  York  City,  *7i4 

P.   R.    R.,   35    years, 

[*I40,  *232 

sections  U.  S.,  *io7-8 

THEORY  OF   GAIN  BY,  708 
TO     BE     CONSIDERED      ONLY 
FOR    3  TO    5  YEARS,  80,  85 

when  to  choose  line  for, 
[583 
handling  by  trains,  169 
importance  of  increasing,  107 
increases  with  facilities,  76 
interpolating  way,  effect,  *7i3 
not  a  monopoly,  52 


978 


INDEX. 


Traf— Train 

Traffic — Continued. 

pass.  p.  c.  local,  through,  etc., 

[*2I5 

gain  from  many  trains,  96 
p.   c.  pass,  and   fr't.   sections 
[U.  S.,  *i8i 
prop'n  affec'd  by  grades,  576 
regular  and  occas'l  rates,  con- 
[trast,  235 
securing,  the  most  imp't  end, 
[193  & 
slight  dififs.,  great  effect  of, 
[62 
through  and  local,  confusion 
[as  to,  211 
triangular  course  of,  608,  615 
true  classification,  212 
trunk  line,  q  v.,  rules  for,  731 
unequal,  balance  grades,  ^.z/., 
[for,  608 
table  of,  *6i2 
volume  of,  and  cable  trac'n, 
[687 
and  long  inclines,  950 
and  wt.  Iocs.,  567 
estimating  probable,  75 
of  world,  *i6o 
statistics  of,  L.  S.  &  M. 

„   „    „  [S.,  ^.z'.,  *99 

P.  R.  R.,5r.r-.,  etc.,  *232 
Traffic-points,  and  branches,  734 
dist.  betw'n,  eff't  on  earn'gs, 

GAIN  BY  MORE,  708  [709 

great  and  small,  diff.  in  gr'th, 
[728 
Train  accidents,  q.v.,  causes,  *zifi 
Train  expenses,  amt.,  133,  *i7o-9 

definition,  117 
Train-load,  Am.  and  foreign,  575 
and  fuel  consump.,  134 
as  aff'd  by  car-couplings,  566 
disprop.  of  traffic,  100 
grades,  q.v.,  536  & 
av'ge  frt.  and  pass,  sections, 
[U.  S.,  *2i7,  *97 
and  p.  c.  local,  234 
effect  on  expenses,  560 
fuel  consump.,  *i36 
English  coal  trains,  *i32 

FOR    ALL    GRADES     AND     LOGS., 

[*543  + 
(condensed  table"),  593 
frt.,  sections,  U.  S.,  *ii5  & 
growth  of,  *97,  *98,  *9q.  *ioo, 
[*ioi,  *i35  & 
pass.,  U.  S.  and  States.  ^97-8 
does  not  regulate  number 
[trains,  96 
less  with  thin  traffic.  99 
p.  c.  change  due  to  change 
[grade,  554-7 
p.  c.  to  Wt.  eng.,  all  grades, 
[669 
relative,  on  high  grades,  *669 
why  cut  down  in  winter,  508 
Train-mile,    coal     burned,     135, 
[140  & 
cost,   maint.  way  per,  U.  S. 
[sections,  *i28 
cost  of,  av'ge  U.  S.,  *i79  — 
British,  +79,  *i78 
trunk  lines.  34  yrs.,  *i29 
how  made  low,  *i8i 
on  lines  of  diff.  grades, 
tendency  in,  116  [583 

unimportance  of,  1S7 


Trains 

TX2:v!\-va\\&— Continued. 

earn'gs  and  exp.,  U.  S.  r'ds 
[and  sees.,  *i7o-9,  *98 
maint.  way,  constant  per,  127 
ratio  of,  to  eng.  mile,  *i45 
Train  resistance,  492 
air,  g.v..,  amt.,  911  & 
as  affected  by  gauge,  753 
temperature,  508  — 
virtual  profile,  f.z/.,  346 
axle,  effect  size  of,  513 
freight,  496 

CONCLUSIONS,  502 
main  elements,  ^10 
recent  decrease  m,  504,  515 
summer  and  winter,  503-6 
grade  of  repose,  q.v.^  def.,  341 
head  q.v.  resistance,  522  — 
locomotive,  q.v.,  530  [918 

lubrication,  import,  of,  509  -|-, 
oscillation  and  concuss'n,  911 
passenger,  518  -(- 
starting,   q.v.,  *5i2,  *5i9 
subdivisions  of,  493 

TABLE  OF  CONCLUSIONS,  ^524 

tests  as  to,  *465,  *498  -|-,  *909  & 
velocity  resist.,  493.  517-8 
wheel,  effect  size  of,  513 
Train  rules,  and  imp't  old  lines, 

[791 
Trains,  breaking  in  two,  358,  488 
centre  of  gravity  in  sags,  q.v., 

descending    grades,    vel.    of, 
[*372 
fastest,  Engl,  and  Am.,  *529 
handling  heavy,  easier  here- 
[after,  488 
frt.  speeds  to  be  higher, 
[488,  804 
safe  assumptions  as  to, 
on  old  lines,  788  [370 

length  of,  and  vertical  curves, 
iq.v.,  364 
and  crossing  stops,  812 
and  curve  comp'n,  634 
effect  on  curve  resist.,  301 
shorter  in  winter,  315 
making  up,  effect  on  loc.  and 
[car  rep'rs,  *203 
yard -room  for,  *82i  & 
motion  of,  and   Newton's  ist 
[law,  342 
and  virtual  profile,   q.v., 
t346 
effect  of  speed,  q.v.,   on, 

t33i 

no.  of,  cost  increasing,  same 

[traffic,  568 

effect  on  rev.,  568      [*S74 

for  same  traffic,  all  grades, 

value    of   avoiding    in- 

[crease,  574 

overturning  by  centrif.  f.,  270 

pass.,  effect  grades  on.  577 

growing  wt.  of,  effect,  491 

reason  for,  567 
wt.  of  fast  tr'ns,  530 
per  day,  always  means  each 
[way,  97 
best  basis  for  est  g,  95 
elev.  r'ys,  646 
Philad'a,  69    [*i28,  *i7o-6 
U.  S.  and  States,  etc.,  *97, 
rights  of,  774       [increase,  369 
speed,  q.v.,  of,  frt.,  tends  to 


Tra— Tru 

'Yx2i:\Ti%— Continued. 

wt.  of,  as  affected  by  grades, 

long  table  of,  *544  [*688 

p.  c.  wt.  eng.,  all  grades. 

Train  supplies,  cost  of,  rds.  and 

[sects.  U.  S.,  *i7o-9 

Train  wages,  q.v.,  168 

as  affected  by  distance,  206 

length  trains,  568 
cost  of,  Chicago  rds.,  *i74-6 
sections  U.  S.,  *i7o-6 
trunk  lines,  "172-6 
mode  of  fixing,  205 
Transfer  side  tracks,  q.v.,*%i\  [883; 
Transit,  graduating  compass  of, 

vs.  compass  lines,  863 
Transition  curves,  869 

examples  of  use,  870  +,  684 
projecting,  892 
reasons  for,  275 
Transit  party,  organiz'n,  867 
Transit  work,  860  -\- 

doing,  by  bearings,  888 
Transportation     expenses,    cost, 
[Chicago  rds.,  *i74-6 
sections  U.  S.,  *i7o-6 
trunk  lines,  *i72-6 
manufacture  of,  48 
Trautwine's  pocket-book,  331 
on  kindling  fires,  *2oo 
Trestles,  iron,  design  of,  900 
ht.,  small  effect  of,  902 
prelim'ry  est's  of,  900. 
wt.  of,  901 
wood,  cost  of,  and  grading, 
[755 
cluster  bent,  900 
design  of,  899,  770 
floor  for,  900 
on  light  r  ys,  754 
plan  for,  770 
proper  use  of,  754,  768 
prelim,  est's  of,  899 
rerailing  guard  for,  900 
Triangular  course  of  traffic,  615-!- 
trips  of  cars,  608      [341,  538  -{- 
Triangle,    right-angled,    solving, 
Tributary  valleys,  q.v.,  good  use 
Trieste  r'y,  profile,  698      [for,  682 
Trucks,  accidents  from,  *246 
Am.  origin  of,  421 
Bissell,  426-30 

frt.    car,  cost  and   deprec'n^ 
[items,  *i63,  *204. 
dimens.  and  wt.,  *i63,  *486 
loco.,  need  for,  425 

pony,  426 
mechanics  of  rolling,  281,  425 
pass,  car,  dimens.,  etc.,  491 
position  taken  on  curve,  282 
swing  motion,  objection    to, 
[428 
Trunk    lines    and  branch  lines, 
bal.  grades  on,  618  [707 

comparative  earnings,  737 
competitive   and    non-comp., 
[718,  723 

CONDITIONS  OF  SUCCESS,  73I 

curves  on,  lost  time  by,  648  & 
fall  of  rates  on,  20  y'rs,  *726  ±. 
good  condition  pays.  276 
lengths  of.  to  Chicago,  240 
maint.  cars  exp.,  34  y'rs,  *ia9 
maint.  locos,  exp.,  34  y'rs,  *t29 
maint.  way  exp.,  34  y'rs,  *i29 


INDEX. 


979 


Tru— Uni 

Trunk  lines — Continued.  P719 
miles  and  earnings,  14  U.  S., 
op'g  exp.    and  traflBc  det'ls, 

[*I73 

p.  c.  opg.    exp.,  law  as    to, 
[109-10 
effect  rates  on,  220 
sidings,  law  as  to,  825 
termini,  q.v.,  reached  by,  729 

N.  Y.,etc.,  818 
ton-mile  rec'ts,  etc.,  *ii5 
traffic,  daily  fluct'ns  in,  612 

changes  in,  609 
train-l'd  and  growth,  *ioo 
train-mile,  cost,  ♦116 
use  too  light  rails,  760       [*204 
Trusses,  fr't-car,  cost  and  depr'n, 
Tubes,  loco.,  q.v.,  life  of,  *42o 
Tunnels,  spiral,  671  -j-,  679, 684,  700 
unnecessary,  242 
wrong  use  of,  ex.,  667 
Turkey,  pop'n,  r'ys,  wealth,  etc., 
[*27,  *45 
Tutor,  natural  end  of,  and  culv'ts, 
[781 
Tyrone  &  Clearfield  grades,  *7oo 

Uetliberg  r'y,  impercep.  slip  tests, 
[44s 
Ulster  &  Del.  align't  statist.,  *259 
'  Uncle  Dick  '  consol'n  loco.,  w't, 
[etc.,  421 
Undergrowth,  deceptive  effect  of, 
[836 
from  clearing  up  do.,  850 
Undulating  grades,  q.v.,  &  imp'g 
[old  roads,  799 
curves  equiv't  to,  633  — 
eliminated  by  speed,  347 
error  as  to,  329 
putting  into  harness,  692 
Unearned  increment.  32 
Unfamiliar,  eye  deceived  by,  843+ 
Union  Pacific,  align't  statist., *26s 
cost  loco,  rep'rs,  142 
flucts.  in  stock,  *ifi 
miles  and  earn'gs,  *7i9 
handling  trains  on,  255 
spiral  on,  680  + 
United   Kingdom :    progress    r'y 
constr.,*44;  pop'n,  r'ys,  wealth, 
etc..  *27,  *43,  *45;  rolling-stock, 
traffic,  etc.,  *43 

{See  Great  Britain.) 
United  R.  R.  N.  J.,  trains  «&  fuel 
[consump.,  *i38 
United  States,  cost  r'ys,  etc.,  *45 
future  r'y  construe' n,  *4i 
growth  of  r'ys,  *42-4  [fr't,  *97 
haul  and  train-l'd,  etc.,  pass.  & 
locos.,  cost  and  miles  per  y'r, 
miles  per  year,  *97     [*i59 
no.  and  work  of,  *i6o 
main     results      op'n       r'ys, 
[1871-85,  *94 
no.  trains  per  day,  etc.,  *97 
opg.  exp.  and   traffic  details, 
£* I 70-76 
r'y  statists,  by  sects.,  *88  & 
rates,  5^.7/.,  of  r'y  divi'ds,  *4i 
ton-miles  per  car,  *97 
train-load,  etc.,  *97 
wealth  of,  *25-78 
1  by  States.  *26     [tries,  *27 

comp.  with    other    coun- 
pop'n,  cost  r'ys,  etc.,  *27 


Unl-Vir 

Unloading  plough,  use  of,  773[59o 

Unnecessary    require'ts,  loss  by, 

Utah  :  area,  pop'n,  sidings,  p.  c. 

opg.  exp.,  earnings  per  mile  and 

head,  *qo;  wealth  per  cap.,  *26 

Utah  &  No,,  align't  statist.,  *265 

Utica  &  B'lk  R.,  align't  statist., 

[*259 

Utica,  Ith.  &  El.,  align't  statist., 

[*259 

Vacuum  brakes,  g.v.,  max.  efi'y, 
[495 

Valley  lines  and  inundations,  783 
and  overlaps,  848 
descend  into  ag'st  slope,  682 
ex.  of  line  in,  693 
gain  by  following,  586 
high-water  in.  850 
Nature  makes  fills,  850 
penetrate  far  into  m'ts,  586 
recon'tring,  errors  in,  844 -f- 
rough  foot  travel,  848,  850,  855 
tributary,  use  of,  682 
undergrowth,  etc.,  836 

Valuation  of  States,  total  and  per 
[cap,,  *26 

Valve-gear,  loco.,  q.v.,  458 

Velocity  acquired  on  grades,  *372 
and  work,  interconvert.,  ex., 

•    .  r  o  t342 

composition  of,  ex.,  287 
due  to  any  h't,  *333 
effect  of,  on  grades,  q.v.^  703 
effect  on  train  q.v.  resist.,  346 
law  of,  and  trains,  331 

Velocity  train  q.v.  resistance,  517 
tests  of,  910 

Velocity-head,  def'n,  333-5 
and  brakes,  q.v.,  494 
computations  by,  357  ±, 

[519 
due  to  all  speeds,  *333-5 
Vera  Cruz,  Jalapa  q.v,  line  from 

Vermont:  area,  popu.,  sidings,  p. 
c.  opg.  exp.,  earnings  per  mile 
and'head,  *9o ;  wealth  per  cap., 

*26 

Vernier,  graduating,  888 
Vertical   curves,  deviation  from 
[intersec.  grades,  *388 

effect  close  coupler,  365 

need  for,  363 

rationale,  360 

rules  for  projecting,  385 

safe  rule  for,  365 

TO  LAY  OUT,  387 

'Vertical  plane'  couplers,  489 
Viaduct,  Baranca  Blanca,  678 
estimating,  900 
indicating  on  profile,  934 
two-story,  683-4 
weights  of,  901 
Victoria,  rolling-stock  per  mile, 
[*47 
Vignoles,  C.  B.,  on  minor  details, 
[187 
Virginia:  alignment  statist.,  *263; 
area,  popu.,  sidings,  p.  c.  opg. 
exp's,    earnings  per  mile  and 
head,  *9o;  wealth  per  cap.,  *26 
Virginia  &  Truckee,  align't  sta- 
[tist.,  *26s 
Virginia   Central,  sharp   temp'y 
[curves,  *325 


Vir-Way 

Virtual  profile,  346,  799  \^oz. 

and  cent.  grav.  of  train, 
and  curve  comp'n,  621  -f- 
as  aff'd  by  length  grade, 

[704 
by  stops,  352 
cautions  as  to,  353 
down  grade,  q.v.,  369 
effect  on  pusher  grades,596 
ex.  of  use,  631,  701 
frt.,  computing,  352     [353 
need  not  be  continuous^ 
of  long  grade,  355 
of    old     lines,    constr'g, 
[794-S 
on  switchbacks,  948 
pass.,  computing,  347  -\- 
summit  speeds,  805,  807 
Visible  defects  most  dreaded,  242 
Von  Nordling,   W.,  est.   of  cost 
[transp'n,  19S 
Von  Weber,  on  curve  resist.,  307 

Wabash,  St.  L.  &  P.,    financial 
[status,  41 
miles  and  earnings,  *7i9 
Wages,  American,  143,  170-9 
Amer.  and  English,  *4i7 
as  aff'd  by  pusher  engines,  671 

by  rise  and  fall,  381 
engine,  past  tendency  of,  156 
English,  *i33 

shop,  English  and  Amer.,  *i5i 
train,  168,  205 
train  and  telegraph,  803 
Wasen,  spirals  at,  673 
Washing  out  boilers,  q.v.,  *42o 
Washington  Terr. :  area,  popu. , 
sidings,  p.  c.  opg.   exp.,   earn- 
ings  per  mile    and    head,  *9o; 
wealth  per  cap.,  *26 
Washouts,  accidents  from,  +247 
and  structures,  782 
and  valley  lines,  783 
derailments  from,  245  [19 

Waste,  avoidance  of,  benefits  all, 
Watchmen,  loco.,  cost  of,  *i47 
Water,  amt.  used  per  mile,  *5i9  & 
distances  across,  est'g,  845 
entrained,  *456,  *47o  -|- 
potable,  etc.,  purity,  *378 
Water-courses,    mental   map    of, 
[836  & 
'  Water- falls '  of  lava,  928 
Water-grate,  wt.,  etc.,  *4i2 
Watering  stock,  32 
Water-power,  U.  S.,rep't  on,  841 
value  of,  *2S 
in  Mexico,  678 
Water-scoop,  cost  new,  *isi 
Water  supply,  loco.,  amt.  used,  156 
cost  of,  147,  170-9 
cost  and  distrib.  of,  156 
in      loco.       q.v.     boilers, 
quality,  *378  [*4i5-6 

effect  on  fire-box,  *42o 
Water-tanks,  spacing  of,  156   [893 
Water-ways,     grade-lines     over. 
Way-freight  and  grades,  577 

av.  load,  etc.,  toi  [of,  54 
towns,  competing  for  traffic 
traffic,  and  curvature,  242 

EFFECT  ON  REVENUE,  70B 

securing  by  distance,  237 

RULE  AS  TO,  238 

ex.  of  error,  928 


980 


INDEX. 


Wea-Wes 

Wealth  of  all  nations,  *i^ 
of  U.  S.,*25 

per  capita,  *26 

U.  S.  States,  *26 

growth  of,  26-7  [227 

does  not  help  poor  lines, 

per  head,  U.  S.  by  States,  *26 

Weber,  Von,  maint.  way  tests,  425 

train-resist,  formula,  517 
West  Alabama,  loco,  perform'ce, 
[*439 
Western  &  Atl'c,  car  repairs  on, 
[full  details,  *i6i-2-3-4 
Western  Pa.,  align't  statist.,  *26o 
Western   States,   align't   statist., 
[*263 
bad  location  in,  6,  21,  330,  588, 
[660 
bonds  and  stock  per  mile,  *io7 
compar've  accidents  in,  252 
curvature  in, 263 
earnings  per  m.,  *io7 
distrib'n  of,  *io8  [^231 

freight  earn.,  thro'  and  local, 
grade  and  curve  limits  in,  6, 
[21,  330,  588,  656 
grade-crossings  in,  809 
growth  r'y  system,  *44 
heavy  grades  in,  *263 
main  results  op'n,  ^93 
rec'ts  per  inhab't,  pass,  and 
[frt.,  *  104-5 
rolling  slopes  in,  844 
rolling-stock  per  mile,  47 
train-load  and  haul,  frt.  and 
[pass,,  *2i7 
growth,  *ioi 
wealth  per  cap.,  26 
West  Md.,  loco  perf'ce,  *439 
West  Shore  r'y.,   an  example  of 
[wrong  judgment,  707 
bridges,  specif'ns  for,  903 

weights  of,  767 
double-track  on,  766 


Wes-Woo 

West  Shore  r'y — Continued. 

history  and  cause  failure,  724 
locos,  and  Howard  Fry,  *409 
dimens'ns,  etc.,  *407-9 
load  on  drivers  per  sq.  ft. 
[grate,  +452 
sidings,  total,  *825 
stand'd  box-car,  *486 
term'l  exp.,  etc.,  N.  Y.,  *8i9 
track  Buffalo  yd.,  *82i 
Wetherill,  W.  C,  report  to,  941 
Westinghouse    brake,  q-v.^   max. 
,„      .     ,  ^        [efific'y,  495 

Westinghouse,    G.,     exp'ts     on 
[brakes,  434 
Wheat  rate,  effect  long  haul  on, 
[710 
Wheel-base  and  curve  resist.,  306 
loco.,  q.v.,  all  types,  *407-4io 
long,  effect  on  wheels,  283 
position   of    trucks,  g.v.^    on 
[curves,  q.v..,  282 
Wheel  covers,  loco.,  *4i5 
Wheels.    {See  Car  Wheels,  etc.) 
Whims,  affecting  traffic,  52-3 
Whinery,  C,  paper  by,  326 
Whistle,  loco,  cost,  *4i2 
Wilmington     and     No.,     align't 
[statist.,  *26o 
Wimmer,  S.,  &  Mex.  r'y,929 
Winans,    R.    M.,    invented  Am. 
[car,  421 
Wind,  accidents  from,  *247 
and  bridges,  902 
vel.  of,  and  train  tests.  798 
Wire-drawing,  loco.,  q.v.^  470  -f- 
Wisconsin:  align't  statist.,   *263; 
area,  popu.,  sidings,  p.  c.  op'g 
exp.,  earnings    per    mile    and 
head,  *9o-  wealth  per  cap,  *26 
Wisconsin  Cent., train-Id.  growth. 
Wood  as  fuel,  139  [*ioi 

for  kindling,  amt.,  *200 
H.  U.  in,  *4so 


Woo— Zam 

Wood,  early  exp'ts  by,  on  adhe- 
[sion,  443 
Woodbury,  C.  J.  H.,  fric.  tests  by, 
504  + 
Wooden  structures,  right  use  of, 
[16,  754,  768 
Work  and  force,  338,  455 
Work  and  vel.,  interconvert,  ex., 
[342,  403 
how  destroyed,  332 
how  expressed,  338 
World,  popu.,  r'ys,  wealth,  etc., 
[*27,  *43,  *45 
r'y  system  of,  *42-5 
rel.  traffic  of,  *i6o 
wealth  of,  ^27 
Wurtemberg,  cost  r'ys,  etc.,  *45 
Wyoming:  area,    popu.,  sidings, 
p.  c.  op'g  exp.,earnings  per  mile 
and  head,  *9o;  wealth  per  cap., 

[*26 

Yon  Bait.  &0.,  279 

Yards  of  cloth,  selling  less,  49 

Yards,  asst.  engs.  q.v.,  at,  599 
classes  of  sidings  for,  *82i 
greatest  in  world,  822 
"N.  Y.  terminals,  q.v.,  *8i9 
N   Y.  vs.  Buffalo,  823 
often  near  bad  grades,  600 
operating  of,  810 
slipping  drivers  in,  797 
standing  idle  in,  cost,  603 

Yard-work,  effect  on  loc.  and  car 
rep'rs,  *203 

Youghiogheny  r'y,  loco,  perf'ce, 
■^438 

Zacatecas,  long  grade  at,  *7oo 

Zangronez,  R.,  &  Jalapa  line,  930 

Zero   temperatures    and    dynam. 
[tests,  508 

Zigzag  developments,  def.,  678 
example  of,  932 

Zimilihuacan,  barranca  of,  942 

Zamora,  location  at,  732 


ADVERTISEMENTS, 


A  D  VER  TISEMENTS. 


•George  Westinghouse,  Jr.,  president. 

C.  H.  Jackson,  vice-president. 

Chas.  R.  Johnson,  signal  eng.  and  gen.  manager. 


Robert  Pitcairn,  trea',urer. 
Asaph  T.  Rowan d,  secretary. 
Henry  Snyder,  gen.  agent. 


UHIOIi  SWITCH  AND  SIGNAL  CO, 


OF   PITTSBURaH,    PA. 


SOLE  MANUFACTURERS  OF  APPROVED 

RAILROAD  SIGNALLING  AND  SWITCHING  APPLIANCES. 


Plans  and  Estimates  and  all  particulars  promptly 
furnished  on  application. 


Junctions  and  Teminals. 


PERrEOT  INTERLOCEING  AND  AUTOMATIC  BLOCK  SIGNALS. 


OFFICE  AND  WORKS  : 

NOTE    CHANGE    OF  ADDRESS. 
"Western  Agent,  H.  H.  McDTJPFEE,  Home  Insurance  Building,  Chicago,  111. 


AD  VER  TISE.VENTS. 


THE 


PEimiiii  m  CO., 


208  South  Fourth  St., 

PHILADELPHIA. 

Works    at   STEELTON,  PA. 


OFFICES  : 

2  Wall  St.,  cor.  Broadway, 

NEVi/  YORK. 


MANUFACTURERS   OF 


STEEL    RAILS, 

All  standard  patterns,  from  i6  lb.  per  yard  to  76  lb.  per  yard  and  upwards. 

STEEL  SPLICES,  Angle  and  Plain,  to  fit  all  patterns  of  Rails. 

STEEL  BLOOMS,  FORGINGS,  and  MERCHANT 

BARS  of  Open  Hearth  or  Bessemer  Steel. 

Capacity  over  400,000  Gross  Tons  of  Steel  per  Annum, 

STEEL    RAIL 
FROGS 

Of  all  the  Standard  Patterns,  with  various  improvements  of  importance, 
suited  to  all  conditions  of  service. 

SPLIT  SWITCHES 

AND  IMPROVED 

SAFETY  SWITCHES, 

OF  MANY  IMPROVED  PATTERNS, 

SWITCH   STANDS  AND   FIXTURES,   OF  ALL  KINDS. 


This  Company  has  the  greatest  capacity  in  the  United  States  for  the  pro- 
duction of  FROGS,  SWITCHES,  &c.,  and  invites  attention  to  prices  and 
quality.     All  work  made  interchangeable,  and  true  to  standards. 


AD  VER  TISEMENTS. 


Established  1831. 


Annual  Capacity,  600. 


\ 


h 


m 


11 


rr 


Iflf 


BURNHAM,  PARRY,  WILLIAMS  &  CO., 

Fropvietovs, 


Broad  and  Nappow  Gaug-e  Locomotives, 
Mine  Locomotives, 

Plantation  Locomotives, 

Compressed  Air  Locomotives, 
Logg-ing"  Locomotives, 

Tramway  Motors  and  Steam  Cars. 


ALL  IMPORTANT  PARTS  MADE  TO  STANDARD  GAUGES 
AND   TEMPLATES, 


Lite  parts  of  tlifferent  Enanes  of  same  clas^  perfectly  interchaDpaWe. 


AD  VER  TISEMENTS. 


—I 


.2551  — — *-- ^ 253 


Z§KSMKffiHK^ii^^^mW0\:z^M!ZKEEE 


™^ 


F.  ANDERSON. 


C.  C.  BARR. 


ANDERSON  &  BARR, 

Engineers  and  Contractors. 

Aildress   S40    Eleventli    Street,   Jersey    Oity» 


TUNNELLING    TH«'-UGH   SILT. 


Pneumatic  Work,  Deep  Foundations,  and  Tunneling  in  Soft  Materials.     Con- 
trol the  Patents  for  the  Automatic  Dredge  and  the  Anderson  System  of  Tunneling. 

The  following  Works,  among  others,  have  been  executed  by  the  present  firm 
of  Anderson  &  Barr,  and  will  show  the  wide  range  of  their  experience. 


Atchafalaya   Bridge. 

Pneumatic  Cylinders  and  Dredges. 
Little  Rock,  Ark.,  Bridge. 

Pneumatic  Caissons. 
Seekonk  River  Bridge,  Providence,  R.  I. 

Cylinders  sunk  by  Dredges. 
Fourteen-Foot  Light  House,  Delaware  Bay. 

Pneumatic  Caissons,  53  feet  below  water, 
20  miles  from  nearest  land. 


Chest7iut  Street  Bridge,  PhiladelpJiia,  Pa, 

Oblique  Pneumatic  Cylinders. 
Main  Sewers,  Brooklyn,  JV.  V. 

4,000  feet  of  i2-ft.  tunnels  through  sand. 
Haivkeshury  Bridge,  Australia. 

Open  Caissons,  sunk  170  feet  below  water, 
by  Dredges. 
Harlem  River  Bridge,  New  York  City. 

Pneumatic  Caisson,  54x104  ft. 


AD  VER  TI SEMEN  TS. 


EDGE  MOOR  IRON  CO., 

—DESIGN  AND  MANUFACTURE— 

RAILAVAY 

BRIDGES,  VIADUCTS,  AND  ROOFS, 

IN   STEEL   AND    IRON. 


Tension    Members  Forged  without    the  addition    of 
extraneous  Metal,  and  without  Welds,  Piles  or  Buckles. 

Compression    Members   manufactured    by   Processes 
which  insure  an  entire  absence  of  constructional  strains. 


WROUGHT-IRON    TURN-TABLES, 

"With.  Centres  of  Conical  Steel  Kollers  and  Steel  Plates. 


GALLO^WAY    BOILERS 

Giving  Greatest  Safety,  Economy  and  Durability. 


Main  Office,  Edgemoor,  on  Delaware  River. 

POST-OFFICE,  WILMINGTON,  DEL. 

Philadelphia  Office,  1600  Hamilton  St 

WM.  SELLERS,  President.  GEO.  H.  SELLERS,  Gen.  Supf. 

JOHN  SELLERS,  Jr.,  Vice-President.  WM.  F.  SELLERS,  Secretary. 

WM.  H.  CONNELL,  Treasurer. 


AD  VER  TISEMENTS. 


SAMUEL  M.   DODD,  President. 
JOHN  B.  GRAY,  Vice-President. 


E.   L,  ADREON,  Sec'y  and  Treas. 
GEO.  H.  POOR,  Supt. 


American   Brake  Company, 

NEW   YORK   OFFICE,    160    BROADWAY. 

JOHN  B.  GRAY,  Viee-Ppesident. 
MANUFACTURERS  OF 

AUTOMATIC   FREIGHT   CAR   BRAKES   AND   STEAM 
DRIVER  AND  TENDER   BRAKES, 

ST.    LOUIS,    MO. 

We  offer  to  Railway  Companies  the  only  Exclusively  Independent  Self-Acting 
Freight  Train  Brake  which  has  yet  been  adopted  by  any  Railway  in  the  world. 
Our  Steam  Driver  and  Tender  Brake  is  acknowledged  to  be  the  Cheapest, 
Simplest  and  BEST  Power  Brake  now  in  use.  Is  now  used  by  250  different 
Railroads. 


THE      NEW 


U 


IRON  CLAD"  FIBRE  TRACK  WASHERS. 


Perfected  by  Ten  Years'  Experience. 

Surpassing  all  other  Lock-Nut  devices  in  Durability, 
Effectiveness  and  Clieapness.  Strengthened  and 
protected  from  the  weather,  cannot  be  crushed,  or  burst, 
will  not  lose  their  elasticity,  nor  rot.  Adapted  for  both 
plain  and  angle-bars. 

Pi-ice,  only  ^18.00  per  Thousand. 


They  also  absolutely  protect  the  threads  on 
the  bolts  from  becoming  chafed,  and  ijermit 
old  bolts  to  be  utilized  upon  which  the  threads 
have  become  battered. 

NEW  YORK  OFFICE  : 

IsTo.    15     Dey     Street. 

mCAMED  FIBRE  CO,  WilmngtoiiJel 


AD  VER  TISEMENTS. 


vu 


THE  CLARK  FISHER  "  BRIDGE"  JOINT, 

OF  WROUGHT  IRON  AND  STEEL. 
All   Parts    Warrafited   against   Breakage, 


1-7  Full  Size. 

This  is  not  a  "suspension"  joint.  It  is  a  ''''supported''^  joint,  with  double  the  amount  of 
support  given  by  any  other  through  the  arched  bearer,  bringing  the  load  upon  tzuo  ties  acting 
together  as  one  directly  under  the  rail  ends.  Combined  support  of  two  ties,  acting  as  one,  for 
each  joint,  and  rail  ends  carried  directly  by  the  arched  beam  and  screwed  DOWN  to  it  with  a 
force  of  15,000  pounds — making  practically  a  continuous  rail.  No  holes  in  web  of  rail — whole 
surface  of  base  for  support  and  wear.  No  breakage  of  rails  or  joints.  No  "low  joints."  No 
"  creeping."  _  No  loose  nuts.  Cost  of  keeping  up  track  reduced  to  one  half  of  that  with  angle- 
bars,  and  giving  smoother  surface.     For  further  information,  address, 


FISHER  RAIL-JOINT  AND  ANVIL  WORKS 


TRENTON,   N.   J, 


THE  BUSH  INTERLOCKING   BOLTS, 


SAFETY 

By  Preyenting- 

Spreading 

of  Rails, 

and 

Derailment 

of  Trains 

from 

Broken  Bails. 


ECONOMY 

By 

Reducing 

the  Cost  of 

Maintenance 

of  Way, 

and 

Prolonging 

Life  of  Ties. 


SPREADING    OF    RAILS  ABSOI.UTEI.T    PREVENTED. 

Tested  for  more  than  FOUR  YEARS,  and  approved  by  some  of  the  most  eminent  railroad 
officials  m  the  United  States.  In  use  on  FIFTEEN  first-class  roads,  with  the  most  satis- 
factory results.     References,  with  price-list  and  full  descriptive  circulars,  sent  on  application  to 

THE    BUSH    INTERLOCKING    BOLT   CO., 

267  South  Fourth  Street,  PHILADELPHIA. 


AD  VER  TISEMENTS. 


ESTABLISHED     184S. 

W.  &  L.  E.  &IJELEY, 

TROY,  N.  Y.,  U.  S.  A., 

Manufacturers  of 

CIVIL  EN&INEERS'  and  SURVEYORS' 
INSTRUMENTS. 


All  Instruments  sent  to  the  purchaser  ad- 
justed and  ready  for  immediate  use. 


Send  for  full  Illustrated  Price-List  and 
Circtdar. 


THACHER'S  CALCULATING  INSTRUMENT. 

This  instrument  overcomes  the    drudi^fpey 
^  of  calculation,   and  accomplishes  rapidly  Dy 

i^  l^'^tttf^'LvuT!-'-.' 'J--'''r!''v^^^^  mechanical  means    otherwise    tedious  aritjv 

IriR      V  '"? 7j'"'!''""i  r ■ ' %" ,j ^ .'.' ,,V_  V.rij;'';iiri~j;:rr  riu  "j |n3        metical  solutions. 

Examples  in  multiplication,  division,  pro- 
portion,   powers    and    roots,   involving    not 
more  than  three  quantities  are  solved  hy  ose 
operation,  and  any  number  of  values  of  a  single  variable  are  found  by  one  setting. 

It  is  designed  for  the  use   of  engineers,  architects,  actuaries,  scientists,  accountants,  me- 
chanics, and  business  men  generally. 

Its  useful  applications  are  as  general  as  the  fundamental  rules  of  arithmetic. 

It  is  quickly  learned,  is  easily  operated,  and  worth  double  its  price.     Send  for  testimonials. 

Price,  in  Mahogany  Box,  $30.00. 


For  further  information,  address 


EDWIN  THACHER,  503  Penn  Ave.,  Pittsburgh,  Pa, 


(Spacto^^  ^ Fre D. C.  Weir's | 

-  Improved  SrEELRAiLFROG^,GRos.siNGS>:| 
-Split  AND  Stu&  Switch  ES,SwiTc:H  Stan  dS>| 


fRED.C.WEIR_. 


An  VER  TISEMENTS. 


OSGOOD  DREDGE  CO., 

ALBANY,  N.  Y.,  U.  S.  A. 


—MANUFACTURERS  OF— 

BOOl  MEDGES  and  EXCAVATOES, 

DITCHING    MACHINES,    CRANES,    &c. 

No.  1  EXCAVATOR.      No.  2  EXCAVATOR. 

Weight 40  Tons.  30  Tons 

Main   Engine... 10x12  Dbl.  Cyl.  S^xio  Dbl.  Cyl. 

Crowding   Engine 6^x8     "       "  6^x8       "       " 

Dipper 2  cubic  yards.  i>^  cubic  yards. 

Average  Capacity,  10  hours 2,500  cubic  yards.  1,800  cubic  yards. 

Boom  and  A-Frame  lowered  to  go  under  bridges.     Will  run  in  any  freight  train. 

No.  I  Excavator  dug  450,000  yards  in  g  months,  1886. 
No.  I  "  "      52,000     "      in  May,  1886,  10  hours  a  day. 

No.  2  **          averaged  1,800  yards  a  day  for  whole  season,  1886. 

No.  2  "         was  taken  down,  run  50  miles,  and  set  up  ready  to  go  to  work> 

in  one  day. 


AD  VERTISEMENTS. 


TRAUTWiME'S   POCKET-BOOK. 

^Ttli  Tlioiisand  (1887)  Now  Ready. 

"  Beyond  all  question  the  best  practical  manual  for  the  engineer  that  has  ever 
appeared." — Prof.  Geo.  L.  Vose,  C.  E.,  in  ''  Manual  for  Railroad  Ettgineers.'''' 

*  *  *  ''The  additions  and  substitutions  are  so  numerous  and  so  well 
chosen  that  there  is  hardly  an  important  topic  of  the  volume  which  has  not  been 
affected  by  them  and  improved." — Railroad  Gazette,  Review  of  1885  Edition. 

*  «  *  "  It  is  the  best  civil  engineer's  pocket-book  in  existence." — American 
Engineer. 


TRAUTWINE'S 
RAILROAD   CURVES 

•*'  Is  probafcly  the  mostr  complete  and  perfect  "treatise  on  the  single  subject  of 
Railroad  Curves  that  is  published  in  the  English  \z.T\^MZ.g^:'— Engineering  News, 
July  3d,  1886. 

TRAUTWINE'S  EXCAVATIONS  AND  EMBANKMENTS. 

9tli  Edition  (1887)  Now  Ready. 
John  Wiley  &  Sons,  New  York.  E.  &  F.  N.  Spon,  London. 

THE  BEST  AND  MOST  PRACTICAL  WORK  ON  EARTHWORK 
COMPUTATION. 


COIPDTATION  OF  EARTHWORK  FROM  DIAGRAMS. 

By  A.  M.  Wellington,  M.  Am.  Soc.  C.  E. 

IN    TWO    VOLUMES. 

Vol.     I.— Text,      SI. 50)  $5.00 

Vol.  II Plates,      3.50  f 

Sold  Separately  or  Together. 

Gives  quantities  on  inspection  to  the  nearest  cubic  yard  for  both  regular  and 
irregular  sections,  direct  from  ordinaiy  field-notes.  Saves  all  multiplication  and 
division.  Very  simple  in  use.  Contains  a  discussion  on  the  theory  of  the  Pris- 
modal  Formula  as  applied  to  earthwork  solids,  which  is  by  much  the  most  complete 
in  print,  being  based  on  the  actual  results  of  various  methods  of  computation  on 
some  thousands  of  actual  solids,  and  showing  that  the  simplest  method  of  apply- 
ing the  formula,  involving  hardly  any  additional  labor,  is  also  the  most  accurate. 

All  the  tedious  part  of  the  coviputation  of  earthwork  is  saved  by  the  methods  oj 
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^'ENGINEERING   NEWS,"  Tribune  Building,  New  York. 


AD  VER  TISEMENTS. 


GUSTAV    LINDENTHAL, 


CIVIL    ENGINEER, 

Pittsburg,  Pa. 


SPECIALTIES— Difficult    Foundations,   Long-Span 
Bridges,  and  all  Iron  and  Steel  Constructions. 

LEWIS  M.  HAUPT,  A.  M.,  C.  E..         " 

Professor  of  Civil  Engineering,  University  of  Pennsylvania,  Philadelphia. 

AUTHOR    OF 
"ENGINEERING,  SPECIFICATIONS  AND  CONTRACTS,  " 
"THE  TOPOGRAPHER:  HIS  INSTRUMENTS  AND  METHODS," 
"THE  AMERICAN  ENGINEERING  REGISTER"  (1886), 

Oi'ders  received  by  the  A  uthor. 


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HARBOR  AND  RIVER  IMPROVEMENTS  A  SPECIAI.TY. 


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Engineering  News  is  a  weekly  record  of  all  important  engineering  works 
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^INFORMATION  AS  TO  NEW  WORK,  and  technical  descriptions, 
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